Variational propensities: development and ultimate causes

Abstract

This paper applies philosophical tools from the causalists/statisticalists debate to the evo-devo idea of variational tendencies as propensities biasing phenotypic change. It contends that variational properties are present in a statistical sense in some population dynamics models, particularly quantitative genetics ones, providing ultimate variational explanations. It further argues that these properties, contrary to some recent views, cannot be subsumed under natural selection. Finally, it advocates for a causalist interpretation of these explanations, where variational statistical properties indirectly refer to evo-devo’s variational propensities.

1 Introduction

In the last 20 years, a considerable amount of work in the philosophy of biology has been devoted to the so-called ‘causalists/statisticalists’ debate, which discusses whether evolutionary theory explanations, as exemplified in the mathematical apparatus of population dynamics models, refer to the causes of evolution (reviewed in Pence, 2021). Natural selection and its relation to fitness and drift is the main point of divergence for contendants. Causalists defend that natural selection is a cause of evolutionary changes, whereas statisticalists argue that it is an explanatory statistical aggregate of causes acting at a different level. The bottom line is that there is some causal story that relates to these population-level explanations, and that philosophers disagree about whether the explanations represent the story (causalism) or abstract away from it (statisticalism) in order to predict how the next chapter goes.

It is not coincidental that population dynamics models have captured so much attention from philosophers. These models are at the core of the Modern Synthesis view of evolution, constituting the main tool for explaining and predicting microevolutionary changes on the basis of fitness differences between traits in a population. Determining whether these models can accurately capture the causal components of the evolutionary process, and especially the role of natural selection within it, is a vital aspect of how evolutionary biology has achieved its ability to provide explanations and predictions. Despite this prominent position, however, the debate has barely been applied outside its own limits. The causal or non-causal nature of selection and drift in population dynamics models is usually taken as an isolated philosophical discussion over what type of explanation evolutionary theory can provide. But contemporary evolutionary biology is a multidisciplinary area where population dynamics models are only part of the story. The historically received idea that these models play a privileged role in the explanation of evolution is nowadays questioned by conceptual approaches coming from very diverse domains within evolutionary biology, such as paleontology, epigenetics, ecology, or evo-devo. The so-called Extended Evolutionary Synthesis debate (EES; Jablonka & Lamb, 2020; Laland et al., 2014; Oyama et al., 2001; Pigliucci & Müller, 2010) discusses the scope of the classical approach to evolution, particularly as exemplified by population dynamics models, in the light of these other research agendas.

From a philosophical perspective, many of the puzzles posed by the EES debate eventually lead to scrutinizing what constitutes a cause of evolution, how to classify evolutionary causes into distinct types, and how these different types relate to one another. One crucial aspect of such scrutinization is the discussion over reciprocal causation and the ultimate/proximate distinction in biology (Laland et al., 2011). Ernst Mayr famously divided the realm of biological causes into those pertaining to the lifespan of organisms, which he labeled proximate causes, and those acting at the level of populations and changing their composition throughout evolution, which he labeled ultimate causes (Mayr, 1961). Accordingly, evolutionary biology was associated with the study of ultimate causes, while organismal causal processes were considered mostly irrelevant for evolutionary explanations. However, some non-classical evolutionary areas emphasize the impact of organism-level processes in determining evolutionary phenomena, in turn challenging the meaningfulness of such a separation between organismal and evolutionary causes.¹ For example, niche construction theory studies the interplay between organisms’ activities and outputs and ecological niches, focusing on how organismal causes affect their own selective pressures (Laland et al., 2011, 2014). A general idea among EES supporters is that such studies broaden the scope of evolutionary thinking by focusing on the mechanistic bases of evolution (Pigliucci & Müller, 2010), in turn grasping causal aspects that are absent from the statistical approach of population dynamics explanations.

Interestingly, and despite a lack of overlap in the discussions, this is precisely what is at stake in the causalists/statisticalists debate with respect to selection, fitness and drift. Those denying a causal nature to selection in population dynamics explanations do it on the basis of an alleged failure to relate to the real ecological causes determining differential survival and reproduction (Matthen & Ariew, 2002; Walsh et al., 2017). In other words, statisticalists believe that evolutionary changes are not caused by selection and drift as in population dynamics models, but by the ecological and developmental organismal processes underlying them. Put in terms that are more familiar to the EES debate, statisticalism considers that evolution only has proximate causes, even if one can build good ultimate, non-causal explanations of the evolutionary process through population dynamics models (Ariew, 2003; Walsh, 2019). Causalists, on the other hand, believe that evolutionary causation can also be depicted at the population level, and therefore that notions such as selection and drift represent genuine, ultimate causes—be them autonomous (e.g., Sober, 1984; Millstein, 2006) or grounded on individual-level causes (e.g., Otsuka, 2016; Pence and Ramsey, 2013). The distinctions made in the philosophical literature over selection, drift and fitness could therefore be applied to the interplay between proximate and ultimate causes that contemporary evolutionary biology seems to imply. While the causalists/statisticalists debate is very unlikely to solve the EES disputes on its own, these distinctions could help to get a deeper perspective on them. For example, differentiating between the mathematical fitness of traits and the causal fitness of organisms as two related but different types of propensities (Sober, 2001) can help in understanding the relationship that ecological, organism-based explanations hold with classical population dynamics models.

