Mutation accumulation in growing asexual lineages.

The stochastic loss of entire classes of individuals bearing the fewest number of mutations-a process known as Muller's ratchet-is studied in asexual populations growing unconstrained from a single founder. In the neutral regime, where mutations have zero effect on fitness, we derive a recursion equation for the probability distribution of the minimum number of mutations carried by individuals in the least-loaded class, and obtain an explicit condition for the halting of the ratchet. Next, we consider the case of deleterious mutations, and show that weak selection can actually accelerate the ratchet beyond that achieved for the neutral regime. This effect is transitory, however, as our results suggest that even weak purifying selection will eventually lead to the complete cessation of the ratchet. These results may have important implications for problems in biology and the medical sciences.

Soluble model for the accumulation of mutations in asexual populations.

Finite asexual populations can accumulate an increasing number of deleterious mutations by a process known as Muller's ratchet, which consists of successive losses of the fittest or least-loaded classes of individuals in the population. We present here a simplified theoretical framework to describe the serial bottleneck passages setup used in experiments to demonstrate the decrease of the population mean fitness due to the operation of ratchet. In particular, we calculate the expected time between consecutive clicks of the ratchet and derive expressions relating the moments of the mean fitness distribution to the mutation and selection parameters.

Effects of random migration in population dynamics.

We study the influence of random migration of a species (may be insects) in the population dynamics when initially all the individuals live in a primordial site (their habitats may be trees). We assume (i) a finite number of sites, (ii) that migration occurs randomly to nearest neighbors, and (iii) an on-site age-structured population whose size varies according to Ricker's map. We find that even for a very small migration rate, the population density becomes appreciably affected. If migration is not allowed, depending on the value of the characteristic parameters, the population may display a chaotic oscillation; however, with migration permitted, the chaos is reduced or even suppressed, and the population density will oscillate with period 2 or period 4. We examined the effects of migration through higher-order iterations of the map, entropy, and time correlation function. We also considered a long chain, analyzing (a) the spatial correlation between sites, noting the occurrence of a transition in the correlation function between sites separated by odd and even units of distance and (b) the fluctuations in time of the populations when initially all sites are populated.