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1 23456789 Geographic distance (meters)

1 23456789 Geographic distance (meters)

Geographic distance (standard deviations)

Figure 3.21 Isolation by distance is characterized by the declining probability of gamete dispersal with increasing geographic distance. The specific shape of the gamete dispersal by distance curve may vary (top), but it is often modeled using a normal distribution (bottom). In a normal distribution, about 95% of observations are expected to fall within two standard deviations from the mean. Empirical estimates of mating and progeny movement in a generation can be used to estimate the variance and thereby the standard deviation of overall dispersal in gametes in order to estimate the area of a genetic neighborhood.

Geographic distance (standard deviations)

Figure 3.21 Isolation by distance is characterized by the declining probability of gamete dispersal with increasing geographic distance. The specific shape of the gamete dispersal by distance curve may vary (top), but it is often modeled using a normal distribution (bottom). In a normal distribution, about 95% of observations are expected to fall within two standard deviations from the mean. Empirical estimates of mating and progeny movement in a generation can be used to estimate the variance and thereby the standard deviation of overall dispersal in gametes in order to estimate the area of a genetic neighborhood.

events would show a frequency distribution like that of Fig. 3.21. The critical feature of the distribution is that the frequency or chance of mating drops off on average as the physical distance between individuals increases. This is a widely observed phenomenon called isolation by distance (Wright 1943a). With enough distance separating them, two individuals have a low probability of mating and can be considered members of distinct genetic populations even if they are not located in geographically distinct populations. The distance required for reproductive isolation by distance may be on the order of meters or thousands of kilometers depending on the species.

Estimating the breeding effective population size depends on the probability distribution of gamete dispersal in space and can be approximated by a normal distribution (other distributions can be used as well). Recall that two standard deviations on either side of the mean contains about 95% of the observations in a normal distribution (see the Appendix). The standard deviation in dispersal, which is the square root of the variance in dispersal, can then be used to describe the probability that a gamete disperses in one dimension (Fig. 3.21). Extending this to gamete dispersal into two dimensions, the dispersal area can be thought of as a circle with the average individual at the center. Since the circle describes a probability distribution, a radius of twice the standard deviation in dispersal in a generation will sweep an area containing about 95% of the observations in a two-dimensional normal distribution (Fig. 3.22). This two-dimensional normal distribution model of gamete dispersal probability combined with the average density of individuals is used to quantify the breeding effective population size. Since the area of a circle is nr2 where r is two standard deviations (or twice the square root of the dispersal distance variance):

Nb = n(2^/dispersal variance)2d which simplifies to

where d is the average density of individuals. The area described by equation 3.61 is known as the genetic neighborhood in continuous populations. Multiplying the genetic neighborhood (an area) by the density of individuals (individuals per unit area)

Figure 3.22 An ideal two-dimensional normal distribution used to model the size of genetic neighborhoods and to estimate the breeding effective size (Ncb) of demes within continuous populations. The radius of the distribution is twice the standard deviation in total gamete dispersal in a generation. The actual physical dimensions of the distribution could range from just a few meters to hundreds or thousands of kilometers.

Figure 3.22 An ideal two-dimensional normal distribution used to model the size of genetic neighborhoods and to estimate the breeding effective size (Ncb) of demes within continuous populations. The radius of the distribution is twice the standard deviation in total gamete dispersal in a generation. The actual physical dimensions of the distribution could range from just a few meters to hundreds or thousands of kilometers.

gives the breeding effective population size in individuals (see Wright 1943a; Crawford 1984).

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