Modelling the evolution of naturally bounded traits in a population

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Author(s)
Cropp, Roger
Norbury, John
Griffith University Author(s)
Year published
2021
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Eco-evolutionary models commonly assume that traits are normally distributed in a population, and that the trait bounds do not influence the adaptation of traits. However, recent empirical evidence suggests that at least some traits are not normally distributed, and there is theoretical support for the view that trait bounds can be fundamental to trait adaptation. These attributes suggest that a beta distribution, which can accommodate unbounded (i.e. normal), singly bounded (i.e. gamma) or doubly bounded (beta) trait distributions, may be an appropriate alternative assumption for eco-evolutionary models. We develop an ...
View more >Eco-evolutionary models commonly assume that traits are normally distributed in a population, and that the trait bounds do not influence the adaptation of traits. However, recent empirical evidence suggests that at least some traits are not normally distributed, and there is theoretical support for the view that trait bounds can be fundamental to trait adaptation. These attributes suggest that a beta distribution, which can accommodate unbounded (i.e. normal), singly bounded (i.e. gamma) or doubly bounded (beta) trait distributions, may be an appropriate alternative assumption for eco-evolutionary models. We develop an evolutionary model that represents how the mean values of a population’s traits change. Implementation of the model requires assumptions to be made regarding the relative fitness of the individuals in the population, and how their traits are distributed within natural bounds. We compare the numerical results of “population” models that evolve a plant population and the means of its two traits using our eco-evolutionary equations with those of “phenotype” models that evolve 10,000 phenotypes, each defined by a pair of trait values, of a plant population. The phenotype models do not assume any particular trait distribution or fitness, and allow phenotypes to wax and wane according to their ability to compete with other phenotypes in the population for a finite resource. Comparison of the trait distributions obtained by solving 3 coupled population odes with those obtained by solving 10,000 coupled phenotype odes reveals very good agreement between the approaches for each of four mortality functions. Further, it supports the ubiquity of the beta distribution in describing evolutionary processes in populations. An advantage of the simple population model is that it provides insights into why particular results are obtained, which augments the predictive power of the modelling, suggesting that in fact a simplified, abstracted modelling approach is sometimes preferable to the detailed, complicated alternative.
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View more >Eco-evolutionary models commonly assume that traits are normally distributed in a population, and that the trait bounds do not influence the adaptation of traits. However, recent empirical evidence suggests that at least some traits are not normally distributed, and there is theoretical support for the view that trait bounds can be fundamental to trait adaptation. These attributes suggest that a beta distribution, which can accommodate unbounded (i.e. normal), singly bounded (i.e. gamma) or doubly bounded (beta) trait distributions, may be an appropriate alternative assumption for eco-evolutionary models. We develop an evolutionary model that represents how the mean values of a population’s traits change. Implementation of the model requires assumptions to be made regarding the relative fitness of the individuals in the population, and how their traits are distributed within natural bounds. We compare the numerical results of “population” models that evolve a plant population and the means of its two traits using our eco-evolutionary equations with those of “phenotype” models that evolve 10,000 phenotypes, each defined by a pair of trait values, of a plant population. The phenotype models do not assume any particular trait distribution or fitness, and allow phenotypes to wax and wane according to their ability to compete with other phenotypes in the population for a finite resource. Comparison of the trait distributions obtained by solving 3 coupled population odes with those obtained by solving 10,000 coupled phenotype odes reveals very good agreement between the approaches for each of four mortality functions. Further, it supports the ubiquity of the beta distribution in describing evolutionary processes in populations. An advantage of the simple population model is that it provides insights into why particular results are obtained, which augments the predictive power of the modelling, suggesting that in fact a simplified, abstracted modelling approach is sometimes preferable to the detailed, complicated alternative.
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Journal Title
Theoretical Ecology
Volume
14
Issue
2
Copyright Statement
© 2021 Springer Netherlands. This is an electronic version of an article published in Theoretical Ecology, 14 (2), pp. 255-268, 2021. Theoretical Ecology is available online at: http://link.springer.com/ with the open URL of your article.
Subject
Ecology
Science & Technology
Life Sciences & Biomedicine
Environmental Sciences & Ecology
Trait evolution