For example, two populations (e.g., distinguished by geographic separation) might be characterized as having only sporadic events of migration in which an individual successfully becomes established and reproduces in a nonnatal population. These events may be measured directly, meaning that propagules must be followed for at least one generation; or indirectly, as with stable isotope markers or genetic markers. Genetic markers are frequently used to identify the relatedness of individuals from different populations, as the propagules of many species are difficult to track in terms of location and subsequent reproductive success.
Most genetic markers are assumed to be selectively neutral - that is, not under the influence of natural selection. Thus, the diversity and distribution of selectively neutral alleles at any given genetic locus are governed solely by the equilibrium between mutation (which adds novel alleles, or distinct markers), genetic drift (which stochastically eliminates alleles over time), and migration (which may introduce alleles that originally arose in a different population). The assumption of neutrality is important for understanding the degree to which populations are isolated from one another, because the diversity of genetic markers then reflects only the demographic characteristics of the populations, such as migration and reproduction.
For a given population size, the relative contribution of the mutation rate (y) and the migration rate (m) to an inference of isolation will be important. If y >> m, new alleles will arise in a population faster than they arrive from other populations, and the diversity in that population will become relatively distinct from that found in other regions. If m >> y, then migration acts as a homogenizing force among populations and they will be composed of a similar set of allelic diversity. As an example, the populations shown in Figure 1 represent a continuum of isolation. If the individuals are distinguishable based on genetic markers, we can measure isolation by quantifying the amount of diversity within each population (dw) relative to among-population (da) diversity. A class of statistics used to measure isolation in this case (Wright's F statistics) use a ratio of
(da - dw)/da to generate a value from 0 to 1, with 1 representing complete isolation. This class of statistics can be used to compare diversity among any hierarchical set of populations. Essentially, if there is equivalent diversity within a given group as among groups, there is little evidence for isolation. The top panel in Figure 1 illustrates 'complete isolation'; the diversity among populations (da) could be represented as 50% based on the frequency of two alleles across populations, while dw would be 0% (there is no variation within either populations). Thus, the isolation for this set of populations is 1. Using similar rough methods, the isolation of the remaining illustrated populations is (0.50 - (1/7))/0.50 = 0.714 (significant isolation), 0.143
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Figure 1 Isolation is measured as the tendency toward different identity. In the case of sexual isolation, the ratio of homospecific to heterospecific matings is measured, considering all available interactions. In the case of using genetic markers to identify demographic isolation, the level of identity by state (e.g., sharing the same allele) is considered within a population relative to among populations. Ecological factors such as phenology differences among populations may contribute to both types of isolation. Here, two populations are shown. They may be defined based on their geographic location or any other distinguishing traits, and symbols within each population represent distinguishable traits of individuals, such as genetic markers, otoliths, or stable isotopic signatures.
(some isolation), and 0 (no isolation). Similar statistics can be calculated for other forms of isolation (e.g., for measures of sexual isolation, the frequency of homospecific to heterospecific mating attempts, or successes compared to the total number of mating opportunities).
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