The survival of recessive lethals in finite populations

Abstract

The behaviour of recessive lethals under recurrent mutation in small populations has been investigated using matrix methods. Equilibrium gene frequencies are then far from their infinite population values and are comparatively insensitive to selection on the heterozygote. Particular emphasis was paid to the allelism, both within and between generations. The life statistics of individual lethals, underlying the similarity between successive generations, was investigated and expressions given for the average age and subsequent expectation of life of lethals present in the population at any time. At equilibrium, the two are equal and the values found from the computer using matrix methods were surprisingly high. For a population size of 50, the average age of lethals, neutral in the heterozygote, present at any time is 10.2 generations. This produces a high correlation between observations in successive generations which leads to great difficulty in obtaining accurate estimates of parameters in any population. For instance, with N = 50 and an overall mutation rate of 0.005, the mean lethal frequency estimated from an analysis of 80 successive generations had a sampling variance slightly larger than the binomial sampling variance from a sample of 100 chromosomes from a single generation. As a consequence, results from single populations are of little value. The effect of linkage was studied using simulation methods. It was found that, for lethals neutral in the heterozygote, linkage had no detectable effect at equilibrium on the proportion of chromosomes containing a lethal or on the allelism between them. Individual lethals appeared to have a slightly higher expectation of life in the absence of crossing over.