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

We investigate the evolutionary dynamics of an age-structured population under weak frequency-dependent selection. It turns out that the weak selection is affected in a non-trivial way by the life-history trait. We can disentangle the dynamics, based on the appearance of different time scales. These time scales, which seem to form a universal structure in the interplay of weak selection and life-history traits, allow us to reduce the infinite dimensional model to a one-dimens...

Competitions can occur on an absolute scale, to be faster or more efficient, or they can occur on a relative scale, to "beat" one's competitor in a zero-sum game. Ecological models have focused on absolute competitions, in which optima exist. Classic evolutionary models such as the Wright-Fisher model, as well as more recent models of travelling waves, have focused on purely relative competitions, in which fitness continues to increase indefinitely, without actually progressi...

In 1995 T.J.Penna introduced a simple model of biological aging. A modified Penna model has been demonstrated to exhibit behaviour of real-life systems including catastrophic senescence in salmon and a mortality plateau at advanced ages. We present a general steady-state, analytic solution to the Penna model, able to deal with arbitrary birth and survivability functions. This solution is employed to solve standard variant Penna models studied by simulation. Different Verhulst...

Many life-history traits, like the age at maturity or adult longevity, are important determinants of the generation time. For instance, semelparous species whose adults reproduce once and die have shorter generation times than iteroparous species that reproduce on several occasions. A shorter generation time ensures a higher growth rate in stable environments where resources are in excess, and is therefore a positively selected feature in this (rarely met) situation. In a sta...

In this study, we couple a population dynamics model with a model for optimal foraging to study the interdependence between individual-level cost-benefits and population-scale dynamics. Specifically, we study the logistic growth model, which provides insights into population dynamics under resource limitations. Unlike exponential growth, the logistic model incorporates the concept of carrying capacity, thus offering a more realistic depiction of biological populations as they...

It is shown that if the computer model of biological ageing proposed by Stauffer is modified such that the late reproduction is privileged then the Gompertz law of exponential increase of mortality can be retrieved.

We study the interplay of population growth and evolutionary dynamics using a stochastic model based on birth and death events. In contrast to the common assumption of an independent population size, evolution can be strongly affected by population dynamics in general. Especially for fast reproducing microbes which are subject to selection, both types of dynamics are often closely intertwined. We illustrate this by considering different growth scenarios. Depending on whether ...

Since the seminal work of Powell, the relationships between the population growth rate, the probability distributions of generation time, and the distribution of cell age have been known for the bacterial population in a steady state of exponential growth. Here, we generalize these relationships to include an unsteady (transient) state for both the batch culture and the mother machine experiment. In particular, we derive a time-dependent Euler-Lotka equation (relating the gen...

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 tradeoff 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 heritabl...

Sexual selection theory models evolution of sexual signals and preferences using simple life histories. However, life-history models predict that males benefit from increasing sexual investment approaching old age, producing age-dependent sexual traits. Age-dependent traits require time and energy to grow, and will not fully mature before individuals enter mating competition. Early evolutionary stages pose several problems for these traits. Age-dependent traits suffer from st...