Why might you NOT observe a tradeoff between two life-history traits?

Why might you NOT observe a tradeoff between two life-history traits?

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I have traditionally thought of and heard about life-history traits (e.g., size at first reproduction, number of offspring, size of offspring, survival, etc., etc.) as drawing from a finite pool of resources that an organism has, and therefore exhibiting tradeoffs. So, for instance, an organism that invests in a lot of offspring would experience a decreased probability of survival.

It has recently come to my attention that this is not always the case, and I'm not sure why. I have been directed to the work of David Houle, who wrote extensively on the topic of life-history traits, but some of his work is inaccessible to me intellectually. I was hoping that somebody had a more digestible explanation or was maybe more familiar with Houle's work.

The simple explanation is that there are three (or more) traits drawing from the pool, and you're only looking for trade-offs between two of them. The unobserved third may show the effect of a trade-off.

Comparing Explanations for "Trade-offs" in Darwinian Theory and ID

Darwinists and theorists of intelligent design refer to "trade-offs" in living systems, but they explain them in ways that are radically different, and tellingly so. Theodore Garland is an evolutionary biologist at the University of California, Riverside. His "Quick Guide" to "Trade-offs" in Current Biology provides an opportunity to compare the explanatory power of ID and Darwinism. First of all, what is a trade-off?

In engineering and economics, trade-offs are familiar enough (e.g., money spent on rent is not available to buy food). In biology, a trade-off exists when one trait cannot increase without a decrease in another (or vice versa). Such a situation can be caused by a number of physical and biological mechanisms. One type of mechanism is described by the so-called ‘Y-model’, which states that for a given amount of resource (e.g., energy, space, time), it is impossible to increase two traits at once. A commonly cited example is a trade-off between the size and number of eggs that, for example, a fish, bird or turtle can produce in a given clutch. Depending on the organism, this trade-off can be caused by a limitation in the amount of energy available, the amount of time available to produce eggs or the amount of space available to hold eggs (e.g., inside the shell of a turtle). Similarly, time spent foraging may be time wasted with respect to finding a mate. Trade-offs also occur when characteristics that enhance one aspect of performance necessarily decrease another type of performance. (Emphasis added.)

Notice that Garland has illustrated biological trade-offs with designed ones (engineering and economics). He quotes Charles Darwin on the point that animals must evolve as "integrated wholes":

The whole organism is so tied together that when slight variations in one part occur, and are accumulated through natural selection, other parts become modified. This is a very important subject, most imperfectly understood.

So what have Darwinian evolutionists learned about this in the past 155 years, since "Biologists have made major advances since then"? One advance, Garland says, is the theory of trade-offs: "Indeed, the concept of trade-offs underpins much of the research in evolutionary organismal biology, physiology, behavioral ecology, and functional morphology, to name just a few fields."

Having set up trade-off theory as a foundation of progress in evolutionary understanding, what does he say it has produced, specifically? We can dismiss his appeals to design as rhetorical misdirection:

Having survived a decade of frigid winters in Wisconsin, I like to use the example of gloves versus mittens. Gloves are good for making snowballs and getting keys out of your pocket, but they do not keep your hands nearly as warm as mittens do. Moreover, you must remove the mittens to get the keys. Returning to biology, limbs can be ‘designed’ for speed, through lengthening and thinning of bone, but this will often reduce strength and make them more likely to break when in use. Hence, a predator that evolves to be a fast runner may have to trade-off its ability to subdue large or strong prey (e.g., cheetah versus lion).

He can’t help but say "designed," even if using scare quotes. Face it a cheetah’s limbs look designed for speed! By using "design" words and examples, Garland has not yet restricted his explanation to mutation and selection. Notice that he has just attributed purpose and planning to the cheetah! The "predator" is the subject of the verb "may have to trade-off its ability" to subdue large or strong prey.

As he goes on to describe more examples, and the ubiquity of trade-offs in nature, he keeps evolutionary theory in the shadows. For all the reader knows, the trade-offs could have been designed.

When push comes to shove, instead of giving a scientific explanation consistent with neo-Darwinism, Garland gives excuses. He says it’s too hard a problem:

In some cases, expected trade-offs based on mathematical models or on basic biological principles are not found. This may occur because nature has more ‘degrees of freedom’ than assumed by simple conceptualizations that predict trade-offs. For one example, aside from changes in fiber-type composition, muscles can evolve to be larger, positions of origins and insertions can shift, legs can become longer, and gaits can evolve (including bipedality). As another example, animals may be able to acquire and process more food (e.g., by altering their preferred prey type), thus allowing them to secure more energy and increase both number and size of offspring.

Saying something "can evolve" is not the same as saying it "did evolve." Garland waffles, saying evolution does things this way sometimes, and that way sometimes, but there’s no way to know. While his references to mathematical models are helpful, there’s nothing about them that is strictly Darwinian. In fact, they can sometimes be counter-Darwinian:

Although it is easiest to conceive of and recognize trade-offs between only two traits, organisms comprise an almost infinite number of ‘traits’, and trade-offs may appear only when we include multiple traits in an analysis. The Y-model can be expanded to include multiple traits at multiple levels of biological organization. Speed and stamina might not trade-off in some group of organisms (perhaps even showing a positive relationship), but a composite measure of locomotor performance abilities might be negatively related to one or more aspects of the life history (e.g., growth rate, age at first reproduction, fecundity). Similarly, a physiological or biomechanical trade-off — even if it affects physical fitness (e.g., locomotor abilities) — does not necessarily indicate any trade-off with Darwinian fitness (lifetime reproductive success). Of course, a small effect on a performance trait (e.g., a 2% reduction in speed associated with a 2% increase in stamina) could, for some organisms under some ecological circumstances, make the difference between eating and being eaten.

Garland ends with more cases where Darwinian evolution might not be the explanation for observed trade-offs:

A negative relationship alone does not prove that two traits necessarily trade-off in a functional or evolutionary sense. Rather, it is possible that natural selection simply never favored the evolution of species that have high (or low) values for both traits. Whether a trade-off (or evolutionary constraint) necessarily occurs can be tested by selection experiments and experimental evolution with tractable model organisms, by phenotypic engineering (such as hormone manipulations), by direct molecular-genetic manipulations, by a search for organisms that break the rules, or by developing a thorough understanding of how organisms work. Finally, it is worth noting that many sexually selected traits, such as the exaggerated tail feathers of male peacocks, may benefit the ability to obtain mates but hinder escape from predators, reduce foraging ability or increase the energetic cost of locomotion. These situations can also be viewed as trade-offs.

A reader looking for a specific tie-in of an observed trade-off to a Darwinian explanation will be disappointed. Merely stating that an animal (like the peacock with its outrageous tail) exhibits trade-offs doesn’t explain how mutation and selection produced it. In support of Darwinian evolution, Garland provides nothing more than a list of exceptions and excuses. Remarkably, he expects intelligently designed "manipulations" involving "phenotypic engineering" to provide support for an explanation based on unguided processes.

The one time he mentions selection leading to trade-offs is in his concluding paragraph about constraints:

Constraints can be defined as anything, internal or external to an organism, that limits the production of new phenotypes. For example, if the circulating levels of a hormone change, then any cell that has receptors for that hormone is likely to be affected. Thus, selection favoring increased aggressive or agonistic behavior may have adverse consequences for parental behavior. This example should make clear that, in biology, the concepts of trade-offs and constraints are often closely related.

That one case, though, is mentioned as a possibility, not a demonstration. From this article, we gain the distinct impression that neo-Darwinism is not helpful to understanding trade-offs.

ID and Trade-offs

The theory of intelligent design looks at trade-offs much the same in observational terms, but very differently in explanatory terms. Discussions of trade-offs generally come up in responses to criticisms of bad design (dysteleology) in nature. Design theorists explain that ID does not imply that every trait must be perfect or ideal. Rather, design must be evaluated holistically. To infer design for the human body does not require that we have the visual acuity of an eagle or the speed of a cheetah. Suboptimal design does not falsify intelligent design.

Paul Nelson has used the analogy of a laptop. Nobody would argue that a laptop is not designed. But given the design goal of a lightweight, portable computer, that goal constrains the individual parts. A laptop can’t afford a heavy disk drive or a giant screen all the parts must contribute to the overall goals of portability, small size and light weight. A desktop computer, with different design goals, will have different trade-offs (e.g., less portability). So will a motorcycle compared with a racing car.

Observationally, therefore, design theorists would agree that trade-offs are ubiquitous in biology. They would deny, however, that the trade-offs arise by unguided natural processes, except maybe to accentuate designed trade-offs over time. Instead, they would say that the functional performance of the whole animal in its niche provides evidence for design, even if specific traits are not the best of what’s possible. A sloth provides as much evidence for design as a cheetah.


Both Darwinian evolutionists and design theorists recognize the ubiquity of trade-offs in biology. Both can evaluate them in terms of constraints. Both agree on the necessity of evaluating trade-offs holistically, viewing organisms as "integrated wholes." But when it comes to explaining their origins, the two ways of thinking part company.

An evolutionary biologist struggles to avoid design terms: engineering, economics, biological organization. He never ties trade-offs to random mutations. He almost personifies selection, saying that if an animal evolves to be fast, it "may have to trade off" its ability to be strong. And he can’t help but use design analogies, like mittens versus gloves.

Design terms and analogies, however, come naturally to intelligent design theory. Since our uniform experience with objects exhibiting trade-offs, whether mittens versus gloves, or laptop versus desktop computers, is that they proceed from intelligent causes, it’s only natural that trade-offs in biology reflect origin by design for functional constraints.

