Genetic Effective Population Size
Ne, (N sub e), the genetic effective population size (Wright 1969), can be thought of as the size of a genetically ideal population which has the same rate of loss of heterozygosity as an actual, non-ideal, wild population. Neutral genetic variation, or heterozygosity, is lost over time in a finite population by random genetic drift and by behavior that produces inbreeding. Since large mammals like grizzly bears have many characteristics that reduce the amount of variation that is passed on from generation to generation, Ne is substantially lower than N , the actual population size. Among these characteristics are unequal number of breeding males and females, fluctuations in population size, non- Poisson distribution in progeny number (unequal probability of an individual contributing to subsequent generations), and geographic structure in the population. When examining populations of wild animals though, it becomes very difficult to estimate parameters for these characteristics.

The original formula (Wright 1931) expressed Ne as a function of number of successfully breeding females (Nf ) and successfully breeding males (Nm):

[IMAGE]



With subsequent refinement Wright (1969)expressed heterozygosity as a function of Ne (originally written as N):

[IMAGE]

where Ho= the amount of heterozygosity (H) at the beginning of a time period H t = the amount of heterozygosity (H) at the end of a time period, and t = the length of time. Ne can thus be estimated from the change in H over time.

A useful measure in conservation biology is the ratio of genetic effective population size to actual population size: how many unique genotypes are effectively present in a population of a known number of individuals. In wild populations of carnivores, Ne is always lower than N. Generalized models of large mammal populations have resulted in an estimate of Ne/N = 0.25 (Wilcox 1986). Harris (1986) estimated a ratio of 0.2 to 0.4 for grizzly bears.

Harris and Allendorf used a simulation model to estimate Ne by tracing the loss of heterozygosity through time, and then comparing results with estimates produced by applying published formulas (Harris and Allendorf 1989). In comparing Ne estimates derived from published formulas with their results from a simulated population, Harris and Allendorf (1989) found that minor population fluctuations had little effect on Ne, but that variation in lifetime reproductive success among males (Vkm) greatly reduced Ne from its expectation under random mating success. Harris and Allendorf also found that Wright's original equation for unequal sex ratio "painted an overly optimistic picture" and that formulas by Hill (1972), Ryman et al. (1981), and Reed et al. (1986) gave more accurate estimates. These formulas however require estimates of various parameters which include variance in lifetime number of progeny (Hill 1972), heritability of fertility and variance of individual lifetime production of offspring who themselves survive to reproductive age (Ryman et al. 1981), and probability that a newborn of each age survives and reproduces (Reed et al. 1986).

In captive breeding populations, variance in family size etc. can be manipulated to increase the Ne/N ratio to theoretically reach 2.0 and thus maintain many more alleles in the population.

Computer simulations indicate that existing grizzly bear populations in the Lower-48 States are not large enough to avoid detrimental loss of genetic variation in the short term (Harris 1985, Harris and Allendorf 1989).

Heterozygosity (H) has been estimated from microsatellite alleles in grizzly bear genomic DNA. An initial small sample of 16 grizzly bears from the northern Rockies was not found to differ significantly from Alaskan populations in heterozygosity, but 5 unique microsatellite alleles were found (Craighead 1994). Additional analysis of a larger sample of 667 grizzlies, 72 of which were from Yellowstone, demonstrated a significantly lower H (55%) for Yellowstone grizzlies compared to a high of 78% in the Kluane sample (n=50) and a low of 26% in the Kodiak sample (n=34) [Paetkau et al. 1997].

One of the main factors affecting levels of genetic diversity appears to be connectedness to larger populations (Paetkau et al. 1996). Estimates of Ne can be obtained from H within the limits of the accuracy with which mutation rates are known (assuming equilibrium for mutation, genetic drift, and migration).

Estimates of Ne for the total Greater Yellowstone Ecosystem population are 15-54 effective grizzly bears (Paetkau et al. 1997).

Thus the Effective Population Size is much smaller than the census size of about 250 bears..

Craighead, F.L. 1994. Conservation genetics of grizzly bears. PhD dissertation, Montana State University, Bozeman, MT. 191 pp.

Harris, R. 1986. (ed.). Results of the workshop on grizzly bear population genetics. Sponsored by U.S. Dep't of Interior, Fish and Wildlife Service. Office of grizzly bear recovery co-ordinator. Missoula, Montana. 8 pp.

Harris, L.D. 1984. The Fragmented Forest; Island Biogeography Theory and the Preservation of Biotic Diversity. The University of Chicago Press, Chicago.

Harris and Allendorf (1989)

Irwin, D.M., T.D. Kocher, and A.C. Wilson. 1991.Evolution of the cytochrome b gene of mammals. Journal Molecular Evolution. 32:128-144

Hill, W.G. 1972. Effective size of populations with overlapping generations. Theor. Pop. Bio. 3:278-289.

Paetkau D., L. Waits, L. Craighead, E. Vyse, R. Ward, and C. Strobeck. 1997. Dramatic variation in genetic diversity in brown bears across North America: implications for conservation. In Press.

Reed, J.M., P.D. Doerr, and J.R. Walters. 1986. Determining minimum population sizes for birds and mammals. Wildlife Society Bulletin 14: 255-261.

Wright, S. 1931. Evolution in mammalian populations. Genetics 16:97-159.

Wright, S. 1969. Evolution and the genetics of populations. Vol. 2 The theory of gene frequencies. Univ. of Chicago Press, Chicago IL.

[IMAGE]


Click on image to return to North American Map