Quantifying the instrumental and noninstrumental underpinnings of Pavlovian responding with the Price equation

2021 ◽  
Author(s):  
Paul S. Strand ◽  
Mike J. F. Robinson ◽  
Kevin R. Fiedler ◽  
Ryan Learn ◽  
Patrick Anselme
Keyword(s):  
Price Equation

scholarly journals The distribution of allelic effects under mutation and selection

1990 ◽  
Vol 55 (2) ◽  
pp. 111-117 ◽  
Author(s):  
Steven A. Frank ◽  
Montgomery Slatkin
Keyword(s):  
Assortative Mating ◽  
Genetic Variance ◽  
Price Equation ◽  
Genetic Character ◽  
Quantitative Genetic ◽  
Mutation And Selection

SummaryThe Price (1970, 1972) equation is applied to the problem of describing the changes in the moments of allelic effects caused by selection, mutation and recombination at loci governing a quantitative genetic character. For comparable assumptions the resulting equations are the same as those obtained by different means by Barton & Turelli (1987; Turelli & Barton, 1989). The Price equation provides a natural framework within which to examine certain kinds of non-additive allelic effects, recombination and assortative mating. The use of the Price equation is illustrated by finding the equilibrium genetic variance under multiplicative dominance and epistasis and under assortative mating at an additive locus. The limitations of the use of recursion equations for the moments of allelic effects are also discussed.

Price Equation

2013 ◽  
pp. 1738-1739
Author(s):  
Philippe Huneman
Keyword(s):  
Price Equation

scholarly journals Disentangling niche theory and beta diversity change

2021 ◽  
Author(s):  
William Godsoe ◽  
Peter J Bellingham ◽  
Elena Moltchanova
Keyword(s):  
Beta Diversity ◽  
Price Equation ◽  
Short Term ◽  
Before And After ◽  
Environmental Requirements ◽  
Habitat Specialists ◽  
Montane Tropical Forest ◽  
Ecological Drift ◽  
Over Time

Beta diversity describes the differences in species composition among communities. Changes in beta diversity over time are thought to be due to selection based on species' niche characteristics. For example, theory predicts that selection that favours habitat specialists will increase beta diversity. In practice, ecologists struggle to predict how beta diversity changes. To remedy this problem, we propose a novel solution that formally measures selection's effects on beta diversity. Using the Price equation, we show how change in beta diversity over time can be partitioned into fundamental mechanisms including selection among species, variable selection among communities, drift, and immigration. A key finding of our approach is that a species' short-term impact on beta diversity cannot be predicted using information on its long-term environmental requirements (i.e. its niche). We illustrate how our approach can be used to partition causes of diversity change in a montane tropical forest before and after an intense hurricane. Previous work in this system highlighted the resistance of habitat specialists and the recruitment of light-demanding species but was unable to quantify the importance of these effects on beta diversity. Using our approach, we show that changes in beta diversity were consistent with ecological drift. We use these results to highlight the opportunities presented by a synthesis of beta diversity and formal models of selection.

Evidence, Other Approaches, and Further Topics

2015 ◽  
Author(s):  
James A.R. Marshall
Keyword(s):  
Social Evolution ◽  
Inclusive Fitness ◽  
Kin Recognition ◽  
Replicator Dynamics ◽  
Empirical Support ◽  
Natural World ◽  
Price Equation ◽  
Evolution Theory ◽  
Inclusive Fitness Theory ◽  
The Many

This book has examined the genesis, the logic, and the generality of social evolution theory. In particular, it has presented evolutionary explanations of the many social behaviors we observe in the natural world by showing that William D. Hamilton's inclusive fitness theory provides the necessary generalization of classical Darwin–Wallace–Fisher fitness. This concluding chapter discusses the limitations of the analyses presented in this book and assesses the empirical support for inclusive fitness theory, focusing on microbial altruism, help in cooperative breeders, reproductive restraint in eusocial species, and the evolution of eusociality and cooperative breeding. It also considers more advanced topics in social evolution theory, including sex allocation, genetic kin recognition, spite, and the evolution of organismality. Finally, it reviews theoretical approaches to studying social evolution other than replicator dynamics and the Price equation, such as population genetics, class-structured populations, and maximization approaches.

The Price Equation

2015 ◽  
Author(s):  
James A.R. Marshall
Keyword(s):  
Natural Selection ◽  
Replicator Dynamics ◽  
Genetic Selection ◽  
Single Locus ◽  
Price Equation ◽  
General Description ◽  
Conceptual Tool ◽  
Evolutionary Selection ◽  
Selective Regime ◽  
Fisher’S Fundamental Theorem

This chapter considers a general description of natural selection: the Price equation. Developed by George Price in the late 1960s, the Price equation can be applied to the change of any quantity under any selective regime. It is thus not limited to considering simple haploid single-locus traits, unlike the replicator dynamics, and indeed it is not even limited to considering evolutionary selection. The Price equation provides an instantaneous description of selection in action. The simplicity of the equation makes it a useful conceptual tool for understanding selective processes such as natural selection. The chapter first describes the general Price equation before discussing its use to understand genetic selection. It then shows how the Price equation can be used to derive two classical results from population and quantitative genetics: Fisher's “fundamental theorem of natural selection” and the breeder's equation.

