mutation accumulation

Lande R 1998 Risk of population extinction from fixation of deleterious and reverse mutations. Genetica 102/103:21-27.

• a simplified model of forward and reverse fixations, ignoring the time a mutation spends segregating
• for genes with additive effects on fitness, this simple model of alternate fixations gives results that closely approximate the equilibrium load under weak selection derived by Kimura, Maruyama and Crow (1963)

• under weak selection the equilibrium load is approximately L(s, N_e, ∞) = s / (1 + e^2N_es ν / μ) (equation 3b) for 2N_es < 5
• for any given population size there is an intermediate value of s that maximizes the equilibrium load, as shown in Figure 2
• by differentiating (3b) with respect to s and equating the result to zero, we find the value of s maximizing the equilibrium load as the solution of e^2N_es (2N_es − 1) ν / μ = 1
• evidently requires that s > 1 / (2N_e)
• for ν / μ = 1, 0.1 or 0.01, the value of 2N_e maximizing the equilibrium load is respectively 1.278, 2.157, or 3.636
• within the range of validity of the approximation (3b)
• (Kimura et al. 1963)

• under weak selection and in a small population, the expected equilibrium load is produced almost entirely by temporary fixations of slightly deleterious mutations
• under strong selection or in a large population the equilibrium load becomes nearly deterministic

• selection intensity must be somewhat above the usual boundary of 2N_es > 1, specifically 2N_es > ln(μ / ν), to shift the balance of alternative fixations in favor of wild type and keep the expected load down to about 2μ

• under irreversible mutation the most damaging mutations increasing the expected rate of loss of fitness by their fixation has 2N_es = 0.796
• (Lande 1994)

• the discrepancy in these numbers can be attributed to the different criteria used to assess damage to the population
• both approaches agree that nearly neutral mutations are the most damaging