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Life-history theory in psychology and evolutionary biology: one research programme or two?

The term ‘life-history theory’ (LHT) is increasingly often invoked in psychology, as a framework for integrating understanding of psychological traits into a broader evolutionary context. Although LHT as presented in psychology papers (LHT-P) is typically described as a straightforward extension of the theoretical principles from evolutionary biology that bear the same name (LHT-E), the two bodies of work are not well integrated. Here, through a close reading of recent papers, we argue that LHT-E and LHT-P are different research programmes in the Lakatosian sense. The core of LHT-E is built around ultimate evolutionary explanation, via explicit mathematical modelling, of how selection can drive divergent evolution of populations or species living under different demographies or ecologies. The core of LHT-P concerns measurement of covariation, across individuals, of multiple psychological traits the proximate goals these serve and their relation to childhood experience. Some of the links between LHT-E and LHT-P are false friends. For example, elements that are marginal in LHT-E are core commitments of LHT-P, and where explanatory principles are transferred from one to the other, nuance can be lost in transmission. The methodological rules for what grounds a prediction in theory are different in the two cases. Though there are major differences between LHT-E and LHT-P at present, there is much potential for greater integration in the future, through both theoretical modelling and further empirical research.

This article is part of the theme issue ‘Life history and learning: how childhood, caregiving and old age shape cognition and culture in humans and other animals’.

1. Introduction

This special issue brings together research from psychology, and learning in particular, with research on life history, which is more typically concerned with growth, physical maturation and senescence. The desire to integrate psychology with life history is not a new one. It has been going on for some time under the banner of ‘life-history theory’ (LHT). LHT originated in evolutionary biology, but in the last 15 years, the term has appeared more and more in the psychology literature, particularly in personality psychology and parts of developmental psychology. Indeed, if present trends continue, it will soon be as frequently encountered in psychology as it is in evolutionary biology (figure 1).

Figure 1. Number of papers per year using the term ‘life-history theory’ in title, abstract or keywords overall in journals whose subject category includes ecology, evolutionary biology or zoology and in journals whose subject category includes psychology. Results are from a Web of Science search ( for complete years up to and including 2017. Note that theoretical work on life history in evolutionary biology goes back further than implied by these data (see §3). Earlier authors preferred the term ‘life-history evolution’. (Online version in colour.)

We have recently shown quantitatively that papers from psychology which invoke LHT don't tend to cite many of the same references as papers from evolutionary biology (under which term we also included ecology) that invoke LHT [1]. This has become particularly true in the period since 2010. Prior to that date, most papers invoking the LHT terminology drew on the same core set of key theoretical references, regardless of their discipline. After 2010, LHT papers from psychology began to draw on a set of core theoretical references of their own, with little direct citation to works from evolutionary biology. These findings raise the question of whether the ‘theory’ in ‘LHT’ is actually the same one in the two cases. In working on our quantitative review, it struck us how different the presentation of the basic principles of the theory was in the papers from psychology as compared to those from evolutionary biology. We concluded the literature suffers from the so-called ‘jingle fallacy’: the sometimes false expectation that if two things bear the same name, they must be equivalent. In this paper, we aim to qualitatively document these differences, give a brief historical analysis of how they arose, and make suggestions for how to move forward. To be clear from the outset, we do not aim to evaluate either the claims or the methods of LHT in psychology or in evolutionary biology. Different aims generate different traditions of theorizing, different methods and different results. These cannot necessarily be judged ‘better’ or ‘worse’ than one another. Our aim is merely to compare what the term LHT currently means in the two disciplines, and hence discuss possible future directions.

We base our analysis around the concept of research programmes [2]. The central question is whether life-history theory in psychology (henceforth LHT-P) and life-history theory in evolutionary biology (LHT-E) constitute the same research programme or not. Authors in LHT-P typically claim that they do. For example, one finds sentences such as ‘LHT, a branch of evolutionary biology, has demonstrated that the human brain is designed to respond adaptively to variations in resources in the local environment’ [3, p. 2]. It is LHT-E that is a branch of evolutionary biology, but primarily LHT-P that concerns the human brain and its responses to the local environment. Thus, the sentence conflates the two. Whether it is valid to do so is in part a ‘ship of Theseus’ problem. The ship of Theseus problem asks, if every plank of a wooden ship is successively replaced, under what circumstances is it appropriate to speak of it still being the same ship? In the present instance, the puzzle is: if a branch of evolutionary biology is extended to new kinds of phenomena and methods, under what circumstances is it still a branch of evolutionary biology?

Research programmes in science have a number of typical characteristics. First, they have a hard core of assumptions and principles: this consists of the ‘assumptions so basic that to question their validity would be tantamount to abandoning [the programme]’ [4, p. 6]. Second, they have suites of auxiliary hypotheses: these are ideas that arose from the programme, but could be superseded or rejected without putting the overall programme in jeopardy. Third, they have methodological rules. These dictate what are viewed as good grounds for proposing hypotheses or counting claims as having been supported, or refuted. Finally, research programmes often contain analogical extensions of their theories [5]. For example, the idea that variation and selection may be used to explain change over time in technologies or cultural traditions [6] is an analogical extension of Darwinian evolutionary theory. The failure of an analogical extension would not lead to the failure of the parent research programme. However, it is sometimes difficult to say where the parent research programme ends and an analogical extension has begun. Whether LHT-P is usefully viewed as the same research programme as LHT-E depends on whether one sees the extensions made by LHT-P as direct application of theories, or just analogies whether the modifications that have been made are to the hard core or just to auxiliary hypotheses of LHT-E and whether the same methodological rules still apply in the two cases.

In §2, we give examples of how the principles of LHT are typically presented in ecological and in psychological papers, based on our systematic search [1] and informal reading of the literature. This leads us to generalizations about what appear to be the core tenets of the research programme in the two cases. The next two sections trace the histories of LHT-E (§3) and LHT-P (§4), in an attempt to understand how the core tenets have become so different. Section 5 attempts to synthesize: we argue that LHT-E and LHT-P share many historical links, but are, as it stands, quite different research programmes. However, they could become more closely linked in the future. We should add a caveat about our methodology: our characterizations of LHT-E and LHT-P are based on randomly selected papers using the term LHT. Our search strategy makes no distinction between the most nuanced, most accurate, most rigorous presentations of the theory, and the loosest. Thus, our characterization is a rough picture of what LHT typically means when the term is used in psychology or in evolutionary biology, not a detailed review of the best or most nuanced presentations.

2. Presentation of ‘life-history theory’ in evolutionary and in psychological papers

In papers from evolutionary biology, the prototypical claims ascribed to LHT are: (i) there are trade-offs between different components of fitness (e.g. survival and reproduction, quality and quantity of offspring) that prevent their simultaneous maximization (ii) natural selection acts on life-history traits, leading to trait-values that maximize fitness and (iii) (therefore) populations inhabiting different ecologies or demographies will evolve different patterns of life-history trait values. Example quotations are shown in table 1. Note these claims are all fairly general. Researchers are typically interested in testing a more specific prediction than any of (i)–(iii). However, those specific predictions are not usually presented as properties of LHT per se. Rather, they arise from lower-level models or hypotheses that were generated by LHT, but are not constitutive of it. A few exceptions—where a very specific claim is described as being ‘predicted by LHT’, rather than by a specific model or sub-theory—are shown in the final row of table 1.

Table 1. Typical tenets of life-history theory as presented in the introductions of papers from evolutionary biology.

Tenet (i) of table 1 has implications for the study of individuals under tenet (i), other things being equal, an individual allocating more energy to reproduction must have less energy to allocate to survival. Tenets (ii) and (iii), however, are best interpreted as concerning population averages and population processes. Tenet (ii) says, at most, that the average individual from a population will show a pattern of life-history traits that maximizes fitness for the statistical composite of environments its ancestors experienced. Individuals will be scattered around the population average for any particular trait—for example because of genetic mutation and recombination—and tenet (ii) does not require that LHT make any particular adaptive claim about this scatter. Tenet (iii) of table 1 entails a claim that differences between populations or species in terms of average life-history traits might reflect evolutionary adaptation to the ancestral environment but not necessarily that differences between individuals within the same population are adaptations to the personal environment (that is, the environment experienced by that specific individual in its lifetime). Neither tenets (ii) or (iii) necessarily entail that individuals have any plasticity to shift their life-history trait values according to the personal environment. This plasticity claim is sometimes made in LHT-E (e.g. in [18]), and there are evolutionary life-history models incorporating plasticity [19]. However, claims about plasticity are not ubiquitous within LHT-E.

In summary, the hard core of LHT-E explicitly consists of the idea that there are evolutionary trade-offs that natural selection acts on life-history traits and that as a result of this, populations or species experiencing different ecologies and demographies end up with divergent patterns of life-history traits. Although there are many more specific claims and predictions, those are, for the most part, seen as auxiliary rather than hard core: they have arisen from specific models generated by LHT, models that might be superseded or refined. There is also another important principle that is clearly inherent in LHT-E: a statement counts as a ‘prediction’ within LHT-E if there is a formal model showing that statement maximizes fitness under some set of assumptions. This methodological rule makes sense because LHT-E aims to provide ultimate-level explanations of phenotypes that result from interacting selective forces [20].

