Evolution of heterogeneity under constant and variable environments.

Ryo Oizumi,Hisashi Inaba

doi:10.1371/journal.pone.0257377

Abstract

Various definitions of fitness are essentially based on the number of descendants of an allele or a phenotype after a sufficiently long time. However, these different definitions do not explicate the continuous evolution of life histories. Herein, we focus on the eigenfunction of an age-structured population model as fitness. The function generates an equation, called the Hamilton-Jacobi-Bellman equation, that achieves adaptive control of life history in terms of both the presence and absence of the density effect. Further, we introduce a perturbation method that applies the solution of this equation to the long-term logarithmic growth rate of a stochastic structured population model. We adopt this method to realize the adaptive control of heterogeneity for an optimal foraging problem in a variable environment as the analyzable example. The result indicates that the eigenfunction is involved in adaptive strategies under all the environments listed herein. Thus, we aim to systematize adaptive life histories in the presence of density effects and variable environments using the proposed objective function as a universal fitness candidate.

Highlights

Since the publication of The Origin of Species by Charles Darwin, many biologists have believed that evolution is promoted by mutation and adaptation
Because the utilization rate does not depend on age or size, we can consider a specific long-term logarithmic growth rate (LLGR) with the following change of coefficients in Eq (65). qfififififififififififififififififififififififififififififififififififi b1 ! b1ð1 À uÞ þ b2v; s1 ! s21ð1 À uÞ2 þ s22u2: Solving r1⁄2u ðεÞ numerically, we find that a variable environment favors heterogeneity, as suggested in the previous section (Fig 4)
This study attempted to construct a systematization of the optimal life schedule problem and population dynamics using the eigenfunction expansion of a structured population model

Summary

Introduction

Since the publication of The Origin of Species by Charles Darwin, many biologists have believed that evolution is promoted by mutation and adaptation. If an allele or an individual with a mutation has greater fitness than other alleles/individuals without a mutation, the mutation will eventually dominate the population. Fitness is not observed in nature; we must rely on indirect indices to analyze evolution. Because it cannot be observed in nature, fitness does not have a unique and quantitative definition. An adaptive gene must meet several requirements to thrive in a population. The indicator must be a measure by which adaptive genes dominate the population, regardless of population dynamics, including saturated growth, exponential growth, or stochastic growth

Objectives

Conclusion