  We define a general class of models representing natural selection between
two alleles. The population size and spatial structure are arbitrary, but
fixed. Genetics can be haploid, diploid, or otherwise; reproduction can be
asexual or sexual. Biological events (e.g.~births, deaths, mating, dispersal)
depend in arbitrary fashion on the current population state. Our formalism is
based on the idea of genetic sites. Each genetic site resides at a particular
locus and houses a single allele. Each individual contains a number of sites
equal to its ploidy (one for haploids, two for diploids, etc.). Selection
occurs via replacement events, in which alleles in some sites are replaced by
copies of others. Replacement events depend stochastically on the population
state, leading to a Markov chain representation of natural selection. Within
this formalism, we define reproductive value, fitness, neutral drift, and
fixation probability, and prove relationships among them. We identify four
criteria for evaluating which allele is selected and show that these become
equivalent in the limit of low mutation. We then formalize the method of weak
selection. The power of our formalism is illustrated with applications to
evolutionary games on graphs and to selection in a haplodiploid population.
