Predicting Evolution: The Price Equation and Its Applications
Conference
Königlicher Pferdestall, Hannover
March 1617, 2023
Is the Price Equation a unifying law for generalized Darwinism, or is it an elegant but ultimately misleading abstraction?
This workshop focuses on the role of mathematics and exact prediction in the evolutionary sciences, with the Price Equation as the center of the debate.
(click here for longer description)
Program
March 16
9:15 – 10:15 Victor Luque
10:15 – 11:15 Laurel Fogarty
Coffee Break
11:45 – 12:45 Matthijs van Veelen
Lunch Break
14:30 – 15:30 Karim Baraghith
15:30 – 16:30 Lorenzo Baravalle
16:30 – 17:30 Ozan Altinok and Stephen Mann
Conference Dinner (Kaiser)
March 17
9:30 – 10:30 Philippe Huneman
10:30 – 11:30 Tim Lewens
Coffee break
12:00 – 13:00 Hugh Desmond
Description of Theme
The muchquoted phrase "the unreasonable effectiveness of mathematics" was one originally made by a physicist  not a biologist. Even in areas of biology where mathematical modelling is common and established, such as in evolutionary biology, such models cannot be used to generate nearly the same accuracy of prediction as in many areas of physics. What is the methodological or explanation function of mathematical (and in general, formal) models in evolutionary sciences?
This issue comes to the fore concerning the Price Equation, the main topic of this workshop. The Price Equation (PE) is a dynamical equation, putting the future change in average trait of a population in terms of present (statistical) properties of the population. Some see the PE as a fundamental ‘law’ of evolution, with an explanatory and predictive status that is perhaps not identical but at least comparable to that of laws in physics. The PE has been used widely as a basis for mathematical models in behavioral ecology. Additional hopes have been pinned on the PE as a means to unify the diverse Darwinian approaches in the social and psychological sciences.
However, strictly speaking the PE is mathematical tautology and only has some predictive power in very idealised conditions. For these and other reasons, others remain skeptical. Skeptical stances on the PE range from categorising it as an elegant heuristic (but not fundamentally explanatory), to deeming it an obstacle to scientific progress when scientists forget the limiting conditions of the PE and overapply it.
Is the PE potentially a unifying law for generalized Darwinism, or is it an elegant but ultimately misleading abstraction? This workshop focuses on specific issues regarding the PE, as well as on more general issues regarding the role of mathematics and exact prediction in the evolutionary sciences.
Questions include the following:

Can the PE be meaningfully applied to areas of research outside biology? What are the conditions of applicability?

To what extent does PE presuppose factors such as reproduction or selection? Can the PE be applied to systems without reproduction or selection occurring?

What predictions does the PE generate in evolutionary biology? What predictions could it generate outside of biology?

How should the idealized and mathematical nature of the PE be understood: does it increase empirical predictiveness, such as Galileo’s frictionless inclined plane? Or does its mathematical exactness come at the expense of empirical predictiveness?