Papers from psychology often have the same starting point as those from evolutionary biology: the existence of trade-offs (see table 2 for examples). The tenets thereafter, however, tend to be different. Psychology papers almost universally allude to idea that multiple traits covary along a principal axis known as the fast–slow continuum (tenet (ii) of table 2). In our quantitative review [1], we found the fast–slow continuum alluded to in 20 out of 20 recent psychological papers we sampled, and just 2 out of 20 papers from non-human research (in one of those, it only appeared in the Discussion). In psychology papers, the suite of traits related to the fast–slow continuum invariably includes not only classical life-history traits such as timing of maturation or reproduction, but also psychological variables such as attitudes to risk, ability to delay gratification, religiosity, prosociality, optimism and others.

Table 2. Typical tenets of life-history theory as presented in the introductions of papers from psychology.

A third recurring tenet is that individuals strategically adjust their (broadly defined) life-history trait values according to their personal environments (table 2, third row), making LHT-P a theory of individual differences, and especially of individual differences attributed to phenotypic plasticity. Early childhood experience is often viewed as an essential input, though genotypic variation may be acknowledged, too. Note the shift from average trait-values of populations being gradually shifted by selection over evolutionary time (LHT-E), to individuals shifting their phenotypes in response to their personal environments over the course of development (LHT-P). Finally (tenet (iv) of table 2), in LHT-P, many very specific predictions are described as issuing directly from LHT itself, rather than from more specific models or sub-theories. These predictions are quite variable, both in the outcome traits they concern, and what the theory is stated to predict. For example, some studies test for effects of acute psychological manipulations in adulthood on putatively ‘fast’ psychological variables, claiming that LHT predicts an immediate response [33] whereas others take LHT to specifically predict that childhood experience, rather than the adult context, will have set the values of these traits [32] and still others take LHT to predict non-additive interactions between childhood experience and adult context in determining the trait value [30].

In our view (and others may disagree), the differences between LHT-E and LHT-P that we have outlined above are more than additional auxiliary hypotheses that LHT-P has added to the core of LHT-E. Instead, the hard cores of the programmes, as described by the papers themselves, appear to be different. LHT-P focuses on individual differences, along a fast–slow continuum, mainly as a result of phenotypic plasticity. These commitments constitute the research programme. The following quotations, with emphasis added by us, illustrate this point:

LHT provides an evolutionary account of individual differences in various traits, including wellbeing. The theory distinguishes between a fast LH strategy, indicated by a short-term perspective (e.g., impulsivity), versus a slow LH strategy [34, p. 277]

LHT is an evolutionary framework that explains individual differences [29, p. 1543]

we draw on LHT, which concerns the relationship between childhood poverty and adulthood preferences for security [24, p. 21]

at its core, LHT is a motivational framework, whereby motivational ‘states’ are determined by the specific problems and opportunities associated with an organism's current develop-mental stage and local ecology [35, p. 1]

By contrast, it would be perfectly possible, and indeed normal, to be interested primarily in interspecific differences, to make no reference to the fast–slow continuum, to plasticity or to proximate motivation, and yet still describe one's work as LHT-E. Thus, our reading of the literature leads us to conclude that LHT-E and LHT-P are largely different research programmes. They differ not just in some extra species-specific auxiliary hypotheses or empirical methods, but rather in their core tenets. In §§3 and 4 we trace historically how this situation has come to pass, before turning, in §5, to suggestions for the future.

3. Life-history theory in evolutionary biology

Life-history traits are those that figure directly in reproduction and survival, such as size at birth, age at maturity, number and timing of offspring, and age at senescence. Biologists had long appreciated that individuals of different species differ dramatically in the value of such traits. From the 1950s onwards, theorists began to explore mathematically how variation in life-history traits would affect fitness, and hence how the values of those traits might be shaped by natural selection [36–41].

An important early proposal was the idea that species could be characterized as more r­-selected or more K-selected. This idea derived from modelling work by MacArthur & Wilson [42]. The former have been selected to maximize their population growth rates when population density is low, while the latter have been selected to maximize their survival at high population densities (r and K refer to corresponding terms in the logistic population growth equation). Influentially, Pianka [43] proposed a suite of traits that ought to go with r and K (body size: small for r, larger for K age at maturation: early for r, later for K fecundity: high for r, lower for K, etc.). The r/K framework had two roles. The first was descriptive generalization: that species might be arrayed on a single continuum with fast reproduction and its correlates at one end and slow reproduction at the other. The second was an evolutionary explanation of the descriptive generalization: owing to the environments they live in, r-selected species have been more shaped by selection for a high maximal population growth rate, and K-selected species have been more shaped by selection to thrive under competition when populations are dense. The suite of traits proposed by Pianka to go along with r and K respectively were not mentioned in MacArthur and Wilson's original work [42] and did not arise from any formal model: they were illustrative suggestions, originally developed for Pianka's undergraduate population biology class [44].

Historians of LHT-E agree that the r/K framework was influential and attracted people to the field, but was eventually largely abandoned [44,45]. The descriptive part was seen as too simplistic. Debates about how much inter-species variation can be explained with a principal axis go on to this day [46–50]. Though life-history traits do tend to covary across species, the strength of a principal-axis pattern depends on the level of entity sampled (populations, species, or higher taxa) how phylogenetic relatedness is handled whether body size, which scales allometrically with many other traits, is corrected for the statistical methods used and which traits are included. Regardless of the outcome of these empirical matters, though, the evolutionary explanation part of the r/K framework was also abandoned. The different modes of selection supposed to underlie r and K were never demonstrated, and artificial selection experiments did not support the predictions [44] (though interest in the different effects of density-dependent and density-independent selection on life-history traits continues to this day [51]).

With the decline in interest in the r/K framework, LHT-E began to focus on models built around other factors, such as age-specific patterns of mortality. These ‘demographic’ models (summarized in [45,52]) went on to be synonymous with the term LHT. These models predict that a wide variety of patterns can be produced by selection under different environmental and demographic regimes, and organismal constraints. Hence the conclusion that:

There are virtually no general predictions in life history theory because some organism can always be found with a tricky and unexpected trade-off…Thus, it is more sensible to treat the theory as a general framework that tells us what questions need to be answered when building a model for some particular organism, than it is to try to use the predictions of general models [45, p. 208]

The consequence is that, rather than being able to collect a ready-made LHT prediction off the shelf for some new trait (e.g. a psychological one) in some new organism (e.g. humans), we would have to build a model fit for that purpose instead:

If you are interested in testing LHT, then collaborate with a theoretician and build a model of your particular organism, testing both assumptions and predictions against your data. There are few predictions…general enough to be convincingly and fairly tested on some randomly chosen organism without modification [45, p. 208]

In light of these comments, researchers in evolutionary biology are left with mostly general claims to constitute the hard core of the programme (there are trade-offs, and life-history traits are under selection). More detailed predictions are often model-specific and auxiliary to the programme. It would be wrong to argue that there are no mid-level generalizations in between (see the examples under tenet (iv) of table 1), but these are perhaps fewer and less clear-cut than is commonly assumed in psychology. However, a clear and defining asset of LHT-E is its methodological rules: the mathematical modelling techniques exist, and are generally agreed upon. Thus, to do LHT-E is to build explicit mathematical models to do so in particular ways and to test model assumptions and predictions for empirical cases. It is these activities more than any specific set of predictions about any particular species that constitute the research programme.

4. Life-history theory in psychology

Early applications of ideas from LHT-E in psychology explicitly referenced the r/K framework. Indeed, some explicitly described themselves as ‘differential K’ theory [53]. That is, humans are generally K-selected, but some humans are more so than others. Thus, the r/K contrasts suggested by Pianka [43] to hold at the species level were being extended to capture differences between conspecifics. These works picked up on two features from Pianka [43]: the first was that while early age at first reproduction was the master signature of being more r-selected, a whole suite of other traits might be needed to support it. For the psychologists, these included behaviours or cognitive traits, although these had not featured in Pianka's account. The second was that r-selection dominated particularly when the environment was variable and/or unpredictable. For Pianka [43] this referred to variability and unpredictability over evolutionary timescales. Some early work in LHT-P retained this focus and argued, controversially, that different human populations had experienced different selective histories [53]. However, the focus soon shifted from differences between populations and experience over evolutionary timescales, to differences between individuals and experience over the life-course. It is unclear whether the changes from the species to the individual as being classifiable as r or K, and from the causally relevant variability and unpredictability being within a lifetime as opposed to over evolutionary time, should be viewed as a direct application of Pianka's theory (i.e. Pianka's theory actually predicts the same to hold for individuals as species, and lifetimes as epochal timescales), or an analogical extension (i.e. individual people are analogous to species in that they can be arrayed on a fast–slow continuum, and having an unpredictable childhood is analogous to evolving in an epoch where the climate changes a lot). The difficulty of resolving this question stems from the fact that Pianka's account of r/K differences was not based on a formal model that can be adjudged either applicable or not applicable to the scenario that LHT-P authors were using it for.

Authors in psychology did notice that the r/K framework had been largely abandoned in LHT-E. One consequence was the disappearance of the ‘differential K’ terminology and the rapid rise of the more neutral term ‘LHT’ in psychology (figure 1). The r/K descriptive distinction was retained but renamed the ‘fast–slow continuum’, to stay in step with later presentations of the principal-axis idea in LHT-E [46,54]. The key explanatory part of the r/K model (that ‘faster’ life histories were the result of variable or unpredictable environments) was also retained, though ‘variable or unpredictable’ tended to become ‘harsh or unpredictable’ [55]. With r and K selection now gone, the claim about environments was now justified with reference to the idea that higher extrinsic mortality rates select for earlier reproduction and greater reproductive effort. This claim, which dates back to Williams [56], is a widespread mid-level idea within LHT-E. However, more recent models show that truly extrinsic mortality does not change the age distribution of the population and thus has no direct effect on selection for any trait [57,58], although it can have indirect effects via increased population density and intensified selection on competitive ability [58]. Sources of mortality often described as ‘extrinsic’ may actually affect older individuals more strongly than younger ones, and this does indeed relax selection on late-life survival [57]. Mortality that differentially affects juveniles actually strengthens selection for late-life survival [57], which strikes directly against the LHT-P idea that a harsh childhood environment might be particularly important in ‘speeding up’ life-history strategy.