Evolutionary developmental biology (evo-devo) has historically vindicated that the development of organisms biases the production of variation in evolution, which constitutes an example of proximate causes having evolutionary effects (Brown, 2021). It stresses the non-random character of such an impact (Nuño de la Rosa & Villegas, 2022), which is in apparent contradiction with the classical idea that “chance reigns supreme” in the production of variation (cf. Mayr, 1963, p. 214). In a nutshell, the received picture of evolution assumed that genotypic variation is random (Merlin, 2010) and left aside the emergence of phenotypic variants, focusing on how natural selection and drift shape the relative frequency of extant ones, and assuming that mutational inputs have negligible, or at least undirected, effects on this process. How such a frequency-based view of evolution can account for the emergence of phenotypic changes is known as “the problem of variation” (Stern, 2000). One main contribution of evo-devo to evolutionary biology is the study of developmental biases in phenotypic variation explaining the origin and nature of phenotypic changes (Brigandt, 2020; Müller, 2007; Oster & Alberch, 1982), in turn contributing to solving such a problem. While recent works have indeed explored the connections between selection as an ultimate cause and its proximate, lower-level determinants (e.g., Hazelwood, 2023), the problem of developmental biases in phenotypic variation remains unexplored from this perspective.

In this paper, I fill part of this gap by applying some aspects of the causalists/statisticalists debate to the EES discussion on developmental biases in phenotypic variation. I first review the main aspects of the statisticalist debate (Sect. 2), and situate the problem of developmental biases with respect to it (Sect. 3). Then, I show that ultimate explanations make reference to developmental biases through the quantitative genetics idea of a phenotypic response to selection (Sect. 4). Finally, I discuss the implications of this for a causal understanding of evolutionary models, and argue that it makes sense to speak of developmental ultimate causes, a distinctive contribution of quantitative genetics and evo-devo to the conceptual foundations of evolution that has not been acknowledged so far (Sect. 5).

2 A primer on the statisticalist debate

Causalism was first vindicated by Sober (1984) through his argument on evolutionary factors being analogous to physical forces. He took natural selection, migration, mutations and genetic drift as forces acting on populations and constituting the “source laws” of evolutionary change (Sober, 1984). Source laws are to be found in theoretical ecology, which explains the ecological interactions giving rise to natural selection and drift, and—to a lesser degree for Sober—in the laws of genetic transmission, explaining the occurrence and inheritance of mutations. In this picture, the models of population dynamics are “consequence laws”, i.e., those that describe the system when forces are applied to it, predicting the dynamics of populations once ecological and heritable factors are considered.

Although it is not the main current causalist position, the forces analogy first made explicit the idea that population dynamics models represent the causes of evolution. This is what the causalists/statisticalists debate has considered for more than 20 years now: how much of actual causes of evolutionary change—“source laws” in Sober’s terms—is in the theoretical framework sustaining evolutionary predictive models—Sober’s “consequence laws”. From the point of view of the EES debate, the dispute concerns whether there are ultimate causes that populational models refer to (cf. Laland et al., 2011).

To be sure, the mathematical apparatus of population dynamics is statistical. Its models predict changes via statistical tools and probabilistic measures. Causalists about these models are not alien to this fact, but they consider that the statistical measures in the models are derived from knowledge about causal factors of evolutionary change, be them natural selection, drift, mutations or migration, and thus represent those causal factors. For instance, they regard the growth ratio of a particular allele to be a measure derived from knowledge about the differential reproduction of organisms bearing that allele in a particular population. From this perspective, the abstract quantities in the models can be associated with causal factors of evolution because of the theoretical framework surrounding the models; in the case of such a growth ratio, it is associated with the natural selection for the trait. Causalists would regard this episode of natural selection as a causal process acting at the population level—and thus as an ultimate cause—because it refers to fitness differences within a population, regardless of the fact that these may be grounded on individual-level properties.

Some causalist advocates have claimed that the mathematical notions of population dynamics models represent causes by virtue of their derivation from a causal principle (Rosenberg & Bouchard, 2005). The idea behind it is that the mathematical apparatus of population dynamics, represented in Fisher’s fundamental theorem, is derived from the Principle of Natural Selection (see Brandon, 1990) as described by Darwin:

“when we consider the Darwinian assumptions, about selection for ecological fitness, from which this [Fisher’s] theorem is derived, its derivative status as a theorem becomes evident” (Rosenberg & Bouchard, 2005, p. 346).

Similarly, other causalists have claimed that what determines the causal nature of the models is their interpretation: it is the interpretative context—including the original purpose for which they were built—of a mathematical construction that assigns any meaning to it (Millstein et al., 2009). This position recognizes a pragmatic relationship between the ecological bases of evolution and the mathematical components of the models of population dynamics, since these intend to—and were built to—explain changes caused by ecological interactions. Finally, some causalists have argued that no particular explanation or prediction can be derived from the statistical models of evolution without introducing causal assumptions about the populations to which they apply (Otsuka, 2016). In particular, the models could not work without assuming that they are considering the ecological causes of population changes: no predictive value could be attributed to them if the statistical measures they employed contained no causal information about the populations they apply to.

In these positions, the predictive notions of fitness and drift in evolutionary models indirectly refer to causal ecological interactions: the theoretical, historical, or pragmatic context of these models grant their causal content. As a consequence of this context, the models are considered to represent ultimate causes. Let us see an example. The higher survival and reproductive capacity of white rabbits in snowy environments is a causal ecological process: there are ecological pressures (such as being seen less by predators) causing the higher rate of reproduction of white rabbits. For causalists, an evolutionary model predicting the increase in frequency of white fur in such a population through assigning a higher fitness value to the trait is indirectly referring to such an ecological process. Even if the notion of fitness involved in the model only refers directly to the growth ratio of the white fur trait, it indirectly refers (because of how the model was derived or because of how it is used or interpreted) to the higher ecological capacity to survive and reproduce of white rabbits in that population.