scholarly journals The Price equation and reproductive value

2020 ◽  
Vol 375 (1797) ◽  
pp. 20190356 ◽  
Author(s):  
Alan Grafen
Keyword(s):  
Natural Selection ◽  
Fundamental Theorem ◽  
Structured Populations ◽  
Reproductive Value ◽  
Price Equation ◽  
Class Structure ◽  
Theme Issue ◽  
Starting Point ◽  
Important Idea ◽  
Fisher’S Fundamental Theorem

The Price equation is widely recognized as capturing conceptually important properties of natural selection, and is often used to derive versions of Fisher’s fundamental theorem of natural selection, the secondary theorems of natural selection and other significant results. However, class structure is not usually incorporated into these arguments. From the starting point of Fisher’s original connection between fitness and reproductive value, a principled way of incorporating reproductive value and structured populations into the Price equation is explained, with its implications for precise meanings of (two distinct kinds of) reproductive value and of fitness. Once the Price equation applies to structured populations, then the other equations follow. The fundamental theorem itself has a special place among these equations, not only because it always incorporated class structure (and its method is followed for general class structures), but also because that is the result that justifies the important idea that these equations identify the effect of natural selection. The precise definitions of reproductive value and fitness have striking and unexpected features. However, a theoretical challenge emerges from the articulation of Fisher’s structure: is it possible to retain the ecological properties of fitness as well as its evolutionary out-of-equilibrium properties? This article is part of the theme issue ‘Fifty years of the Price equation’.

scholarly journals Group and individual selection during evolutionary transitions in individuality: meanings and partitions

2020 ◽  
Vol 375 (1797) ◽  
pp. 20190364 ◽  
Author(s):  
Deborah E. Shelton ◽  
Richard E. Michod
Keyword(s):  
Group Selection ◽  
Contextual Analysis ◽  
Price Equation ◽  
Individual Selection ◽  
Evolutionary Transition ◽  
Theme Issue ◽  
Heritable Variation ◽  
Selection Models ◽  
Evolutionary Transitions ◽  
Multi Level

The Price equation embodies the ‘conditions approach’ to evolution in which the Darwinian conditions of heritable variation in fitness are represented in equation form. The equation can be applied recursively, leading to a partition of selection at the group and individual levels. After reviewing the well-known issues with the Price partition, as well as issues with a partition based on contextual analysis, we summarize a partition of group and individual selection based on counterfactual fitness, the fitness that grouped cells would have were they solitary. To understand ‘group selection’ in multi-level selection models, we assume that only group selection can make cells suboptimal when they are removed from the group. Our analyses suggest that there are at least three kinds of selection that can be occurring at the same time: group-specific selection along with two kinds of individual selection, within-group selection and global individual selection. Analyses based on counterfactual fitness allow us to specify how close a group is to being a pseudo-group, and this can be a basis for quantifying progression through an evolutionary transition in individuality (ETI). During an ETI, fitnesses at the two levels, group and individual, become decoupled, in the sense that fitness in a group may be quite high, even as counterfactual fitness goes to zero. This article is part of the theme issue ‘Fifty years of the Price equation’.

scholarly journals Simple unity among the fundamental equations of science

2020 ◽  
Vol 375 (1797) ◽  
pp. 20190351 ◽  
Author(s):  
Steven A. Frank
Keyword(s):  
Information Theory ◽  
Natural Selection ◽  
Frame Of Reference ◽  
Price Equation ◽  
Physical Work ◽  
Total Probability ◽  
Theme Issue ◽  
Total Change ◽  
Fundamental Equations ◽  
Change Concerns

The Price equation describes the change in populations. Change concerns some value, such as biological fitness, information or physical work. The Price equation reveals universal aspects for the nature of change, independently of the meaning ascribed to values. By understanding those universal aspects, we can see more clearly why fundamental mathematical results in different disciplines often share a common form. We can also interpret more clearly the meaning of key results within each discipline. For example, the mathematics of natural selection in biology has a form closely related to information theory and physical entropy. Does that mean that natural selection is about information or entropy? Or do natural selection, information and entropy arise as interpretations of a common underlying abstraction? The Price equation suggests the latter. The Price equation achieves its abstract generality by partitioning change into two terms. The first term naturally associates with the direct forces that cause change. The second term naturally associates with the changing frame of reference. In the Price equation’s canonical form, total change remains zero because the conservation of total probability requires that all probabilities invariantly sum to one. Much of the shared common form for the mathematics of different disciplines may arise from that seemingly trivial invariance of total probability, which leads to the partitioning of total change into equal and opposite components of the direct forces and the changing frame of reference. This article is part of the theme issue ‘Fifty years of the Price equation’.

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