Oliver Redner | PubMed Health

PubMed2004

Unequal crossover dynamics in discrete and continuous time.

We analyze a class of models for unequal crossover (UC) of sequences containing sections with repeated units that may differ in length. In these, the probability of an 'imperfect' alignment, in which the shorter sequence has d units without a partner in the longer one, scales like qd as compared to 'perfect' alignments where all these copies are paired. The class is parameterized by this penalty factor q. An effectively infinite population size and thus deterministic dynamics is assumed. For the extreme cases q = 0 and q = 1, and any initial distribution whose moments satisfy certain conditions, we prove the convergence to one of the known fixed points, uniquely determined by the mean copy number, in both discrete and continuous time. For the intermediate parameter values, the existence of fixed points is shown.

Crossing Over, Genetic↗

PubMed2002

Mutation-selection balance: ancestry, load, and maximum principle.

We analyze the equilibrium behavior of deterministic haploid mutation-selection models. To this end, both the forward and the time-reversed evolution processes are considered. The stationary state of the latter is called the ancestral distribution, which turns out as a key for the study of mutation-selection balance. We find that the ancestral genotype frequencies determine the sensitivity of the equilibrium mean fitness to changes in the corresponding fitness values and discuss implications for the evolution of mutational robustness. We further show that the difference between the ancestral and the population mean fitness, termed mutational loss, provides a measure for the sensitivity of the equilibrium mean fitness to changes in the mutation rate. The interrelation of the loss and the mutation load is discussed. For a class of models in which the number of mutations in an individual is taken as the trait value, and fitness is a function of the trait, we use the ancestor formulation to derive a simple maximum principle, from which the mean and variance of fitness and the trait may be derived; the results are exact for a number of limiting cases, and otherwise yield approximations which are accurate for a wide range of parameters. These results are applied to threshold phenomena caused by the interplay of selection and mutation (known as error thresholds). They lead to a clarification of concepts, as well as criteria for the existence of error thresholds.

Animals↗