Fluctuations in the Size of Isolated Single‐Species Populations and Natural Selection

Abstract

This paper discusses the basic types of dynamicel behavior of populations obtained in discrete models, such aa monotonous dynamics. stable limited cycles, and chaotic variations. 811 these modes are shown to have possibly arisen in the evolution of limited populations under the effect of density-independent selection. This effect together with that of density-dependent non-selective factore haa been termed F-selection, which is characterized by independenoe of relative fitnesaee from population density, whereas populations may be ecologically limited; in other worda, absolute fitneesee prove to be a function of population size. The characrcteriatic of P-wlection is to be not sensitive to changes in population size but to lead to fluctuetiom, that create conditions for achieving density-dependent selection.Key words: Mendelian single-species population, natural selection, population size, discrete models. fitness, genotype, FIsmB's theorem.Discrete Models of Changes in Local Population Size.The life cycles of many biological species of multi-cellular organisms have a distinctly pronounced time periodcity, m a rule coinciding with seasonal changes in the earth's climate. An overwhelming majority of such species have a clearly outlined (o!ten very short) reproductive period, during whch each local population represents a totality of discrete single-aged groups. In many cases, the number of these groups is determined solely by the size of age groups in the preceding reproductive period. It is therefore natural t o characterize the number of the aex and age groups of a given population by a set of discrete magnitudes whch acquire certain values in certain fixed moments of time, e.g. by the beginning (or end) of the usual reproductive periods. The relationship between the values of such numbers in a given and fiubsequent moment,s of time may then be described by a system of recurrent equations.Let us examine the simplest situations, which nonetheless describe real population processes. For many insect species, each inchidual population represents one age group (or developmental stage), and adjacent generations of this popu- 38'

The Evolutionary Dynamics of a Sex-Structured Population with Non-Overlapping Generations

“…As mentioned earlier, the ecological limitation of population growth is assumed by a decreasing female and male survival with an increasing total abundance [18]. We consider the linear decrease with different limitation (or competition) coefficients for females and males.…”

“…On the other hand, as a rule, fluctuations in abundance are caused by changes in the population structure caused by the combined effects of environmental factors and self-regulatory mechanisms [12][13][14]. Therefore, when modeling population dynamics, it is advisable to use an ecological-genetic approach that allows us to study the interconnected changes in the abundance and genetic structure of a population [15][16][17][18][19][20][21][22][23][24][25][26][27].…”

Evolutionary Transition to Complex Population Dynamic Patterns in an Age-structured Population

“…The following equation was examined most frequently (Cook, 1965;Moran, 1950;Ricker, 1954;and others): Frisman and Shapiro (1982) examined the behavior of population dynamics using Eqn (2). Some of the results of their investigation are the following.…”