Another influential development within LHT-P was the argument that plasticity and genetic evolution might be equifinal. That is, if harsh or unpredictable regimes select for genetic variants that accelerate development, they should also select for plastic mechanisms that allow individuals to shift strategically towards accelerated development if they personally experience harshness or unpredictability. This move is what allowed the shift in focus, within LHT-P, to strategic responses to individual environmental variables (table 2). The move is intuitive: the parallel between tanning and genetic variation in skin colour provides a familiar exemplar of how plasticity does in the short term what selection does in the very long term. However, it is not theoretically trivial. Appropriate models (of which there are currently few) are required, and they predict circumstances under which plastic responses and effects of selection can be decoupled [19].

As more psychologists entered the arena of LHT, particularly since 2010, they added additional psychological traits that they were interested in to the ‘fast–slow’ umbrella. The criteria for doing this seem to be, partly, the existence of some intuitive reason why that particular trait could help individuals achieve more rapid reproduction (e.g. impulsivity or future discounting [26]) and partly whether, empirically, the trait does indeed correlate with other psychometric variables already deemed to be ‘fast’ (see for example [59] on obesity). This means, in effect, that an important part of the grounds for saying that LHT predicts two traits will correlate is that they do in fact correlate. This is clearly a different, more inductive type of theory-building to the explicit a priori modelling of LHT-E. This should not surprise us: LHT-P has perhaps adopted the mode of theorizing of psychology more broadly, whereas LHT-E has stuck with its particular mode of theorizing. Again, we emphasize that we document these differences without judgement: different disciplines theorize in different ways in part because their aims and subject matters are different. Understandably, given the typical disciplinary concerns of psychology, LHT-P has become largely an account of proximal psychological processes. This is exemplified in the quotation from [35, p. 1] reproduced in §2: ‘At its core…LHT is a motivational framework’. In other words, while LHT-E is predominantly a framework for generating formal models aiming to produce ultimate explanations, LHT-P is predominantly a framework for non-formal theorizing, describing empirical patterns and investigating proximate causes [20].

Many authors within LHT-P are aware that the moves from species differences to individual differences, from selection to plasticity, and from strict life-history traits to a broader suite of behavioural, motivational and attitudinal traits, constitute extensions of the LHT-E framework. They have written about how these moves can be justified [55,60,61]. Moreover, critiques of LHT-P's core claims have begun to be generated from within LHT-P itself [21,62,63]. It is not our purpose to evaluate those justifications or review those critiques here. We just wish to point out that neither the justifications nor the critiques feature formal modelling, as formal modelling is not a methodological rule of LHT-P. The justifications rely on plausible analogies (it is intuitive that the effect of personal environment on an individual ought to be the same as the effect of selective environments on populations, or that you should reproduce fast if you are likely to die sooner). The critiques often come down to empirical matters such as how much variation in individual psychological differences can or cannot be explained by a principal fast–slow axis [21,64,65] and what that means [62]. Thus, LHT-P and LHT-E are currently talking past one another.

5. Prospects for future integration of life-history theory

We have argued that LHT-E and LHT-P have developed as two largely separate research programmes, with different aims, different interests and different modes of theorizing. This state of affairs causes difficulties if the two are not clearly distinguished. For example, were the core assumptions of LHT-P to be refuted, readers might believe that LHT-E had fallen or LHT-E might be invoked to support claims of LHT-P that actually have no formal evolutionary basis. Awareness of the distinction will be essential in building the emerging bridge between the areas of life history and learning. Broadly, this interface might have two foci: species-typical development and individual differences. The former focuses on how species-typical learning capacities relate to species-typical life-history variables this area is relatively mature (as evidenced by the examples in this volume). The latter focuses on individual differences in learning patterns in relation to individual differences in life-history variables this area is relatively new. In humans and rats, for instance, exposure to psychosocial adversity may shorten development, accelerating the onset of certain learning abilities (e.g. aversive fear conditioning, needed to navigate the world independently), while reducing others (e.g. attachment-related learning, forming a preference for cues associated with the parent) [66]. Exactly how evolutionary thinking should be deployed in understanding these phenomena is an area for future theory development.

We have argued that although LHT-E and LHT-P are clearly distinct, they are also historically and conceptually linked. Rather than abandoning those links, we believe researchers should strengthen them. Psychological theories do need to be grounded more deeply in our understanding of evolutionary processes and evolutionary history. We conclude with a few observations about how this strengthening might be done.

Formal evolutionary models should be developed to explore the concrete situations LHT-P is interested in. For example, although many LHT-E models deal explicitly with how multiple life-history traits should covary across species [67], fewer have explicitly dealt with how traits should covary across individuals within the same population [68]. This is challenging because it will depend on the genetic and developmental architecture of the traits, but predictive frameworks are being developed [51]. Modelling should be extended to incorporate behavioural and psychological traits as well as life-history traits [51]. For example, models have begun to appear predicting when individuals should be impulsive (in the sense of discounting the future heavily), depending on their environment and current state [69,70]. Importantly, these models do not rely on extrinsic mortality as the sole or even main explanatory factor, and they make potentially testable predictions. However, the models are complex: the predicted outcome depends on the precise assumptions about the structure of the environment and about the mapping between the behaviour and fitness. Thus, as well as developing the models and trying to test their predictions, it will be critical to gather data from natural human populations in order to validate, as far as possible, the modelling assumptions.

Formal modelling should also be applied to LHT-P's claims about developmental plasticity. The claims within LHT-P that childhood experience should be a key accelerator of life-history strategy are potentially problematic in a number of ways. Increased juvenile mortality, unless adult mortality is also increased, should if anything slow life history down (see §4). It is also, as noted above, problematic to assume that the effects of plasticity on the phenotype should necessarily evolve to look the same as the effects of selection. If the argument is that childhood experience serves as a ‘weather forecast’ of the conditions that will be experienced in future in adult life [71], the validity of this argument depends on assumptions about the statistical structure of environments [72], assumptions that needed to be validated empirically [73].

In short, there is scope for a programme of work establishing an ultimate evolutionary basis for the key claims of LHT-P: of a fast–slow continuum of individuals of the inclusion within it of some psychological traits but presumably not others and of evolved plasticity using childhood cues to calibrate the position on this axis. The appeal of this kind of work is that would allow psychologists to ground their claims in evolutionary theory in a way that evolutionary ecologists also feel satisfied by, as the grounding would have used the methodological rules of that discipline. We hope that more collaboration will develop between evolutionary modellers and empirical psychologists.

If LHT-P could move closer to LHT-E by adopting a more formal approach, evolutionary biology could also be more informed by LHT-P's concerns with proximate cognition, and with empirical patterns of individual differences. There has been an increased focus on individual differences in ecological research recently, and the covariance structure of those individual differences is an important concern [74]. Much of this research is organized within the ‘pace-of-life’ framework [75], whose findings speak directly to LHT-P. Key empirical findings are that the genetic correlations between traits are often different from the phenotypic correlations and can also differ between populations of the same species [76]. This could provide important impetus for extending the measurement of a ‘fast–slow’ continuum beyond a narrow range of Western research participants: perhaps the key generalizations are restricted to certain physical and social environments (see also [77]). Thus, there is scope for a comparative empirical science of individual differences and trait covariation that could be initially data-focused and agnostic about the evolutionary or environmental factors responsible for the patterns.

In conclusion, although LHT-E and LHT-P currently have less in common than their names imply, they share historical sources. Importantly, they could come into much closer relationship in the future, by sharing both methodological resources and empirical generalizations across the divide. This would contribute to the integration of human psychology into the more general framework of organismal biology, and be to the scientific benefit of both sides.


We thank S. Beran, S. Fine, S. Fountain, A. Huebner, J. McNair, A. Smith, E. Steckler, W. Steinbach and M. Sullivan for assistance with the research. We also thank E. Hebets, C. Mitra and A. Zera for feedback on the manuscript. The research was supported by the School of Biological Sciences and Initiative for Ecological and Evolutionary Analysis at the University of Nebraska-Lincoln (AET), a GAANN award from the US Department of Education (AET), and NSF grants IOB 0521743 and IOS 0818116 (WEW).


The National Research Foundation (NRF) and the Andrew Mellon Foundation funded this research. SCP thanks the NRF, Oppenheimer Memorial Trust and the University of Cape Town for personal funding during his PhD. We thank Edward Chirwa, Kervin Prayag and Anastas Belev for field assistance and Ian Newton (Department of Archeometry, UCT) for conducting the MS analysis. We are grateful to the South African National Parks for providing permission (CRC/2015/005–2012) to conduct research in Table Mountain National Park.