A statistical interpretation of evolutionary models has rivalized this view for two decades. Statisticalism was first introduced in Matthen and Ariew (2002) and Walsh et al. (2002) as a response to Sober’s (1984) forces analogy. Its advocates argue that the models of population dynamics do not represent the causal processes that Darwin described in his works, which rather referred to ecological processes. For them, the notions involved in dynamical explanations are way too abstract to qualify for real causal factors. For instance, when predicting that the frequency of white fur will increase in the next generation of rabbits, a population dynamics model will consider the fitness mean and variance of white fur in the population, both statistical measures that, according to statisticalists, do not demand any causal knowledge about the composition and dynamics of the particular rabbit population under consideration. Following Fisher’s (1930) seminal work, they suggest that a better analogy than the theory of forces for the role of population dynamics models is that of the statistical models of thermodynamics. This way, models represent probabilistic trends that emerge at the population level, where no real causes are acting, and merely describe the consequences of a statistical property, namely variation in fitness.

A crucial point for this position is the distinction between fitness in the Darwinian sense—what they call “vernacular fitness”—, and fitness as a predictive measure (Matthen & Ariew, 2002). “Predictive fitness” is an abstract property of types of individuals and refers to the population level, whereas Darwin alluded to a causally efficacious property of particular individuals, “vernacular fitness”, which refers to an ecological property. The way in which these two notions of fitness relate to each other, statisticalists argue, involves considering non-selective and non-causal populational factors, implying that predictive (population dynamics) fitness is not strictly speaking derived from vernacular (ecological) fitness. While one could depict a “fundamental” type of causation acting at the level of ecological interactions, where vernacular fitness would surely play a causal role (Mathen & Ariew, 2002), and could be seen as a propensity (Walsh et al., 2017), the processes described by population dynamics models do not reflect such causal interactions: they are stochastic or probabilistic models instead.

This implies that, for statisticalists, ecological studies are needed to get a causal understanding of evolution, and particularly selection. Indeed, some statisticalists believe that areas such as evolutionary ecology, in studying the ecological processes underlying fitness differences, provide “causal studies of selection”, in opposition to what they call the “selection models” of population dynamics, which, in their view, simply assign a predictive fitness value (Walsh et al., 2017). In turn, these theoreticians consider that evolution, even if it can be explained in ultimate, population-level terms such as selection, drift or migrations, is not really caused by those factors (Ariew, 2003). Population dynamics explanations do not incorporate source laws (cf. Sober, 1984), but they abstract away from causes to build predictive models.

In sum, the statisticalist debate concerns whether the “ecological causal story” underlying evolution is captured by the population dynamics notions of selection and drift. But as the appreciation about the role of evolutionary ecology suggests, the debate could be relevant for discussing how the different branches of evolutionary biology, understood in a broader sense, relate to one another. In particular, some EES discussions over the need for ecological and developmental notions such as niche construction and developmental biases for understanding evolution could benefit from considerations about the causal or non-causal nature of populational models. In this sense, the philosophical tools of this debate (e.g., different modes of conceiving of representing evolutionary causes in predictive models, or the separation between causal and statistical understandings of dispositional notions such as fitness) might be relevant for addressing evolutionary causation beyond selection and drift in population dynamics models. That is what the remainder of this paper is about.

3 Developmental biases and ultimate causes

3.1 Bridging the statisticalist and the extended synthesis debates

As mentioned in the introduction, much of the EES debate concerns what causes shall be considered in evolutionary explanations. Many EES proponents argue that classical population dynamics explanations fall short in accounting for the causes of evolutionary change because of their failure to give organismal processes the explanatory role they deserve in evolution. The idea that proximate, organismal causes have evolutionary effects has been conceptualized as “reciprocal causation” in the EES literature (Laland et al., 2011; Müller, 2021). This notion intends to challenge the separation between proximate and ultimate processes by pointing out that they shape one another in non-trivial ways. The case of niche construction is paradigmatic, where EES defenders state that organisms, in building their own ecological niches, change the very selective pressures they are subject to.

As Hazelwood (2023) argues, however, the relation between organismal niche construction and selection is one of composition rather than reciprocal causation, since the changes that organisms make to their own environments are part of natural selection, and not different from it. Similarly, Ramsey and Aaby (2022) have recently argued that these two levels of causation are part of the same complex causal nexus, where populational properties structure possibilities and organismal ones trigger particular evolutionary outcomes. These recent proposals seem to entail that proximate causes are in fact components of ultimate causes, making sense out of both causalism and the vindications of EES supporters. From this causalist point of view, the models of the Modern Synthesis need not be “extended” in order to account for the causes of evolution, at least when it comes to selection and drift, since they already make reference to causal factors. An extension might nonetheless provide a different kind of causal content—mostly lower-level—to evolutionary explanations.

The natural fit for reciprocal causation supporters, however, is statisticalism. As Walsh (2022) argues, reciprocal causation refers to the feedback loop between organisms and their environments—not selection—in shaping evolution. Thus, the reciprocal causation supporter does not point at an iterative cycle of proximate and ultimate causes, but at the fact that proximate causes have evolutionary effects, and thus that the separation between proximate and ultimate causes doesn’t really hold (Walsh, 2022). EES proponents have thus one interesting feature in common with statisticalists: both approaches regard that the population dynamics view of evolution cannot grasp the real causes of evolutionary change, which they pose at the organismal level.²

Let us pause here for a moment to consider what this means for population-level causes. None of these discussions seem to concern explanatory capacity, since both statisticalists (Ariew, 2003) and EES supporters (Scholl & Pigliucci, 2015) have acknowledged that the proximate-ultimate distinction, even if ontologically wrong from their viewpoint, has explanatory value. I suspect, however, that they are not strictly speaking disputes over levels of causation either, which causalists would likely “win” given many recent views on higher-level causation (e.g., Strevens, 2018; Woodward, 2010)—and given the intertwined relationship between causation and explanation (Ross & Woodward, 2023).³ In a minimal sense, differences in fitness within a population can be safely said to be a cause of evolutionary change in such a population, even if very abstractly, regardless of the position one takes in these debates. What the disputes are about, I believe, is whether population dynamics models capture such a process in their explanations. In other words, it is about whether higher-level causes are ultimate causes, in the sense of causes that explain evolutionary changes by referring to the relevant causal components.

