Another Way to Calculate Fitness from Life History Variables: Solution of the Age-Structured Logistic Equation

In this paper we present a new modelling framework combining replicator dynamics (which is the standard model of frequency dependent selection) with the model of an age-structured population. The new framework allows for the modelling of populations consisting of competing strategies carried by individuals who change across their life cycle. Firstly the discretization of the McKendrick von Foerster model is derived. It is shown that the Euler--Lotka equation is satisfied when...

It has been shown that differences in fecundity variance can influence the probability of invasion of a genotype in a population, i.e. a genotype with lower variance in offspring number can be favored in finite populations even if it has a somewhat lower mean fitness than a competitor. In this paper, Gillespie's results are extended to population genetic systems with explicit age structure, where the demographic variance (variance in growth rate) calculated in the work of Eng...

In this work we construct individual-based models that give rise to the generalized logistic model at the mean-field deterministic level and that allow us to interpret the parameters of these models in terms of individual interactions. We also study the effect of internal fluctuations on the long-time dynamics for the different models that have been widely used in the literature, such as the theta-logistic and Savageau models. In particular, we determine the conditions for po...

A deterministic model of an age-structured population with genetics analogous to the discrete time Penna model of genetic evolution is constructed on the basis of the Lotka-Volterra scheme. It is shown that if, as in the Penna model, genetic information is represented by the fraction of defective genes in the population, the population numbers for each specific individual's age are represented by exactly the same functions of age in both models. This gives us a new possibilit...

We consider a model for Darwinian evolution in an asexual population with a large but non-constant populations size characterized by a natural birth rate, a logistic death rate modelling competition and a probability of mutation at each birth event. In the present paper, we study the long-term behavior of the system in the limit of large population $(K\to \infty)$ size, rare mutations $(u\to 0)$, and small mutational effects $(\sigma\to 0)$, proving convergence to the canonic...

Competition between species and genotypes is a dominant factor in a variety of ecological and evolutionary processes. Biological dynamics are typically highly stochastic, and therefore, analyzing a competitive system requires accounting for the random nature of birth and death processes (demographic stochasticity) as well as the variability of external conditions (environmental stochasticity). Recent studies have highlighted the importance of species life history, showing tha...

We present a model for evolution and extinction in large ecosystems. The model incorporates the effects of interactions between species and the influences of abiotic environmental factors. We study the properties of the model by approximate analytic solution and also by numerical simulation, and use it to make predictions about the distribution of extinctions and species lifetimes that we would expect to see in real ecosystems. It should be possible to test these predictions ...

Biological aging is characterized by an age-dependent increase in the probability of death and by a decrease in the reproductive capacity. Individual age-dependent rates of survival and reproduction have a strong impact on population dynamics, and the genetic elements determining survival and reproduction are under different selective forces throughout an organism lifespan. Here we develop a highly versatile numerical model of genome evolution --- both asexual and sexual --- ...

The aim of this study is to compare the growth speed of different cell populations measured by their Malthus parameter. We focus on both the age-structured and size-structured equations. A first population (of reference) is composed of cells all aging or growing at the same rate $\bar v$. A second population (with variability) is composed of cells each aging or growing at a rate $v$ drawn according to a non-degenerated distribution $\rho$ with mean $\bar v$. In a first part, ...

New models for evolutionary processes of mutation accumulation allow hypotheses about the age-specificity of mutational effects to be translated into predictions of heterogeneous population hazard functions. We apply these models to questions in the biodemography of longevity, including proposed explanations of Gompertz hazards and mortality plateaus, and use them to explore the possibility of melding evolutionary and functional models of aging.