Successful colonizer species have a high reproductive rate, short generation time, and strong dispersal ability (Dingle, 1972 ). In the present study, the newly invasive FAW clearly possesses traits that make it a successful colonizer species. Compared with the life-history traits of the native FAW (also fed on corn leaves) observed by Garcia et al. ( 2018 ) (see their data in their Tables 1 and 2), the duration of larval development of the invasive FAW was shorter in the current study at all similar temperatures (11.1 ± 0.1 days at 31°C compared with 14.6 ± 0.1 days at 30°C 16.3 ± 0.1 days at 25°C compared with 18.3 days at 26°C 22 ± 0.2 days compared with 27.5 ± 0.2 days at 22°C) the invasive FAW also required less time to complete a generation (e.g., 20 days from egg to adult at 31°C compared with 23 days at 30°C) the number of eggs produced per mated female was also higher at all similar temperatures (1,432.7 ± 81.1 eggs at 31°C compared with 790.1 ± 105.3 eggs at 30°C 1,671.7 ± 77.4 eggs at 25°C compared with 1,071.0 ± 80.6 eggs at 26°C 1,555.0 ± 66.6 eggs compared with 993.5 ± 109.4 eggs at 22°C). Furthermore, the newly invasive FAW had higher larval and pupal survival rates (more than 96% and 86%, respectively, at 22, 25, 28, and 31°C) and a higher mating success rate (96%–100% at 22, 25, 28, and 31°C) (see Table 1). The excellent performance of the invasive FAW on corn leaves under constant temperature conditions suggests potentially severe future damage to this crop in China. Moreover, we observed the development time of 66 individuals of the newly invasive FAW that hatched on 29 July and experienced a mean daily temperature of 32.3°C and the fecundity of ten mated females under natural conditions by using the same rearing methods above. We found that the FAW exhibited excellent performance with 10.4 days larval period, 5.7 days for the pupal period, and 1,424 eggs per mated female. These results suggest that performance of life-history traits tends to be better in the newly invasive FAW than the native FAW. Compared with the life-history traits of the South Africa FAW (also fed on corn leaves) observed by Plessis et al. ( 2020 , see their data in their Table 1), we found that the duration of pupal development of FAW was shorter in the current study at all similar temperatures (such as, 12.6 ± 0.1 days for females and 14.4 ± 0.1 days for males compared with 17.1 ± 0.24 days at 22°C).

More interestingly, we found that a small proportion of females delayed oviposition and began to lay eggs on the 7th to 9th day after adult emergence at all rearing temperatures. This suggests that these females do not mate with males in the first four days after emergence because mated females lay eggs either on the same day or the next night after mating. Thus, we speculate that these few females leave their location and migrate to elsewhere. It is known that migrants can be classified as either obligate or facultative (Dingle & Drake, 2007 ). The present study suggests that a fraction of the population may move away, while most of the population may remain in their breeding area. Of course, to confirm this hypothesis, we need to perform further experiments by using a tethered-flight technique or to test ovarian development.

In the FAW, the pupal developmental time was significantly longer in males than females at all temperatures (Figure 1), resulting in the early emergence of females (protogyny). This protogyny phenomenon has been demonstrated in some lepidopteran species, such as the tobacco cutworm Spodoptera litura (Li et al., 2014 ), the cotton bollworm Helicoverpa armigera (Chen et al., 2014 Nunes et al., 2017 ), and the diamondback moth Plutella xylostella (Uematsu & Morikava, 1997 ). However, the biological reason for this emergence pattern is not well understood in insects. It may represent an evolutionary strategy to promote mating between individuals from distinct populations (Bento et al., 2006 Uematsu & Morikava, 1997 ) or it may be a strategy to reduce inbreeding (Li et al., 2014 ).

We found that 25°C conditions led to shorter larval development time but higher pupal weight than at 22 and 19°C (for larval development time: 16 days vs. 22 and 39 days for female pupal weight: 163.9 mg vs. 154.2 mg and 159.4 mg for male pupal weight: 181.3 mg vs. 173.3 mg and 177.9 mg, respectively) (see Table S1). Thus, the FAW did not follow the TSR. Furthermore, the fecundity was also highest at 25°C with a mean of 1,672 eggs per female. The shorter development times caused by higher temperatures result in larger body weights and higher egg production in the FAW, which clearly enhances its reproduction and results in serious damage to corn. Then, why do some insect species follow the TSR and some exhibit the reverse TSR? We speculate whether an insect species follows the TSR or not may be related to its diapause traits. Those species with summer diapause may exhibit the TSR, as indicated by the cabbage beetle, Colaphellus bowringi (Tang et al., 2017 ) and the cabbage butterfly, Pieris melete (Tang et al., 2019 ) because their reproductive periods occur in the spring and autumn and they have experienced strong selection for body size under relatively low environmental temperatures during the process of evolution. Those species with winter diapause triggered by shortening day lengths combined with high autumn temperatures may exhibit the reverse TSR, as indicated by the Asian corn borer, O. furnacalis (He et al., 2019 Xia et al., 2019 Xiao et al., 2016 ), and the rice stem borer, Chilo suppressalis (Fu et al., 2016 Huang et al., 2018 ). These two species enter winter diapause in response to high autumn temperatures and experienced strong selection for body size under warm conditions. The present study in the FAW suggests that migratory tropical insects may not follow the TSR, because the FAW experienced strong selection for body size under warm conditions. Similar reverse response was found in an invading population of the small cabbage white butterfly Pieris rapae (Kingsolver et al., 2007 ). However, to verify this speculation, additional insect species with similar characteristics should be investigated.

We found a significant positive relationship between pupal weight and larval development time at almost all temperatures, following the theory that animals with a longer growth period should be larger (Nijhout et al., 2010 ), that is, “one must grow for a longer time to get larger” (Roff, 2000 ). Thus, our results reveal that there is a trade-off between the two traits. The relationship between development time and body size has been observed in 77% of Lepidopteran insect species (122 of 146 datasets) (Teder et al., 2014 ). However, a negative relationship between the two traits has been reported in the rice stem borer C. suppressalis reared under field conditions (Huang et al., 2018 ) and the Asian corn borer O. furnacalis reared at constant temperatures (Xia et al., 2019 ), in which a relatively shorter larval developmental time resulted in a relatively larger pupal weight.

The fecundity advantage hypothesis suggests that larger females produce more offspring than smaller females (Andersson, 1994 Darwin, 1874 Honek, 1993 Omkar & Afaq, 2013 ). Our data support this hypothesis. The FAW exhibited significant positive relationship between adult weight and adult fecundity at all temperatures (Figure 6). This significant positive relationship between pupal weight and adult fecundity has been reported in other lepidopteran species, such as the spruce budworm Choristoneura fumiferana (Miller, 1957 ), the sugarcane borer Diatraea saccharalis (Bessin & Reagan, 1990 ), the Mexican rice borer Eoreuma loftini (Spurgeon et al., 1995 ), the oriental armyworm Mythmna separate (Luo et al., 1995 ), the moth Streblote panda (Calvo & Molina, 2005 ), and the diamondback moth Plutella xylostella (Zhang et al., 2012 ).

Longevity is expected to involve a trade-off with reproductive effort in most organisms (Bell & Koufopanou, 1986 Flatt, 2011 Harshman & Zera, 2007 Tatar, 2010 ) that is, reproduction tends to shorten the lifespan, the so-called “cost of reproduction” (Williams, 1966 ). The present study in FAW supports this prediction the females that reproduced more lived shorter lives (Figure 7). Such a negative relationship between the two traits has been recorded in the grasshoppers Chorthippus brunneus (de Souza Santos & Begon, 1987 ), the melon fly Bactrocera cucurbitae (Miyatake, 1997 ), the fruit fly Drosophila melanogaster (Flatt & Kawecki, 2007 Sambucetti et al., 2015 ), and the cotton bollworm H. armigera (Thyloor et al., 2016 ). However, little is known about the proximate mechanisms underlying these trade-offs. Fecundity might reduce survival because of the costly production of gametes or survivorship might be decreased due to the elevated mortality risk associated with courtship and mating behavior (Bell & Koufopanou, 1986 ). In Drosophila and other insects, juvenile hormones have been proposed to stimulate reproduction at the expense of survival (Flatt et al., 2005 Tu et al., 2005 ).

The very high survival rates of larvae and pupae and the high mating success rates in the present experiments indicate that our rearing technique is very successful that is, larvae reared individually in Petri dishes until adult eclosion and individual pairs of male and female moths placed in sealed plastic bags (20 × 30 cm) with cotton balls moistened in sugar solution for mating and oviposition. These rearing techniques may be adopted in other similar laboratory studies.


Vertebrate locomotor behaviors are powered by functional components with well-known trade-offs: musculoskeletal systems are geared with a specific ratio, and output displacement and force cannot be simultaneously optimized, muscle fibers develop phenotypes that increase either fatigue resistance or power at the cost of the other, and body shapes that augment acceleration have low mechanical efficiency. Physiologists typically expect these trade-offs at lower levels of organization (sub-cellular to organ-system) to scale up to whole-organism performance. Nevertheless, unexpected positive correlations between performance traits are frequently observed (Marras et al., 2013 Vanhooydonck et al., 2014).

Reidy et al. (2000), working with swimming cod, were the first to comment on these positive correlations and proposed that some cod are simply ‘good athletes’ and others ‘bad athletes’, which is a useful way to describe but not explain the pattern. Van Damme et al. (2002) and Wilson et al. (2014b) observed only positive correlations among human athletic performances and suggested that trade-offs at the whole-organism level are masked by individual quality, which Wilson et al. (2014b) explain as: ‘Because individuals vary in health, physical fitness, nutrition, development or genetics, which is the underlying basis of individual quality, some individuals perform better or worse across all types of motor tasks than others. This means that when researchers try to understand intra-individual functional trade-offs using inter-individual variation in performance, then trade-offs that do occur within individuals can be masked’. We try to clarify this meaning of individual quality with Fig. 1.