For the purposes of this paper, I will consider, with causalists, that proximate causes can be component parts of causes acting at the level of populations. Thus, I align with Hazelwood (2023) and with Ramsey and Aaby (2022) in that organismal causal properties are necessarily connected to ultimate causes. What I will regard as contentious is in what sense population dynamics models make reference to these ultimate causes (rather than just to abstract properties of populations, as statisticalists hold), as well as how much of that reference is grounded on causal knowledge about organismal properties.⁴ This, of course, touches upon the connections between theoretical population dynamics and other evolutionary areas with an organismal inclination. In the case of developmental biases, it concerns the connections between these models and evo-devo. Thus the main interrogations of this paper can be formulated in the following way: Which population-level causes, if any, do developmental biases pertain to? And, are these causes represented in population dynamics models?

3.2 Whence development?

To address these questions, we need to get a better grasp of what developmental biases are and what is the approach taken in evo-devo to study them. Evo-devo studies the impact of evolution in development as well as the impact of development in evolution, and thus has been portrayed as yet another example of reciprocal causation (Müller, 2021), or of a field where proximate causes have ultimate effects (Brown, 2021). The recent works on the ultimate/proximate distinction indeed point out at development as part of the proximate causes considered, together with ecological ones, to be important for natural selection:

“a behavioral innovation (a case of constructive development) ... introduces novel variation ... [which] structures the action of selection” (Ramsey & Aaby, 2022, p. 31. Stress in original)

“the process of natural selection is composed of ecological and developmental processes such as niche construction” (Hazelwood, 2023, p. 25)

In these examples, development is emphasized as composing or intervening on the process of selection. In particular, these works take development as a crucial organismal component determining variation in fitness. Fitness differences within a population can indeed be strongly dependent on developmental processes such as phenotypic and behavioral plasticity. In these phenomena, developmental properties are responsible for non-genetic variation at the ecological level. As such, they realize evolutionarily relevant ecological processes. If we think once again in Sober’s (1984) terms of source laws, we could say that these developmental processes pertain to the domain of theoretical ecology, which studies the source laws or causal bases of fitness differences, and thus of selection. Here, variation in fitness is the relevant population-level causal property that developmental properties ground. This variation in fitness is a population-level cause of evolution by natural selection.

However, the classical vindication about developmental biases in evolution from evo-devo supporters concerns a different evolutionary component: phenotypic variation. An important source of criticism to the Modern Synthesis view of evolution is its adaptationist bias, namely the assumption that adaptation is the main explanandum of evolutionary biology, and therefore that its main explanatory notion is selection (see Huneman, 2017). Evo-devo defines itself as the study of the evolution of organismal form, rather than adaptations (Müller, 2007), and as such it is interested in phenotypic change beyond fitness differences. In particular, evo-devo concerns the nature and origin of phenotypic variation, including biases in phenotypic dimensions that are prior to and independent from their impact in fitness (Nuño de la Rosa & Villegas, 2022). For example, developmental biases can make a specific neutral change in a trait way more likely than a different one just because of the nature of the developmental processes generating the trait.

The different research agendas composing evo-devo address distinct problems and questions that go beyond the umbrella of classical population dynamics explanations (Love, 2017). With respect to phenotypic variation, studying the interplay between evolution and development has enlarged our understanding of how phenotypic changes and novelties can arise in reproduction. In particular, there are two specific questions beyond the scope of the classical picture that evo-devo addresses. On the one hand, it studies changes in developmental mechanisms throughout evolutionary time, exploring the mechanistic bases of the generation of variants. This provides a distinct type of explanation beyond the ultimate and proximate: lineage explanations (Calcott, 2009).

A lineage explanation is a set of mechanistic models that intend to represent the different stages that a specific mechanism may have undergone in evolution. Such models are linked through a continuity requirement, meaning that they are similar enough so that a small change in one could generate the next one. An example is the different stages the limb bud underwent in the fin to limb transition. The details of this specific developmental mechanism “and how it changed over time” in evolution (Calcott, 2009, p. 52) are considered to explain the developmental bases of such an evolutionary transition. In cases like this, the properties of developmental mechanisms are proximate causes that change over evolutionary time, mediating in their own historical transformation. Most comparative and phylogenetic studies of development exemplify this first evo-devo approach in as much as they concern which specific aspects of developmental mechanisms have undergone changes in evolution to generate phenotypic variation.

On the other hand, evo-devo studies the structure and evolution of the relation between genes and phenotypes through the genotype-phenotype map (hereafter, GPM). GPMs are an abstraction of developmental processes that associates phenotypes to genotypes, accounting for the way phenotypes change over genotypic changes and thus for developmental biases. These maps are modeling tools that abstract away from the specificities of the developmental mechanisms actually connecting genes and phenotypes, and thus allow for explanations with a different scope than lineage explanations. Although perhaps less consensually, these explanations have also been considered to be of a distinct type, labeled as evolvability-based explanations (Brown, 2014),⁵ or understood as an intersection between lineage and populational explanations (Sterelny, 2011). These explanations also account for the emergence of variants, but they do so by studying the biases development imposes on the production of phenotypes in populations (Müller, 2007) and its general variational tendencies (Wagner, 2014). The idea is that one can use these maps to study how likely certain phenotypic changes are given the developmental structure of the trait and the mutational and environmental inputs it may receive.

