Genetics - A. V. Sivolob 2008

Population Genetics
Properties of a Population
Abundance

In the simplest case, ignoring migration processes, population size depends on the balance between two variables: birth rate and death rate. If the birth rate (the number of newborns per individual over a given time t) is denoted as a, and the death rate (the number of deaths per individual over the same time) as b, then the difference between them, r, provides insight into the population size change over the studied period:

Class="center">r = а - b.

Named after Thomas Robert Malthus, who was the first to highlight the differing growth rates of human population and essential resources, r is referred to as the Malthusian parameter. Using this parameter, the instantaneous rate of change in population size N (The change in population size at a specific moment when the duration of the studied period t approaches zero) can be expressed by the equation

dN/dt = rN,

the solution to which yields an exponential pattern of population growth over time (the rate is higher the larger the population size is).

This exponential Population Growth Model accounts for only two parameters: birth rate and death rate. It describes explosive population growth in the absence of environmental resistance and with infinitely abundant resources (Fig. 8.2).

Fig. 8.2. Two population growth curves for size N: exponential (1) and logistic (2). No is the initial population size, K is the upper critical limit of population size determined by environmental resources

Resource limitation imposes a certain "environmental resistance" on the population's capacity for exponential growth (see Fig. 8.3). In other words, there is an upper critical population limit K, which is determined by the capacity of the environment to support only a limited number of individuals of a given species within a restricted habitat. The population growth rate will then depend on how closely the current size N approaches K (logistic population growth model, Fig. 8.2):

dN/dt = rN(1 - N/K).

Fig. 8.3. Growth of Yeast colonies On the surface of a nutrient medium in a Petri dish. A noticeable deceleration of colony growth can be seen in the direction of adjacent neighboring colonies, along with more intense growth in the opposite direction. This difference in growth rates can be explained by the reduced concentration of nutrients (environmental resources) and the increased concentration of metabolites in the adjacent zone

Population size and its dynamics are vital indicators of the state of a population. An equally important parameter is the so-called effective population size (N_e). The point is that not all individuals capable of leaving offspring actually make a reproductive contribution to the population's Gene pool. In the simplest case, N_e can be defined as the number of individuals that successfully leave progeny. If the numbers of males (N_m) and females (N_f) are approximately equal (assuming all males and females are reproductively competent), the effective population size is simply equal to their sum:

N_e = N_m + N_f,

In cases where There is a significant difference between the numbers of males and females, the effective population size is calculated using the expression

The dependence of the effective population size on the sex ratio for various groups with identical total numbers is shown in Table 8.1. Obviously, this value equals the sum of reproductively aged males and females only when their numbers are equal (the latter equation reduces to the previous one when N_m = N_f). In all other cases, N_e < (N_m + N_f). The value of N_e is also influenced by the size of the non-reproductive portion of the population (different age groups or "worker" individuals in bees or ants), unequal reproductive capacity, fluctuations in the overall population numbers, and A number of other factors.

Table 8.1. Theoretically calculated effective population size N_e for a group of 100 individuals at various ratios of males N_m and females N_f