How individual quality masks functional trade-offs. The double-headed arrow connecting a true and counterfactual individual represents the ‘intra-individual functional trade-off’ (Wilson et al., 2014b). The double headed arrow between true individual A and true individual B represents the ‘inter-individual variation’ in quality (Q effect) that masks the intra-individual trade-off. For simplicity, the trade-off is determined by a single underlying morpho-physiological (M-P) trait that has opposite effects on the two performances (M effect). A counterfactual individual is one that is like the real individual in every way except for a change in the underlying M-P trait and the consequent changes in both performances. Individuals A and B do not differ in their M-P trait but individual B is better at both performances because of a difference in exposure to some extrinsic quality variable. This quality might result from something like differences in training or health status (for example, individual A might have a respiratory infection that both narrows respiratory tubes and decreases muscle contractility or motor unit recruitment).

How individual quality masks functional trade-offs. The double-headed arrow connecting a true and counterfactual individual represents the ‘intra-individual functional trade-off’ (Wilson et al., 2014b). The double headed arrow between true individual A and true individual B represents the ‘inter-individual variation’ in quality (Q effect) that masks the intra-individual trade-off. For simplicity, the trade-off is determined by a single underlying morpho-physiological (M-P) trait that has opposite effects on the two performances (M effect). A counterfactual individual is one that is like the real individual in every way except for a change in the underlying M-P trait and the consequent changes in both performances. Individuals A and B do not differ in their M-P trait but individual B is better at both performances because of a difference in exposure to some extrinsic quality variable. This quality might result from something like differences in training or health status (for example, individual A might have a respiratory infection that both narrows respiratory tubes and decreases muscle contractility or motor unit recruitment).

Both Van Damme et al. (2002) and Wilson et al. (2014b) argue that the intra-individual trade-offs can be recovered by statistically adjusting for quality. And, both found that the expected negative correlations emerged only after this adjustment. Importantly, both Van Damme et al. (2002) and Wilson et al. (2014b) are cited in the evolutionary and human performance literature as evidence of performance trade-offs without acknowledging that the measured correlations were positive (MacArthur and North, 2005 Flueck, 2009 Ruiz et al., 2010 Eynon et al., 2013 Lailvaux and Husak, 2014 Wilson et al., 2014a Servedio et al., 2014). We emphasize this because all four methods used to infer trade-offs in Van Damme et al. (2002) and Wilson et al. (2014b) are poor estimators of quality-free correlations. These methods are: (1) culling all but the top performers, which is guaranteed to produce a negative correlation, even if no underlying trade-off exists (Garland, 1994), (2) the correlation between the residuals of performance traits regressed on first principal component scores, which is guaranteed to produce strongly negatively biased correlations (Aitchison, 2003), (3) the interpretation of principal component (PC) loadings of opposite signs as indicating an underlying trade-off, which is not a valid interpretation of loadings, and (4) the partial correlation between two performances conditional on all other performances, which removes too much of the shared correlation (Mitteroecker and Bookstein, 2009). We find similar misuses of multivariate methods common in the performance literature and strongly encourage reading our detailed criticism of all four methods (Walker, 2015a).

Despite these methodological issues, individual quality is a compelling hypothesis to explain a common phenomenon in both human and non-human performance data. In order to explore the concept of quality in performance correlations, we compiled a dataset of decathlon performance data for US collegiate athletes, and used Sewell Wright's (1932) path-analytic factor analysis to estimate ‘quality-free’ correlations among these 10 events. In this paper, we use a model of functional trade-offs (Ghalambor et al., 2003) to (1) show how functional trade-offs at the cell, organ or system level contribute to performance trade-offs at the whole-animal level, (2) decompose quality into intrinsic and extrinsic components and show how the extrinsic component can mask the underlying architecture of the form–function mapping, (3) show why ‘bottom up’ approaches to predict performance trade-offs at the whole-animal level based on limited knowledge of trade-offs at the cell or organ level are likely to fail, and (4) show how to estimate a quality-free correlation matrix. Through analysis of the National Collegiate Athletic Association (NCAA) decathlon data, we then show that, compared with the results of Van Damme et al. (2002), the pattern of measured correlations is similar but our estimates of quality-free correlations differ in key respects. We also re-analyze the performance data from sub-elite male soccer players (Wilson et al., 2014b).

A model of extrinsic and intrinsic components of performance correlations

The concept of intra-individual variation (Wilson et al., 2014b) is similar to a counterfactual conditional statement such as, ‘were the mechanical advantage 0.3 and not its real value 0.2, the force output would be 0.6 N and not its real value 0.4 N’. But there is nothing special about applying this concept to morpho-physiological traits as opposed to individual quality factors (‘were my training 750 h per year and not its real value 500 h, my marathon time would be 2 h:18 min and not its real value 2 h:28 min’). We suggest that the masking problem is not one of inter- versus intra-individual variation but of intrinsic versus extrinsic variation, where extrinsic variation results from differences in exposure to extrinsic factors such as training intensity or style, diet, recovery, stressful life events, pathogens, etc. All intrinsic factors should be left unadjusted.

We developed a model of how functional trade-offs, which arise at the sub-whole-animal level, combine with extrinsic quality factors to contribute to performance correlations that we measured at the whole-animal level. This model uses the graphical algebra of path models, which were specifically developed by Sewell Wright (1918, 1932, 1934) to model the underlying factors (‘causes’) generating correlations among measured traits. While elegant, path models are not necessary for any conclusion that we illustrate. The basic algebra of path models is available in some biostatistics textbooks (e.g. Sokal and Rohlf, 2012). Shipley (2002) is a more thorough introduction to path models in functional biology and ecology. Pearl (2009) formalizes many of the concepts of causal graphs. Our path models are models of simplified functional systems and used only to develop a general theory we do not attempt to test detailed causal models of performance variation in humans. Our models ignore some complexities of real systems in order to focus on the fundamental principles. But ignoring the complexities of real systems does not make our simplified models irrelevant on the contrary, the complexities make the goals of discovering underlying trade-offs that much more difficult. The scripts for generating simulated data using all of the path models introduced below are available elsewhere (Walker, 2015b).

where β1 and β2 have opposite signs. The U represent ‘noise’ or additional variance that is uncorrelated with all other effects. In all later path models, the U are implied but not written out.

We refer to this kind of path diagram as a form–function map. The pattern of causal arrows from M-P traits to performance traits is one component of the functional architecture of an organism. The single-headed arrow indicates a causal effect and the path coefficient represents the sign and magnitude of the effect. Here and elsewhere in this paper, all variables in a path model are standardized to unit variance, which makes the path coefficients standardized. The consequence of this standardization gives the path diagram its most elegant feature: the expected correlation between any two traits can be quickly computed as the sum of the products of the coefficients along all paths connecting the two variables. The expected performance correlation between P1 and P2 is β1β2. The performances are correlated because they share the common cause (M). The U do not contribute to the correlation because neither is a common cause of P1 and P2. We call the expected correlation due to the mapping of M-P traits to performance the ‘functional correlation’. In this simple model, but not in more complex models (see below), the functional correlation is the expected performance correlation. A negative functional correlation is a functional trade-off and occurs if β1 and β2 have opposite signs. A positive functional correlation is a functional facilitation (Ghalambor et al., 2003).

While it appears that Q affects performance by some mechanism other than through M-P traits, our model is a mathematical simplification of, but precisely equivalent to, a full model with Q acting through the M-P traits (Walker, 2015b).

The functional correlation in Eqn 2 is β1β2 but the expected performance correlation is α1α21β2. The component α1α2 is positive adding Q to the model shifts the expected performance correlation in a positive direction. Regardless of the magnitude of the α, the effect of the functional trade-off is masked. If the α are small relative to the β, only the magnitude will be masked (i.e. a smaller, negative performance correlation than would occur if there were no variation in training). But if the α are large relative to the β, the sign will be masked too.

where rraw is the measured correlation. Below, we show that rquality-free is equivalent to the functional correlation only in the special case of no correlation among the M-P traits.

Note that we have changed the coefficient symbols to reflect the fact that our second causal variable represents an underlying M-P trait and not an extrinsic factor. The expected performance correlation (β11β1221β22) is the sum of two functional correlations, each due to its own common cause. We call the sum of the functional correlations the ‘net’ functional correlation. A net functional trade-off is a negative net functional correlation. It is a pattern of form–function mapping where a set of M-P traits causally affects two performance traits in opposite directions.

In Eqn 2, we have a functional system in which the underlying form–function mapping is being masked by Q. We quite reasonably consider Q a nuisance factor and want to adjust the raw correlation to get rid of its effect. By contrast, in Eqn 4, we have a functional system with two underlying M-P traits. Trait M1 causes a trade-off (its path coefficients are of opposite sign). Trait M2 causes a facilitation. Holzman et al. (2011), among others, emphasized that the M2 facilitation mitigates the M1 trade-off but it makes equal sense to say the M1 trade-off attenuates the M2 facilitation. If the facilitation is larger, the net functional correlation is positive. A positive performance correlation faithfully represents the underlying functional architecture that is, the pattern of how M-P traits map to performance. We most definitely do not want to adjust the correlation to control for M2. Instead, we have high- and low-quality athletes because of the functional architecture. Quality is determined by the intrinsic properties of the causal mapping from M-P traits to performance.