Developmental systems differ in the way they can generate phenotypic variation under such inputs, and their tendencies can be associated with general properties of the GMPs representing them. Some systems tend to retain their phenotype under mutational perturbations, represented in a mutationally robust GPM that maps many genotypic variants to the same phenotypic outcome (de Visser et al., 2003). Contrarily, other maps are very variable, associating different phenotypic variants to genotypic changes (Wagner & Altenberg 1996). Some GPMs represent plastic developmental systems, meaning that they map the same genetic variant to different phenotypic variants depending on the environmental background (DeWitt & Scheiner, 2004). Finally, some GPMs are modular, in the sense that they are composed of traits that vary relatively independently from one another (Wagner et al., 2007).

This study of structural properties of the GPM is a central focus in the research agenda of developmental evolution, or devo-evo (Pavličev, 2021; Wagner et al., 2000). While much of the evo-devo agenda focuses on lineage explanations, developmental evolution is a specific branch within it that focuses on the impact of developmental biases at the population level, including its long-term, macroevolutionary effects. Interestingly, part of this agenda precisely intends to build conceptual and methodological bridges between a developmental approach and the classical understanding of evolution as a statistical theory capable of predicting changes based on the properties of populations. In other words, one of its purposes is to integrate the study of the GPM (thus the study of structural properties of development) with population dynamics models in order to provide the latter with a much wider scope of application and greater generalizability (Pavličev, 2021).

For doing so, it uses the modeling tools of quantitative genetic theory, a branch grown out of classical population dynamics theoretical models that deals with statistical representations of GPMs at the population level. Thus, it provides population-level statistical tools for the study of developmental biases in phenotypes,⁶ independently of the developmental contribution to fitness differences. Therefore, instead of focusing on the developmental bases of fitness differences, which some recent works have rightly acknowledged (Hazelwood, 2023; Ramsey & Aaby, 2022; Walsh, 2019), inquiring about the role of developmental biases in ultimate causes demands wondering about the developmental bases of variational tendencies as they appear in quantitative genetics explanations. To this I turn in the next section.

4 Variational explanations

4.1 Variational tendencies in quantitative genetics

Population dynamics mathematical models can be divided into population genetics and quantitative genetics ones. At the time of the Modern Synthesis, only the models of population genetics were fully articulated. They describe the genetic composition of a given population (with respect to a particular genetic locus) in order to predict the fixation of alleles based on their fitness values and the population structure. Since they identify evolution with change in the frequency of alleles in a population, they concern the study of extant genetic variants. These are the models that the EES debate associates with the “Modern Synthesis” view of evolution, and they are also the ones typically considered, even if tacitly, in the statisticalist debate. The models of quantitative genetics, by contrast, consider the phenotypic level and the way it varies. Instead of describing the genetic composition of a given population, they describe its phenotypic composition with respect to a given quantitative (that is, numerically measurable) trait. They were fully articulated when empirical grounds for measuring the strength of natural selection in populations were established (Lande & Arnold, 1983), and they predict phenotypic changes in response to such selection in the form of a change in the mean value of a quantitative character. For example, quantitative models can predict a decrease in the average size in a population through the iterative selection of smaller individuals.

For predicting phenotypic changes, quantitative genetics models incorporate a statistical consideration of the GPM that is of interest to some variational aspects under the scope of evo-devo. In quantitative genetics, GPMs are statistical tools representing the patterns of correlation of specific evolutionary events (Hansen, 2008). Quantitative geneticists identify a phenotypic trait in a given population, and from measures of extant variants of the trait they define its mean value and variance. Phenotypic variances (V_P) and genetic variance-covariance matrices (G-Matrices) are the most common representation of GPMs in these models. The former is a statistical measure of how much deviation from the mean a certain trait shows in the population. It is typically divided into the genetic variance (V_G) and the environmental variance (V_E), which represent how much of this diversity is attributed to genetic effects and to the environment, respectively:

$${\text{V}}_{{\text{P}}} = {\text{ V}}_{{\text{G}}} + {\text{ V}}_{{\text{E}}}$$

Additionally, the genetic variance can be divided into several components, of which the most important for quantitative genetics is the additive variance (V_A), representing how much of the genetic-based variation is attributed to the additive effects of genes.⁷ To this standard characterization, we may include a stochastic factor in the variance due to developmental noise (V_error), and a gene-environment interaction component (V_G×E), which refers to variation that depends on specific environment-dependent individual developmental properties. A more complete characterization of the phenotypic variance of a trait is thus (DeWitt & Scheiner, 2004):

$${\text{V}}_{{\text{P}}} = {\text{ V}}_{{\text{G}}} + {\text{ V}}_{{\text{E}}} + {\text{ V}}_{{{\text{G}} \times {\text{E}}}} + {\text{ V}}_{{{\text{error}}}}$$

This statistical characterization of variation within traits enables to establish a quantitative measure of variational properties at the population level. As introduced in the previous section, variational properties—variability, robustness, plasticity and modularity—are involved in evolvability-based explanations, and they refer to the properties of biological systems responsible for non-selective biases in phenotypic changes.

The ratio of additive genotypic variance (V_A) over phenotypic variance (V_P) of a trait is called its heritability, which is typically used to estimate the capacity of the trait to respond to selection, that is, to change its mean value in the direction of selection, and can be considered a proxy for its variability under certain circumstances. Mutational robustness can be seen as the weak correlation between the genetic variance (V_G) of a phenotype and its phenotypic variance (V_P), namely the low impact of genotypic variation in phenotypic variation. On the other hand, phenotypic plasticity can be understood as the gene–environment interaction component (V_G×E) combined with the environmental component (V_E) of the phenotypic variance (DeWitt & Scheiner, 2004). The distinction between V_E and V_G×E reflects the difference between those systematic effects of environmental variance in a population (V_E) and the effect of specific genotype–environment interaction in different individuals, thus of differences in plasticity across individuals (V_G×E).