If the PE can be interpreted causally, as decomposing change over time as being caused by certain “forces” like natural selection, drift, or meiotic drive, to what extent can generalized applications of the PE to cultural evolution also be interpreted causally?
Abstracts
Social Asymmetries and the Cultural Price Equation: A Problem for the Concept of Cultural Fitness?
Karim Baraghith
In this talk, I will address a particular problem that might occur within the research program of cultural evolutionary theory (CET), which I call the “fitness issue of social asymmetries”. The starting point is that CET leaves some crucial aspects of culture and society unexplained. ‘Power’, understood as a social asymmetry, is one such aspect. CET mostly focused on ’prestige’ or prestige bias in this context but other important facets of cultural/social power asymmetries are coercion, force, or dominance. These latter forms of power seem to reverse the logic behind the concept of cultural fitness: dominant individuals, unlike prestigious ones, are not imitated more frequently, which means that neither their cultural strategies/variants, nor the individuals themselves will probably ever reach high frequency in a cultural population. From a classical population dynamical approach, such a phenomenon is hardly explainable. In this talk, I am going two ask two questions: First, could the Price equation, applied to cultural evolution, make more sense of this issue, i.e. what does the Price equation effectively has to say about the relation “the higher the fitness the higher the frequency”? Second, I will explore whether there are other alternatives to explain social asymmetries within CET. To so, I will talk about different forms of selective strategies (r an K selection) and how they might be related to the topic, as well as cultural niche construction.
Kinematic and Dynamical Aspects of the Price Equation
Lorenzo Baravalle and Victor J. Luque
In a previous article (Luque and Baravalle 2021), we argued for an analogy between (genetic) evolutionary theory and Newtonian mechanics. In this talk, we aim to make this analogy clearer. We think that many disagreements about the empirical content of the Price equation are, to a greater or lesser extent, related to the fact that a certain description that Price provided of evolutionary processes is incorrectly taken as an explanation of such processes. By reconstructing and analysing the phenomenological framework from which the Price equation is derived, we shall argue that this framework supplies the kinematic of evolution. We shall suggest that we can think of this framework – which we call the “Pricean framework” – in analogy to Galilean kinematics. This has two consequences. The first is that the Price equation is not trivial. On the very contrary, the analogy with Galilean kinematics entails that the Price equation identifies an empirical relation between magnitudes, which any evolutionary theory is called on to explain. The second consequence, however, is that the Pricean framework, by itself, lacks of dynamical features; it needs to be complemented by further theoretical assumptions. These assumptions, intended to make explicit the causes of evolutionary change, are not included in the original Pricean framework. Nevertheless, different dynamical laws (e.g., Hamilton’s rule) can be derived from the Pricean formalism, plus additional assumptions, with relative ease. These dynamical laws explain the behaviour described by the Pricean kinematics in specific contexts. Thus, differently from Newtonian mechanics, in evolutionary biology we do not have just one fundamental law of motion (i.e., Newton’s second law), but rather a constellation of laws, grounded on a common framework.
Why Mathematicize Evolutionary Theory?
Hugh Desmond
What is the scientific function of the Price equation (PE)? Need it be predictive? Many functions besides predictiveness have been proposed, ranging from definitional functions (e.g. Gardner, 2020: the PE defines what evolutionary change consists of) to heuristic functions (e.g. Okasha & Otsuka, 2020: the PE can be used to estimate the parameters of causal and predictive models of evolutionary change). Interestingly, Luque and Baravalle argue that direct predictiveness is not an appropriate measure by which to judge the value of fundamental laws of nature, including Newton’s second law (Luque & Baravalle, 2021).
In this paper I argue that a mere heuristic function is insufficient given the mathematical form the PE assumes. The rationale for Galileo to mathematicise physics was to generate exact predictions. Similary, we cannot discount a “positivist view” of the PE (in the style of Hempel & Oppenheim, 1948): the scientific function of the PE, if any, must lie in the scientist being able to use the PE to derive predictions (with auxiliary hypotheses). The PE may in pure form be void of predictive content, but the mathematical apparatus must be indispensable to generate exact predictions. For if mathematicising evolutionary theory does not generate exact predictions, what then is the function? The sociological explanation looms, where evolutionary theory is mathematicised only in order to signal to the wider academic and societal context that it deserves the same epistemic authority as physics.
In this talk I will take the preceding setup to motivate looking at three specific areas of evolutionary research which involve concrete predictions: breeding, pest control, and evolutionary medicine (Blouin et al., 2015; Metcalf et al., 2015; Roderick et al., 2012; Wortel et al., 2023). I will discuss to what extent the PE actually and potentially shape predictions in these areas.
Nongenetic inheritance and niche construction in the Price equation
Laurel Fogarty
The combination of ecosystem engineering and ecological inheritance is often referred to as ‘niche construction’. A central tenet of niche construction theory is that organisms can alter their environments in heritable and evolutionarily relevant ways, often by altering selection pressures. A growing body of theory addresses the evolutionary consequences of such processes most typically in a population genetic framework. However, the physical changes that niche constructors make to their environments might also alter the response of phenotypes to selection by changing breeding values through the introduction of indirect genetic effects, by creating nonzero genotypeenvironment covariance, or by allowing environmental components of phenotype to be heritable. We have previously developed models of trait evolution that examined some effects of niche construction on trait heritability separately from those on selection. We showed that the response of a phenotype to selection can be considerably altered in the presence of niche construction and that this effect is compounded when a small number of transgenerational interactions are considered.
Here, I aim to expand on these models and discuss potential avenues towards the correct formulations of different kinds of ecosystem engineering alongside ecological inheritance in the context of the Price equation.
On the Cultural Price Equation
Tim Lewens
The Price Equation is a powerful, and unusual, tool within evolutionary theory. Because it is completely general in application, and also very nearly free of distorting idealisations, the Price Equation is widely regarded as having exceptional power for understanding evolutionary change. It is no surprise, then, that it has been applied to many different contexts outside of traditional ‘organic’ evolution, including the domain of cultural evolution. In this talk I argue for various ways in which the Price Equation can mislead about cultural evolutionary theory. They all derive from difficulties that processes of cultural reproduction pose for attempts to distinguish ‘selection’ from ‘transmission’. This does not mean the cultural Price Equation is of no use: its value remains as an analytical tool in those circumstances where a distinction between selection and transmission can be drawn without too much distortion.