The contrast between the path diagrams in Eqns 2 and 4 raises the concern, what kinds of traits do we call Q (extrinsic quality) and consider a nuisance variable that should be statistically adjusted and what do we consider M (intrinsic quality) and part of the functional architecture? For example, recent work on the genetic predictors of the individual response to training in humans suggests the presence of networks of muscle-plasticity genes that affect the ability of muscle to remodel. These networks are activated in the same way in both resistance and endurance training (Timmons, 2011 Phillips et al., 2013). If these plasticity networks have large magnitude effects on performance, we would expect some individuals to excel in both high-power and high-endurance events and some to perform poorly in both types of events, even if all athletes had precisely the same training. This variation in the response to training is an intrinsic component of phenotypic design, as opposed to the extrinsic variation in different training plans. Do we measure this response to training, score it as Q and adjust for its effects on the correlations, or do we score it as another M-P trait M and allow it to contribute to the net functional correlations? Other traits, especially physical traits (pain and stress signaling systems related to tolerance, including CNS feedback limiting muscle strain and, consequently, performance) that contribute to psychological factors like ‘mental toughness’ or ‘competitiveness’ may be even more ambiguous as to how these should be considered. We believe all these intrinsic traits should be scored as M.

This concern is augmented if Q is a latent variable, as in Wilson et al. (2014b) and Van Damme et al. (2002). Latent variables are mathematical constructs (such as the first principal component) but are generally interpreted to be something meaningful, for example ‘general intelligence’, ‘general size’ or ‘individual quality’. With a latent Q, how do we differentiate the system in Eqn 2 from that in Eqn 4, both of which result in a first PC with all positive loadings? Even worse, the first PC can be a mixture of intrinsic and extrinsic contributions to quality. In Walker (2015b), we generated simulated data representing 10 performance traits affected by two M-P traits and a single, extrinsic quality trait. The M-P traits had a modular mapping to performance with one having moderate effects on performance traits 1–5 and the other having moderate effects on performance traits 6–10. The quality trait had a small effect on six of the 10 performance traits and zero effect on the other four performance traits. The loadings on PC1 were all the same sign, suggestive of a single, global factor even though none existed. While a PC1 with all positive loadings is an axis representing athletic quality, a pattern of all-positive loadings cannot justify interpreting the axis as representing extrinsic sources of variation that need to be adjusted away.

Why performance correlations may be poorly predicted

Predicting a correlation between a pair of performance traits based on a qualitative relationship between one or a few underlying M-P traits and the performance traits is nearly ubiquitous in the performance literature (e.g. increased upper limb muscle mass should increase shot put but cost high jump performance). But a net functional correlation is the sum of all the expected component correlations (Ghalambor et al., 2003). For example, in the path diagram in Eqn 4, the net functional correlation is β11β1221β22. This raises a major concern with bottom-up approaches to predicting correlations between performance variables. Many of the performance traits that we care about, especially at the whole-animal level, have many tens, hundreds or even thousands of underlying common causal factors, many of which we are ignorant of, and for most of which we have little information on the magnitude of the effect on each performance, and thus the expected component correlation. Given our knowledge of only a fraction of the common causes, and quantitative estimate of effect size for only a fraction of these, it would seem our ability to predict a performance correlation is extremely limited. Vanhooydonck et al. (2014) make a similar argument but without the benefit of a graphical or mathematical model.

where r12 is the correlation between the M-P traits. The expected performance correlation is β11β1221β22+r12β11β22+r­12β12β21. This correlation is not only due to both the sign and magnitude of the net functional correlation but also to the sign and magnitude of the phenotypic correlation between the M-P traits. A phenotypic correlation can cause a performance correlation to be larger, smaller or even of opposite sign relative to the net functional correlation (Holzman et al., 2011 Walker, 2015b). Indeed, if M1 maps only to P1, M2 maps only to P2 and r12 is negative, the expected performance correlation is negative despite the lack of any underlying M-P trait that has opposite effects on performance.

A brief introduction to estimating a quality-free correlation matrix

where F is the p×m matrix containing the path coefficients of the causal effects of p M-P traits on m performances. The matrix contains the expected trade-offs and facilitations among the performance variables at the whole-animal level given only the functional mapping. The problem with this bottom-up approach, as discussed above, is that we would need to know all causal effects to compute the net functional correlations with any accuracy.

where is the vector of path coefficients from some measure of Q to each performance variable. If is estimated as the loadings on PC1, then Eqn 7 is equivalent to the covariance matrix of the residuals of the regression of each performance trait on PC1. The matrix contains the component correlations due to Q only. As an estimate of the net functional correlation, Eqn 6 assumes (1) Q contains only extrinsic variables, (2) Q contains all extrinsic variables, (3) is an unbiased estimate of the effects of Q on performance, and (4) there is no phenotypic correlation among the morphological traits. We introduced assumptions 1, 2 and 4 above. Assumption 3 is violated using standard measures of a latent Q and we offer a solution here. Because assumption 4 is violated, we use the term ‘quality-free’ and not ‘net functional correlation’ to refer to the matrix Rquality-free.

where and are the mean off-diagonal elements in Rraw and RPC1, respectively. We note that Wright (1932) used only the subset of ‘among-module’ correlations in the computation of and r PC1, where ‘among-module’ refers to a pair of morphometric traits occurring in different development modules defined a priori. Here, we relax the necessity of an a priori factor structure and use the means of all off-diagonal elements in Rraw and RPC1. We refer to the uncorrected (Eqn 7) and bias-corrected (Eqn 8) residuals as Wright's uncorrected (WUC) and Wright's bias-corrected (WBC) correlations.

4. Discussion

Reproduction is costly, leading to a trade-off between reproductive investment, survival and growth [61]. The part of ingested energy remaining after allocation to metabolic process is allocated to both somatic growth and reproductive investments, which are hence in mutual competition. Recently, an increase of trophic overlap between small pelagic fish species was observed in the Gulf of Lions at the same time as a decrease in fish body condition [33,62], supporting the hypothesis that food resources could be currently more limiting than in the past [45,62]. In such context of food shortage, one might wonder how the trade-off between reproduction and growth or maintenance has been dealt with in both species, especially in light of their fast life-history pace as well as their opposite breeding strategies. To investigate reproductive allocation, we used a combination of three measurements: (i) the length of the breeding season, (ii) the age or size at which they first reproduce, and (iii) the weight of the gonad relative to the individual total weight.

First, the spawning period seems to have been slightly extended compared to previous studies from the 1960s [46,47]. In particular, anchovy starts reproducing a bit earlier, now starting at the end of April instead of in May. These changes could be the result of physiological adjustments to increasing sea temperatures and changing environment. Anchovy spawning was shown to be induced by temperatures higher than 17ଌ [34], so that advanced warming water [63] could promote earlier gonad maturation. As the reproductive performance is known to increase with age (constraint [64], restraint [5] and selection [65] hypotheses), especially in terms of breeding duration [61,66], spawning period was expected to be shorter for younger females than older ones [67,68]. Surprisingly, none of our studied species displayed a shorter spawning period despite a rejuvenation of the population, suggesting high reproductive investment for both species.

Furthermore, our results suggest a decrease in length at first maturity of both species. Sardine length at maturity was high during the 1970s and early 2000s, but has decreased strongly after 2009. An abrupt change in size at first maturity from 2007 to 2008 has also been observed in anchovy, which have matured at extremely small size since 2012. Surprisingly, the decline in L50 did not happen progressively [69], but very fast around 2008 in both species, confirming the high plasticity of their reproductive characteristics as already observed for other short-lived species, such as Daphnia [70], fish [71] or toad [72]. Under unfavourable environmental condition (reduced growth), organisms should adjust size at maturity to maximize fitness [73]. For instance, growth reduction often leads to earlier reproduction at a smaller size [74] in short-lived species. Similarly, under reduced adult survival, selection should favour genotypes capable of reproducing earlier, at a smaller size and with a higher reproductive effort [75]. Accordingly, sardine reproductive effort (as measured through the GSI) showed a strong increase during the last 7 years, anchovy GSI increasing as well though less strongly. Such increase in reproductive effort might be a response to the decreasing proportion of large females, which usually produce more eggs. Moreover, the gradual increase over the last years in sardine GSI (and also but more slowly so for anchovy) may reflect the progressive increase in the number of individuals able to invest highly in reproduction, supporting the idea that there was a selection favouring this phenotype.

Our results thus indicate that when confronted by low energy resources, small pelagic fish seem to increase reproductive allocation. This might be an important source of demographic changes as well as fishing pressure. As Van Beveren et al. [76] underlined the relatively low exploitation of both species during the study period in the study area, we do not think that fishing could be the main factor that has induced the observed changes in the studied indices. However, fishing can act as a covariable, and its impact might be difficult to differentiate from environmental ones. Fishing activities can largely affect the condition and reproductive potential of exploited fish in complex ways such as reducing the food availability or inducing physiological stress (reviewed by Lampert [15]), and therefore we cannot fully discard that fishing activities in the area targeting anchovy and sardine, despite being moderate, can play a role on the observed changes. Therefore, further investigations are needed to consider the fishing pressure on the condition and reproductive potential of small pelagic fish populations. By devoting more energy per individual to reproduction, small pelagic fish seem to favour their reproductive output over somatic growth under unfavourable conditions. These results support life-history theory, as short-lived species are expected to favour reproduction over survival [3], as previously shown in a large number of fish species (e.g. in vendace [71] or herring [77]). Contrary to longer-lived species able to safeguard their own survival by ceasing to breed at any time (e.g. amphibian [78] and reptile [79]), such a strategy could greatly affect other small pelagic life-history traits and explain the recent reduction of growth rates and sardine adult survival highlighted by Van Beveren et al. [33]. This might even be further amplified by the fact that the survival cost of reproduction is known to be higher in individuals maturing at smaller size and earlier age [80].