Variational modularity, by contrast, cannot be associated with a component of the variance of one trait. Rather, it is related to patterns of covariation among at least two traits. For considering relations among traits in their response to selection, quantitative geneticists make use of the G-Matrix, which is an estimate of the genetic correlations among the traits. In the statistical approach to variation, the G-Matrix serves for estimating modularity: the more independent the variance of a trait is with respect to variation in other traits, the higher modularity it shows with respect to it.

It is important to stress that these properties are not subsumed by selection (or drift) but rather codetermine phenotypic changes in combination with it. In quantitative genetics, the result of an episode of selection is given both by the selective gradient and the variational properties of the phenotype under study as represented in statistical GPMs (Hansen, 2023). While the selective gradient refers to fitness differences between quantitative values of the phenotype, the statistical GPM provides the variational properties determining the phenotypic response to selection, namely the way phenotypic properties change given an episode of selection. This response is not only determined by what is selected and inherited, but also, and importantly, by how the recombination of alleles (and mutations) give rise to quantitative changes in the selected and inherited traits.

This adds one layer to the discussions over evolutionary causes that is relevant for the statisticalist debate. This debate has mostly focused on population genetics models, where selection, drift, mutations, and migrations are arguably enough factors to consider. In such a framework, genes map directly to fitness values, and thus the only additional information needed to predict evolution is how genes are inherited and how that affects their fitness values. In quantitative genetics, in contrast, it is quantitative phenotypic values that map to fitness (e.g., the length or width of a particular body part). Predicting changes in phenotypes demands an additional component, namely how genotypic changes map to these phenotypic values. This is given by the statistical GPM as sketched above, and particularly by the G-Matrix when more than one trait is considered:

“The G-Matrix determines how much the selection response is deflected from the selection gradient, how easy it is to evolve in different directions in morphospace” (Hansen, 2023, p. 82)

The allusion to morphospace is key here; selection and drift can move the population only in the morphological dimensions allowed by the variational properties of traits. For example, a strong selective pressure towards long fur will only generate even longer fur than already present in the population if there is enough additive genetic variance in fur length. The variational properties, in turn, codetermine the effects of selection in populations (compare: just the selected length vs new length values in the direction of selection). The statistical GPM is therefore a distinct component determining the phenotypic direction of evolutionary change. Such a distinct component is also a distinct explanatory factor in the models, in the sense of being independent of other explanatory factors such as selection or mutational inputs. This component, I suggest, provides variational explanations of evolutionary change.

Phenotypic variances and patterns of covariation are properties of populations, and it is as such that they confer an explanation of phenotypic evolutionary changes. Therefore, they shall count as ultimate explanatory factors within quantitative genetics. The key point of their ultimate nature is that these variational explanatory factors are based on deviations from phenotypic means and from trait associations. Thus it is populational differences in genotype-phenotype connections (thus in developmental properties) that make the explanatory work, just like differences in fitness are explanatory of selection episodes at the population level. These ultimate explanations regard the impact of developmental biases in phenotypic evolution, and not the impact of fitness differences.

4.2 The developmental causal story behind variation

The statistical characterization above estimates variational potential from extant phenotypic variation within a given population. Genes in quantitative genetics are abstractions based on the average deviation from the mean phenotypic value of organisms carrying them, and they are assumed to combine additively, namely to add their quantitative effects to the effects of other genes without restriction. When statistical approximations of this type are used in microevolutionary studies, the developmental interactions among genes are completely abstracted away, assuming that the extant pattern of additivity and correlation provides enough information about short-term future patterns. These estimations are successfully used for short-term predictions because the patterns of additive genetic variances and covariances can be very stable locally (Lande, 1979; see Hansen, 2008).⁸

It is not straightforward what the causal basis of statistical variational properties, or of patterns of additivity and covariation, could be. At first sight, these properties differ from the “vernacular fitness” of statisticalists in the sense of not being a propensity or causal property of organisms. It seems closer to what they call “predictive” fitness. Just like growth ratios, variational parameters are statistical, meaning that they are only predicated on a population of individuals (e.g., only a population exhibits variance in a trait). But what is the source of these populational patterns of additivity and covariation that ground the robustness, variability, plasticity and modularity of phenotypes? Theoreticians attribute these properties to the “genetic architecture” underlying traits, namely “the pattern of genetic effects that build and control a given phenotypic character and its variational properties”, including “patterns of pleiotropy... and epistasis” (Hansen, 2006, p. 124). That is, complex gene-to-phenotype relations. There is an “obvious complexity” of developmental processes underlying genetic architecture (ídem), responsible for variational properties in a causal, rather than statistical, sense. In other words, there is some developmental causal story that relates to the statistical patterns represented in quantitative genetics models. This “vernacular” sense shall be found in turn in the developmental properties of organisms, just like ecological propensities of organisms are the vernacular sense of fitness differences in models of selection and drift. In turn, the complexities of organismal development provide the causal story behind variational patterns.

