Foundations of a mathematical theory of darwinism

Batty, C. J. K.; Crewe, Paul; Grafen, Alan; Gratwick, Richard

doi:10.1007/s00285-013-0706-2

Cited by 15 publications

(21 citation statements)

References 38 publications

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“…The first is the ‘new’ interpretation of Fisher's fundamental theorem of natural selection, on which the theorem is exactly true for any evolving population that satisfies some minimal assumptions (Price, ; Ewens, , , ; Frank & Slatkin, ; Edwards, , ; Lessard, ; Plutynski, ; Okasha, ; Bijma, ). The second development is the Formal Darwinism project of Alan Grafen and colleagues, which forges links between formal representations of gene frequency change and optimal strategy choice (Grafen, 1999, 2000, 2002, 2003, 2006 a , b , 2007, 2014; Gardner & Grafen, ; Gardner & Welch, ; Batty et al ., ).…”

Section: Introduction: Conflicting Paradigmsmentioning

confidence: 97%

Natural selection and the maximization of fitness

Birch

2015

Biological Reviews

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The notion that natural selection is a process of fitness maximization gets a bad press in population genetics, yet in other areas of biology the view that organisms behave as if attempting to maximize their fitness remains widespread. Here I critically appraise the prospects for reconciliation. I first distinguish four varieties of fitness maximization. I then examine two recent developments that may appear to vindicate at least one of these varieties.The first is the 'new' interpretation of Fisher's fundamental theorem of natural selection, on which the theorem is exactly true for any evolving population that satisfies some minimal assumptions. The second is the Formal Darwinism project, which forges links between gene frequency change and optimal strategy choice. In both cases, I argue that the results fail to establish a biologically significant maximization principle. I conclude that it may be a mistake to look for universal maximization principles justified by theory alone. A more promising approach may be to find maximization principles that apply conditionally and to show that the conditions were satisfied in the evolution of particular traits.2

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Section: Introduction: Conflicting Paradigmsmentioning

confidence: 97%

Natural selection and the maximization of fitness

Birch

2015

Biological Reviews

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“…This assumption implies that the condition of pairwise exchangeability (assumed by Grafen 2002 , 2006a , b ; Batty et al. 2014 , for fitness-maximixisation results) is met here too. It also prevents one individual affecting other individuals according to coancestral links.…”

Section: Preliminariesmentioning

confidence: 94%

Defining fitness in an uncertain world

2017

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The recently elucidated definition of fitness employed by Fisher in his fundamental theorem of natural selection is combined with reproductive values as appropriately defined in the context of both random environments and continuing fluctuations in the distribution over classes in a class-structured population. We obtain astonishingly simple results, generalisations of the Price Equation and the fundamental theorem, that show natural selection acting only through the arithmetic expectation of fitness over all uncertainties, in contrast to previous studies with fluctuating demography, in which natural selection looks rather complicated. Furthermore, our setting permits each class to have its characteristic ploidy, thus covering haploidy, diploidy and haplodiploidy at the same time; and allows arbitrary classes, including continuous variables such as condition. The simplicity is achieved by focussing just on the effects of natural selection on genotype frequencies: while other causes are present in the model, and the effect of natural selection is assessed in their presence, these causes will have their own further effects on genoytpe frequencies that are not assessed here. Also, Fisher’s uses of reproductive value are shown to have two ambivalences, and a new axiomatic foundation for reproductive value is endorsed. The results continue the formal darwinism project, and extend support for the individual-as-maximising-agent analogy to finite populations with random environments and fluctuating class-distributions. The model may also lead to improved ways to measure fitness in real populations.

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“…In Section 5.2, we generalise this result for an arbitrary number of heritable traits that affect the sex-specific tradeoffs and life-history parameters. A common approach to such problems is discrete formulations aiming to generalise Price's equation (for examples see Batty et al [1] and Grafen, A. [7]), which is a mathematical statement of how trait frequencies in a population change over time, given the initial population frequencies over trait space and the fitnesses of the traits (see Frank [6] for a detailed discussion and also Price's original papers [15,16]).…”

Section: Introductionmentioning

confidence: 99%

Modelling the Evolution of Traits in a Two-Sex Population, with an Application to Grandmothering

2017

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We present a mathematical simplification for the evolutionary dynamics of a heritable trait within a two-sex population. This trait is assumed to control the timing of sex-specific life-history events, such as the age of sexual maturity and end of female fertility, and each sex has a distinct fitness trade-off associated with the trait. We provide a formula for the fitness landscape of the population and show a natural extension of the result to an arbitrary number of heritable traits. Our method can be viewed as a dynamical systems generalisation of the Price equation to include two sexes, age structure and multiple traits. We use this formula to examine the effect of grandmothering, whereby post-fertile females subsidise their daughter's fertility by provisioning grandchildren. Grandmothering can drive a shift towards increasingly male-biased mating sex ratios due to a post-fertile life stage in females, while male fertility continues to older ages. Our fitness landscapes show a net increase in fitness for both males and females at longer lifespans, and as a result, we find that grandmothering alone provides an evolutionary trajectory to higher longevities.

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Foundations of a mathematical theory of darwinism

Cited by 15 publications

References 38 publications

Natural selection and the maximization of fitness

Natural selection and the maximization of fitness

Defining fitness in an uncertain world

Modelling the Evolution of Traits in a Two-Sex Population, with an Application to Grandmothering

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