Despite similarities, our results also highlighted differences between the two species. Indeed, the increase in anchovy GSI values was much lower than sardine's one. This has to be put in relation with the steeper decline in growth and condition in sardines compared to anchovies, as well as the adult overmortality which only occurred in sardines [33]. Such results could come from their reproductive strategies, anchovy being an income breeder and sardine mainly a capital breeder [35,36]. If we assume that growth is mainly realized during spring and summer [81], when planktonic resources are more important, anchovy strategy allows them to take advantage of higher resource availability to invest in both somatic growth and reproduction. By contrast, sardine has to store energy and incur costs due to accumulating fat store and maintaining storage compound to then spend this capital during winter [82]. Following breeding at the end of winter, sardine reserves should thus be exhausted making them more vulnerable to lower food availability (whether due to a general decrease in prey quantity or quality). Together with really low energy stores, high reproductive investment at a period at which food is scarce could deeply lower the survival and prevent the majority of sardine from surviving past their first reproductive season, explaining the observed disappearance of large sardine since 2008 in the Gulf of Lions [31]. Nevertheless, some sardine populations were shown to feed during the spawning period while some anchovies rely on somatic reserves for part of their reproduction [42], smoothing off the income versus capital strategy opposition. Even if strict income or capital strategy might not happen all the time in the Gulf of Lions, our results still suggest potential differences in the effect of reproductive investment on other life-history traits depending on breeding strategies (income/capital), which would merit further investigation.

Results also suggest significant preovulatory maternal condition effects on the egg quantity and quality of sardine and anchovy. Reproductive features are similar to numerous species of birds [83], Daphnia [15], snakes [84] or turtles [14]. As the number of eggs increases linearly with fish size for both species and the RBF also increases with body length for sardine, reproductive capacity can therefore be assumed to be higher in large individuals. This emphasizes the hypothesis that the reproductive potential of a species is highly dependent on large individuals (i.e. dependent on the age structure of the population, e.g. [85]) as previously reported for many taxa (e.g. [86]). However, contrasting with several other species, e.g. birds [25] or reptiles [22], anchovy and sardine females in better condition did not produce more eggs relative to their weight than females in a poorer condition. On the contrary, egg quality did depend on female lipid content, so that maternal condition may be relevant for the survival of egg and larvae. Indeed, Riveiro et al. [87] demonstrated the link between larval survival in hatching condition and the egg quality underlining its importance in larvae survival rate and in short-term fish recruitment. Consequently, we may reasonably think that later years' egg quality of sardine and anchovy was affected by the decrease of adult body condition [33]. While a positive size effect had been previously detected on egg quality in cod [88] but also in turtles [14] or birds [89], none of our species displayed such relationship. Moreover, the occurrence and intensity of atresia were not related to fish condition or size in either of the two species, despite maternal condition being know to rule oocytes resorption mechanism depending on fat quantity in several species, e.g. in insects [90] or fish [91]. This could be due to the really low level of atresia observed in these indeterminate fecundity species, for which atresia occurs almost only in the regression phase.

In the light of the current small pelagic fish situation in the Gulf of Lions, characterized by small sardine and anchovy in poor condition [33,54], our results indicate that the individual reproductive potential could be strongly affected both in terms of quantity and quality. However, earlier maturation could potentially lead to a higher number of breeders and compensate at the population level for the decrease in individual reproductive capacity, as described in other short-lived species such as Daphnia [92] or insects [93]. Indeed, the back-calculated yearly population egg number production values indicated that anchovy egg production has been slightly higher since 2009 and thus not affected by low resource levels and smaller fish dominance. On the contrary, the change in L50 was not sufficient to counteract the more pronounced disappearance of large and old individuals in sardines. Indeed, the model highlighted an estimated fourfold reduction of the sardine egg number in the Gulf of Lions between years when large sardines dominated (i.e. 2005�) and when small sardines dominated (i.e. since 2008). As sardine and anchovy condition has decreased since 2007 and influences egg quality, we suggest that along with egg number reduction, egg quality also decreased. This enhances the idea of a stronger degradation of sardine reproductive capacities paralleling the decline in the lipid reserves of the stock compared to anchovy. Nevertheless, no data were currently available to obtain an accurate estimation of recruitment for both species, leaving as a challenge for future studies to test whether egg number and quality might explain a significant part of recruitment variability of small pelagic fish.

Long-lived species are able to prioritize their energy allocation between life-history traits and usually favour their own condition over their propagules' condition [3]. For example, fish [42] as well as birds [94] or reptiles [95] are able to skip or delay breeding under poor environmental condition to attempt to maximize fitness by allocating resources optimally among growth, maintenance and future reproduction. In contrast, short-lived anchovy and sardine clearly guided the trade-offs between reproduction and survival towards a maintenance (if not an increase) of their reproductive investment even during a poor condition period in the Gulf of Lions. According to the costs associated with reproduction, females favouring reproduction led to a reduced growth and a reduction in survival and might explain the current lack of large old small pelagic fish in the Gulf of Lions. Even if reproduction was prioritized, egg quantity and quality decreased between 2006 and 2015 for sardine. While the effect of decreasing sardine egg production on its recruitment could not be investigated in this study, these findings brought to light strong evidence on the need to consider fish reproductive and condition characteristics together. Both are essential to understand forage fish fluctuations and evaluate the long-term sustainability of the forage fish stocks.


Experimental Manipulation of Horn Development.

We looked for a trade-off between horn growth and testes growth in O. nigriventris by experimentally manipulating horn development. Experimental O. nigriventris were derived from adult beetles collected from pastures of the Parker Ranch on the island of Hawaii. Mated females were established in plastic breeding chambers (8 cm diameter × 20 cm deep) in the laboratory (University of Montana) and maintained in growth chambers at 25°C with unlimited access to cow dung. Females build a series of individual brood balls, each of which provides the resources for the development of a single offspring from hatching until adult emergence. Brood balls were sieved from breeding chambers and placed in shallow soil-filled containers in the same growth chambers. Individual broods were opened and larvae checked for their stage of development. Toward the end of the third larval instar, during the gut purge, the area of proliferating cells that would otherwise become the principal thoracic horn was cauterized by application of a hyphrecator. The larvae were held in place with forceps during cauterization and care was taken not to discolor the larval cuticle. The larvae were then returned to their individual brood balls and allowed to continue their development. Emerging adult beetles were checked for horn growth. No cauterized beetles developed horns. A series of controls were established in which larvae were removed from their broods, handled in a similar manner to cauterized beetles, and then returned to their broods. Seven days after adult emergence (after testes have matured), beetles were weighed and then dissected, and their testes were removed and weighed to an accuracy of 0.01 mg. Weights were log transformed before statistical analyses.

Comparative Analyses.

We collected data on thorax width (as a measure of body size), testes weight, body weight, and horn morphology from 25 species of Onthophagus. For all species beetles were sampled from the field, collected from fresh animal dung. Beetles were returned to the laboratory and maintained at 25°C with access to fresh dung for 7 days. Before dissection, beetles were held without access to dung or water for 24 h. This procedure was adopted to ensure that beetles were sexually mature, of equivalent recent mating history, and that they had purged their guts before weight determination. Thorax width was cubed to convert it to the same scale as our weight measures.

The genus exhibits complex patterns of variation in horn morphology, developing horns at one or several of five locations on the head and thorax (16, 32). We used two metrics of horn morphology (Table 1). First we measured the length of the largest or most exaggerated horn and again cubed this value to achieve the same scale as our weight measures. Second, we examined the degree of developmental plasticity in horn growth by calculating the scaling relationship between horn size and body size. For many species of Onthophagus, the scaling relationship of horn size on body size deviates from linearity because of the occurrence of minor males that in some species are hornless, whereas in others develop only rudimentary horns (32). We therefore fitted data for each species to the following equation: where y 0 is equal to the minimum horn length, a describes the range of horn lengths present in the sample, b the maximum rate of increase in horn size per unit increase in body size, c represents the body size at the point of inflection of the sigmoid, and x represents our measure of body size, thorax width. We used the software package SigmaPlot (SYSTAT) to estimate the parameter b from this equation and used this value as our measure of horn allometry for each species. Where species possessed both head and thoracic horns, we calculated the scaling relationship for the largest or most exaggerated horn.

Again, in addition to measuring a species' absolute testes weight, we quantified each species' degree of developmental plasticity in testes growth as the allometric slope of log testes weight on log body weight. We calculated the major axis slope (MA in Table 1) because we are interested in the true relationship between these two variables, both were measured with error, and both were measured on the same scale (49).

Of the species listed in Table 1, all but O. blackwoodensis, O. nodulifer, and O. rupicapra were included in a recent phylogeny, based on regions of four nuclear and three mitochondrial genes (3,315 bp total 837 parsimony-informative) from 48 Onthophagus species and three outgroups (16, 32). Based on this phylogeny, we used the software package CAIC (33) to calculate phylogenetically independent contrasts. We also used the phylogeny to test for correlated evolutionary changes between gains of novel horns (on the head on the thorax) and changes in the level of sperm competition as estimated by the presence/absence of hornless minor (sneak) males (male-dimorphism male-monomorphism see results for justification). For these analyses, we used the concentrated changes test (50) as implemented in MacClade 4 (36).