Evo-devo has long been concerned with this developmental causal story behind phenotypic change in evolution. As mentioned in Sect. 3.2, much of its research has been devoted to depicting changes in developmental mechanisms responsible for particular evolutionary changes in phenotypes, such as changes in the patterns of gene expression and cell proliferation that underpinned the fin-to-limb transition (Wagner, 2014). In a way, this is similar to how an ecological mechanism is part of the causal story of a particular selective regime: developmental mechanisms are part of the causal story behind the generation of variation. As such, this evo-devo approach can be conceived as a depiction of the “developmental causal story” behind these processes within the evolutionary framework. In this sense, evo-devo can be regarded as analogous to fields such as eco-evolutionary dynamics or niche construction theory with regards to the demanding of causal completeness when it comes to evolutionary models and explanations. That is, as mechanistic explanations of the parameters found in population dynamics models. However, notice that these explanations are not subsumable under the same category with respect to their evolutionary impact. On the contrary, the developmental causal story determining the generation of variants is not a lower-level component of selection itself, but of the phenotypic changes that occur when selection takes place. If we use Sober’s (1984) terms, this developmental causal story concerns the laws of transmission of characters rather than the laws of theoretical ecology (see Sect. 2).⁹

Given this situation, I agree with Vidya and colleagues (2023) in that it is quite surprising that the field of quantitative genetics doesn’t typically appear in EES discussions.¹⁰ As they argue, it might well be that the “genetics” label has obscured the fact that quantitative genetics mathematical tools make no assumptions about the type of inheritance responsible for the transmission of phenotypic traits (which could be, i.e., epigenetic), leading to an association between quantitative genetics and the genetic reductionism that EES supporters are so critical about (Vidya et al., 2023). In this regard, they notice that quantitative genetics models can make reference to developmental properties, although they still subsume this impact of development under selection “broadly conceptualized” (Vidya et al., 2023, p. 311).¹¹ As I’ve argued, nonetheless, these properties are a distinct explanatory factor, and should be considered as part of a population’s phenotypic response to selection rather than to any broad understanding of selection itself. Being explicit about the distinctiveness of quantitative genetics in EES discussions should, I believe, open up the discussion about the causal representation of developmental biases in population dynamics models. The last section of this paper discusses this with further tools of the statisticalist debate.

5 Towards variational causalism: developmental ultimate causes

Do statistical GPMs represent the causal story behind developmental biases (causalism) or do they abstract away from it (statisticalism)? A position a statisticalist could take is that the response to selection that G-Matrices predict is just as epiphenomenon as selection itself. Philosopher Massimo Pigliucci indeed made a compelling argument challenging the quantitative genetics research program based on the statistical nature of the G-Matrix (Pigliucci, 2006). On the one hand, he contended that G-Matrices don’t serve as tools for inferring the genetic architecture, or the developmental causal story, underlying traits, which, according to him, means that they fail in delivering what they are supposed to. This is nonetheless doubtful, since G-Matrices are not intended to explain the genetic architecture of traits, but to explain and predict its effects in evolution. Thus they could in principle represent a causal factor (developmental biases) without representing at the same time a fine-grained description or a causal explanation of such a factor (genetic architecture). On the other hand, he pointed out that G-Matrices are local and thus don’t serve for long-term evolutionary predictions. This is in fact a fair criticism, but one that can be extended to selection in these models (and population genetics ones) as well: without a comprehension of how the fitness landscape evolves, selection won’t be able to predict long-term evolution. Similarly, without a comprehension of how G-Matrices evolve, variational properties won’t be able to make long-term predictions (Hansen, 2008; Pavličev, 2021). Thus, just as it is the case with selection and drift, perhaps the relevant thing to consider is whether the statistical GPMs of quantitative genetics make indirect reference to causal knowledge about development, rather than whether that causal knowledge is fine-grained or predictive enough in the long term.

Quantitative genetics explanations surely don’t consider developmental mechanisms, just like they don’t consider specific ecological mechanisms either (Villegas 2024). In the case of selection and drift, causalists typically refer to the ecological notion of fitness as a way to incorporate the evolutionarily relevant causal aspects of ecology that are not identifiable with concrete mechanisms (Millstein, 2006; Pence & Ramsey, 2013; Rosenberg & Bouchard, 2005; Sober, 2001). Fitness is often understood as a probabilistic disposition or propensity, which in its most general sense means that it is a causal property of organisms or traits responsible for their tendencies to survive and reproduce. Thus the relevant question is whether something analogous to fitness plays any role in the theoretical framework of quantitative genetics for variational properties.

The natural fit for this request is the devo-evo understanding of variational tendencies (Wagner, 2014), which can be seen as the “causal study” (cf. Walsh et al., 2017) of these properties.¹² As discussed in Sect. 3.2, the GPM in devo-evo is understood as representational of the developmental process (Pavličev et al., 2023). Within this view, GPMs are abstract representations of how genetic and environmental factors shape the developmental process for generating distinct phenotypic outputs, and not merely statistical summaries. A variational tendency such as modularity can be found in devo-evo GPMs, rather than as a specific pattern of covariation in a population, as a structural property representing the dynamical process generating phenotypes (Wagner et al., 2007).

For example, developmental models can account for the level of modularity between mammal teeth (Kavanagh et al., 2007) or vertebrate digits (Lange et al., 2018). Such models consider the dynamical generation of traits through gene expression patterns as well as cell and tissue level interactions, and serve for exploring the way in which different genotypic and environmental inputs map into phenotypic variation within and across populations. Although their bases are mechanistic, they are not meant to account for specific mechanistic changes in evolutionary transitions but for the variational tendencies of such mechanisms that explain patterns of phenotypic variation within a single genotype-phenotype logic. In the mammal teeth case, one developmental mechanism explains size and morphological relationships across molars, thus predicting low variational modularity for individual teeth, that is, low independence in their patterns of variation (Kavanagh et al., 2007).

Within the devo-evo agenda, variational tendencies can be said to represent the vernacular sense of variational properties, similarly to how ecological properties represent the vernacular sense of fitness. Indeed, it is typical to find allusions to variational properties as propensities of developmental systems (Müller, 2007; Salazar-Ciudad, 2007; Wagner, 2014), meaning that they are considered a causal aspect of the developmental process. Philosophers have indeed pointed out that it is the evolutionary dispositions (Austin & Nuño de la Rosa, 2021; Brigandt, 2015), or propensities (Nuño de la Rosa & Villegas, 2022) of development that play a crucial explanatory role in accounting for the way variation is generated.

