Genetic changes in small populations

As suggested by the fact that we refer to these changes as threats due to genetic stochasticity, the genetic changes specific to small populations are random. To talk about this in more detail, we need to develop a little background in population genetics, specifically the theory of genetic drift.

It's been known for 80 years that the randomness associated with reproduction leads to changes in the genetic composition of a population through time. Consider this: if gametes are chosen at random to be included in zygotes, the genetic composition of the zygote pool will, on average, be the same as the gamete pool, but there is a distribution of possible outcomes. We won't go into the mathematical details here, but there are four basic properties of drift important for our purposes:²

1. Allele frequencies tend to change from one generation to the next simply as a result of sampling error. We can specify a probability distribution for the allele frequency in the next generation, but can't say with certainty what the exact value will be.

2. There is no systematic bias associated with the change in allele frequency, i.e., we can't predict which alleles will become more common and which will become rarer.

3. Populations eventually become fixed for one of the alleles originally present in the population, unless mutation or migration introduces new genetic variation, i.e., they tend to lose genetic diversity (Figure 1).

   Figure 1: Frequency distribution of predicted heterozygosity loss for 80 mammal species (from [1], Figure 11.4 [5])

   

4. Time to fixation (and other properties of drift) are inversely proportional to population size - the larger the population, the smaller the effect of drift (Figure 2). The time to common ancestry of two randomly chosen alleles in a population is $2N_e$. The time to common ancestry of all alleles in a population is $4N_e$ [9].

   Figure 2: Fraction of genetic diversity lost in each generation for populations of different effective size (Figure 11.3 [5]).

   

This last point is perhaps the most important, and the most problematic, for it turns out that simply counting the number of reproductive plants or animals in a population is not sufficient to determine whether the population is large or small. It is not the census number³ of individuals in the population that matters, but the effective number.⁴ The formulas that follow are from [2, p. 362].