Isolation by distance (IBD) is a term used to refer to the accrual of local genetic variation under geographically limited dispersal. The IBD model is useful for determining the distribution of gene frequencies over a geographic region. Both dispersal variance and migration probabilities are variables in this model and both contribute to local genetic differentiation. Isolation by distance is usually the simplest model for the cause of genetic isolation between populations. Evolutionary biologists and population geneticists have been exploring varying theories and models for explaining population structure. Yoichi Ishida compares two important theories of isolation by distance and clarifies the relationship between the two. According to Ishida, Sewall Wright's isolation by distance theory is termed ecological isolation by distance while Gustave Malécot's theory is called genetic isolation by distance. Isolation by distance is distantly related to speciation. Multiple types of isolating barriers, namely prezygotic isolating barriers, including isolation by distance, are considered the key factor in keeping populations apart, limiting gene flow.
Sewall Wright- Ecological Isolation By Distance
Wright introduced two different models of population structure, one not taking short-distance dispersal into account and one model incorporating short-distance dispersal. The "island model" is quite artificial and proposes the idea that a population is divided into two geographically, unique subpopulations (islands) with random mating occurring with exchange of individuals occurring when a migrant is drawn randomly from the total population. In a more realistic model, where short-distance dispersal is taken into account, a population is compiled of continuously distributed individuals over a region of space. Populations in remote locations may become differentiated simply by isolation by distance, restricting the probability of individuals mating with one another. Local populations are small in comparison to the total population and reproduction occurs solely within the local population. This ecological isolation by distance, according to Wright, can create genetic differentiation among subpopulations, leading to evolutionary change. Individuals within the subpopulation are neighbors in the sense that their gametes may come together and inbreeding within the subpopulation increases homozygosity. Wright's statistical theory for isolation by distance looks at population genetic consequences measured by F-statistics where the correlation of randomly uniting gametes within a subpopulation relative to those of the total population is the FST value.
The equation takes into account the variance in the distribution (var), the allele frequency within the total population (qT), and the allele frequency within the subpopulation (qST). Neighborhood size affects the local genetic differentiation (FST). Higher FST values indicate greater local genetic differentiation
Gustave Malécot- Genetic Isolation By Distance
Malécot's theory refers to a population genetic pattern where genetic differentiation among individuals increases as geographical distances increases. Dispersal is normally localized in space, lending to the expectation that individuals from closer subpopulations will be more genetically similar. Malécot argues that neighborhood size is not important because a decrease in the kinship coefficient does not depend on neighborhood size. This probabilistic theory solely depends on distances between that of offspring and their parents. A population, at equilibrium, displays genetic isolation by distance with stochastic processes producing genetic isolation. This genetic isolation by distance theory involves concepts of gametic kinship chains, identity by descent, and migration probabilities. The kinship coefficient (φ) is the probability that two homologous loci are identical by descent.
The equation takes into account distance (r), mutation rate (k), and the standard deviation of migration (σ). The kinship coefficient decreases as a function of distance and if a mutation occurs in either locus or if the gamete kinship chain is zero, the kinship coefficient will be zero. Yoichi Ishida interprets alteration in neighborhood size as alteration in dispersal variance linking both Wright's statistical theory and Malécot's probabilistic theory explaining why they both invite similar conclusions. Alteration in neighborhood size is alteration in dispersal variance and alteration corresponds to alteration in the variance of the probability of distribution associated with migration probabilities. Both dispersal variance and migration probabilities contribute to local genetic differentiation.