Is tacit knowledge of devo-evo propensities part of the theoretical framework of quantitative genetics? Let us recall that causalism has been defended either by pointing at the historical derivation of properties from causal principles (Rosenberg & Bouchard, 2005), by regarding the pragmatic context as granting a causal interpretation of such properties (Millstein et al., 2009), or by considering their application in predictions to demand causal assumptions (Otsuka, 2016). One first difficulty to notice is that, unlike the case of the principle of natural selection, the historical derivation of variational components in population dynamics models does not seem to reflect an inference from causal principles at first sight. The point made by Rosenberg and Bouchard about these models is that their mathematical structure, particularly Fisher’s theorem, is derived from Darwinian ecological principles (Rosenberg & Bouchard, 2005). It is not clear how this would apply to the statistical measures of variation in quantitative genetics models. They too are related to Fisher’s fundamental theorem, but it makes no sense to defend that developmental knowledge is derived from ecological one. On the other hand, it is well-known that Darwin alluded to the “laws of correlation of growth” (Darwin, 1859)—which he regarded as mysterious—to refer to the developmental connections between traits biasing variation. The classical works of quantitative geneticists about the response to selection do make reference to ontogenetic connections of traits (e.g., Lande & Arnold, 1983), but it is unclear to what extent the mathematical apparatus is “derived” from any causal principle about development beyond the quite obvious fact—though perhaps not so obvious at the time—that developmental interactions generate correlations in phenotypic changes.

This apparent lack of causal developmental principles may be partially due to the fact that, from the philosophical perspective of the classical view of evolution, developmental biases don’t qualify as causes of evolutionary change. As we have seen, evolutionary causes are typically restrained to selection, drift, mutations and migration. Variational properties, if considered, usually take instead the form of stable parameters of the models that account for how a given population reacts to a cause of evolutionary change. In other words, mutations, drift or selection transform populations following the possibilities established by the parameters of the models, which can include some statistical version of their variational properties. This canonical view parallels Sober’s (1984) forces analogy in considering populations as recipients of external forces.¹³ If there is one fundamental lesson to be learned from reciprocal causation advocates, however, it is that organismal properties compose population-level causal processes (Hazelwood, 2023), making the division between internal and external factors completely meaningless. The reaction of a population to an episode of selection is just as internal—and as external—as the episode of selection itself: both are populational causal processes grounded in organismal properties. Selection is the process whereby variation in fitness biases the representation of a variant from one generation to the other. The phenotypic response to selection is the process whereby variation in developmental properties biases changes in the variant (or even a change of variant) from one generation to the other. They obviously act together, but they are distinct causal components of evolutionary change.

Although the existence of developmental causal knowledge in the historical derivation of variational properties is at least debatable, the truth is that the field of quantitative genetics is progressively moving from a treatment of genetic architecture as background condition to its treatment as biases with “systematic influences on evolutionary dynamics, which [quantitative geneticists] should aim to model and measure” (Hansen, 2006, p. 124), in a broadening of the empirical applicability of its models (Huneman, 2017; see also Okasha, 2021). This finally brings us to the other two ways to argue for variational causalism. The causal character of variational properties can be implied in their empirical application to particular populations (sensu Otsuka, 2016), or in the pragmatic context surrounding quantitative genetics models (sensu Millstein et al., 2009).

Regarding the application of the models and their predictive capacity, more and more empirical studies—both experimental and in the field—model the very evolution of G-Matrices in populations (e.g., Houle et al., 2017), which indeed demands causal knowledge about the population in question (Otsuka, 2016), and particularly about the phenotypic aspects that are relevant for calculating the response to selection of a given trait. Regarding the context surrounding the models, there is a growing area of interaction between theoretical quantitative genetics and developmental evolution (Pavličev, 2021). Although many developmental studies of variational propensities abstract away from population processes, and explore the possibility of variation without considering its potential for fixation, some contemporary models are being integrated in the quantitative genetics framework. These include models of populations of developmental systems predicting changes in their G-Matrices based on changes in their developmental properties (e.g., Milocco & Salazar-Ciudad, 2022), as well as the inclusion of more developmentally-based GPMs in traditionally statistical studies (Pavličev et al., 2023). These inquiries combine the idea of developmental variational propensities with the classical populational approach to evolution, thus pointing at an increasing causal inclusion of the generation of variation into population dynamics modeling.

These remarks, even if modest, make it plain that variational causalism is as legitimate a philosophical position as causalism about selection. From this perspective, the variances and covariances of quantitative genetics models refer to the causal aspect of variational causes at the level of populations just as much as selection and drift refer to the causal aspect of differences in ecological fitness for causalists. For example, the correlation patterns between two traits in a population can be considered as indirectly representing the modular developmental structure of those traits and how small variations in it are distributed in the population.¹⁴ These patterns would represent ultimate developmental causes, or variational propensities, acting at the population level. Even if these causes are realized at a lower level by proximate, individual properties, their causal impact on the evolutionary composition of the population is, in many cases, indirectly represented in statistical GPMs and G-Matrices.

6 Concluding remarks

The preliminary application of the statisticalist debate tools to the problem of developmental biases brings up the idea of developmental properties as ultimate causes, that is, as causes acting at the population level changing their phenotypic composition. I hope my argument was convincing that the evolutionary causal factors grounding developmental biases are not entirely subsumable under the more widely accepted idea of an ecological ultimate cause such as selection. As I have argued, the evolutionary developmental properties of populations do not only ground differential survival and reproduction—which they can do through developmental niche construction—but also the phenotypic changes that reproduction itself brings about. Ecological and developmental causes are distinct yet act together to produce phenotypic changes. Our population dynamics models can refer to that interaction at the population level.