The rapid evolution of antibody molecules during an immune response enables the immune
system to respond efficiently to an immense variety of challenges. To investigate this …

We analyze a mathematical model of protein evolution in which the evolutionary process is
viewed as hill-climbing on a random fitness landscape. In studying the structure of such …

A theory for evolution of either gene sequences or molecular sequences must take into
account that a population consists of a finite number of individuals with related sequences …

We extend an earlier model of protein evolution on a rugged landscape to the case in which
the landscape exhibits a variable degree of correlation (ie, smoothness). Correlation is …

I consider the adaptation of a DNA sequence when mutant fitnesses are drawn randomly
from a probability distribution. I focus on “gradient” adaptation in which the population jumps …

Adaptive evolution, to a large extent, is a complex combinatorial optimization process. In this
article we take beginning steps towards developing a general theory of adaptive “walks” via …

Adaptive evolution is, to a large extent, a complex combinatorial optimization process. Such
processes can be characterized as “uphill walks on rugged fitness landscapes”. Concrete …

Given two mutants, A and B, separated by n mutational steps, what is the evolutionary
trajectory which allows a homogeneous population of A to reach B in the shortest time? We …

We examine properties of adaptive walks on uncorrelated (ie random) fitness landscapes
starting from moderately fit genotypes under strong selection weak mutation. As an …

We consider an asexually reproducing population on a finite type space whose evolution is
driven by exponential birth, death and competition rates, as well as the possibility of …