Price, uncertain and not useful? The Price equation as a mediation between optimisation, causality and statistics.
Philippe Huneman
The Price equation is a description of evolutionary change, purely analytically derived. Since its formulation, it has been used in many occasions to demonstrate some fundamental statements about evolution. Most famously, one derived from it Fisher’s fundamental theorem of natural selection (FTNS); Grafen based on it an attempt to bridge population genetics and behavioral ecology labelled Formal Darwinism; the notion of multilevel selection has been justified by the decomposition Price equation proposes; and the same equation has been used to propose a general description of darwinian evolution beyond genes. Paradoxically, while Price equation itself can be seen as analytically true and thus undisputable, all these applications have been very contentious, as if Price equation was of no use for someone who wants to base a theoretical general formulation of evolution by natural selectionn on a firm grouding.
The Price equation indeed is is one of the very general formulations of evolution, together with the FTNS, the replicator equation, the breeder's equation, the canonical equation in adaptive dynamics, Formal Darwinism or Robertson’s secondary theorem in quantitative genetics and Li’s theorem, among others. Yet Price equation has been in fact used more than the others to derive both a justification for other general claims (e.g. the FTNS) or an extension of the Modern Synthesis core theory beyond biology. Given the (partial) equivalences existing between those formulations this fact may seem puzzling.
In this talk I’ll examine the connection between the content of the equation and its various explanatory uses, wondering how an analytical statement can ground major explanatory claims about evolving populations. I will distinguish between the content of the theorem itself and interpretative assumptions, among which are a concept of fitness or an ontology of groups vs individuals; I’ll claim that the explanatory weight of Price equation is based on these assumptions. Thus, the purely statistical character of the Price equation allows for statements that can be either causal, as the MLS decomposition, or pertaining to an optimality approach. Hence, rather than a claim about Darwinian evolution, one should rather see the Price equation as a constraint upon any characterization of evolution by natural selection
The Price equation and the laws of evolution
Victor J. Luque (University of Valencia) and Lorenzo Baravalle (University of Lisbon)
Due to its high degree of complexity and its historical nature, evolutionary biology has been traditionally portrayed as a messy science. According to the supporters of such a view, evolutionary biology would be unable to formulate laws and robust theories, instead just delivering coherent narratives and local models. Our aim in this talk is to challenge this view by showing how the Price equation can work as the core of a general theoretical framework for evolutionary phenomena. To support this claim, we will borrow some conceptual tools from metatheoretical structuralism, which is a sophisticated semantic approach to the reconstruction of the structure of scientific theories. This approach allows us to outline some unnoticed structural similarities between physical theories (in particular, classical mechanics) and evolutionary biology. More specifically, we shall argue that the Price equation, in the same way as fundamental formalisms in physics, can serve as a heuristic principle to formulate and systematise different theories and models in evolutionary biology.
The Generalized Price Equation
Matthijs van Veelen
The main ingredient of this paper is the derivation of the generalized Price equation. This generalizes the original Price equation in the sense that it produces a set of Pricelike equations, one for every different underlying model that one could assume has generated the data. All of these different Pricelike equations are identities, and all of them only have a meaningful interpretation if the data are indeed generated by the model they belong to. The criteria for choosing between these different Pricelike equations are the exact same as the criteria that standard statistics uses when choosing the right statistical model, based on the data. The original Price equation in regression form is the generalized Price equation that goes with the simplest linear model. The problem with the widespread misuse of the Price equation is caused by the fact that it loses its meaning if the data are not generated by this model – in the same way that any of the other Pricelike equations lose their meaning if the data are not generated by the model they belong to.
Poster Session
Diseases as prices to pay; Trade offs within Price Equation
Ozan Altinok
One of the most central elements of Evolutionary Medicine (EM) is supposed to give accounts of disease, although they seem to be taking the concept of disease usually not philosophically interesting or easy to define. One general attitude has been going directly to trade off answers within evolutionary medicine. They open the possibility for disease vulnerability, since through tradeoffs it becomes possible to understand that, from an orthodox MS perspective, why our traits are not perfected. For every adaptation, there was a cost. Some adaptations were even evolving antagonistically. Even the harshest supporters of a selectionist understanding such as Dawkins (2016 [1976]) did not have a problem with balancing the adaptive benefit of running fast for a cheetah and the possibility of hurting its own bone and muscle structure if it evolves to have faster and longer legs. One interesting example is Brett and Niermeyer’s (1999) study on bilirubin levels and baby development. While in adults bilirubin is seen as poisonous, they claim that from an evolutionary perspective, the increased amount of bilirubin in newborns is normal since it stops radicals that might harm the baby in the younger age. Upon this analysis, they propose new methods to measure and interfere with bilirubin levels to the babies, since the pressure for the radicals have changed in our modern environment. Similar to tradeoffs, parasitology and evolutionary ecology also employ a tradeoff like understanding of natural selection when it comes to systems with more than one organism. In order to explain the mutual evolution of more than one species in close proximity (such as hosts and parasites) Van Valen (1977), put forward the Red Queen Hypothesis. Red Queen Hypothesis is based on the adventures of Alice when she encounters the queen in Lewis Carroll’s Through the Looking Glass. Similar to the story, hosts and parasites had to evolve, even to stay where they are. From this perspective too, since evolutionary structures interactive systems, the fact that they evolved did not guarantee that they had increased fitness overall. Conflict and tradeoff theory is employed even in the baby mother relationships, making the womb, a battleground for father’s and mother’s genetic investment if we keep a gene centric position on the issue. (Haig, 1993) I will here look at a more individualised account of concept of disease to better understand the trade off concept of disease within price equation's understanding of environmental value.
Categorical variables and the strength of selection
Stephen Mann