Effective Population Size/Adult Population Size Ratios in Wildlife: a Review

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Effective Population Size/Adult Population Size Ratios in Wildlife: a Review Genet. Res., Camb. (1995), 66, pp. 95-107 With 1 text-figure Copyright © 1995 Cambridge University Press 95 Effective population size/adult population size ratios in wildlife: a review RICHARD FRANKHAM School of Biological Sciences, Macquarie University NSW 2109. Australia. Phone: (612) 850-8186. Fax: (612) 850-8245. E-mail: rfrankhafa rna.bio.mq.edu.au (Received 27 June 1995) Summary The effective population size is required to predict the rate of inbreeding and loss of genetic variation in wildlife. Since only census population size is normally available, it is critical to know the ratio of effective to actual population size (NJN). Published estimates of NJN (192 from 102 species) were analysed to identify major variables affecting the ratio, and to obtain a comprehensive estimate of the ratio with all relevant variables included. The five most important variables explaining variation among estimates, in order of importance, were fluctuation in population size, variance in family size, form of TV used (adults v. breeders v. total size), taxonomic group and unequal sex-ratio. There were no significant effects on the ratio of high v. low fecundity, demographic r. genetic methods of estimation, or of overlapping v. non-overlapping generations when the same variables were included in estimates. Comprehensive estimates of NJN (that included the effects of fluctuation in population size, variance in family size and unequal sex-ratio) averaged only 0-10—0-11. Wildlife populations have much smaller effective population sizes than previously recognized. these predictions (Borlase et al. 1993; Briton et al. 1. Introduction 1994; Woodworth et al. 1994). Finite population size results in inbreeding and loss of Widely divergent views have been expressed about genetic variation. Its genetic effects are predicted to the magnitude of NJN. Empirical estimates were depend on the effective population size (Ne) rather reported to be 0-5-0-8 (Falconer, 1989; Spiess 1989), than the actual size (TV). The predicted relationships 0-2-0-4 (Denniston, 1978; Mace, 1986), 0-2-0-5 (Mace of genetic variation and inbreeding with effective & Lande, 1991), 0-25-1 -0 (Nunney & Campbell, 1993), population size are given by equation (1) (Falconer, or 0-56-1-27 (Nunney & Elam, 1994), while values as 1989) low as 10~6 have been reported (Hedgecock, Chow & Waples, 1992). Nunney (1993) predicted that special HJH0 = [1 -\/2Ne)]> = l -F, (1) circumstances would be required for the ratio to be where Ht is heterozygosity after / generations, Hn is much less than 0-5, Nunney & Campbell (1993) initial heterozygosity, and F is the inbreeding co- suggested that it would usually be greater than 0-25, efficient. while Nei & Tajima (1981) suggested that it would be Since census sizes are the only demographic data less than 0-1 in small organisms. In spite of the critical available for most populations, the ratio of NJN is a importance of NJN ratios in conservation and critical parameter for evolutionary genetics and evolutionary biology, there has been no recent wildlife management. For example, a minimum ratio comprehensive review of estimates. of 0-2 is assumed in the Mace-Lande criteria for To predict the effects of finite population size on endangerment (Mace & Lande, 1991), and inbreeding and loss of genetic variation, estimates assumptions for NJN are inherent in estimates of must encompass the effects of unequal sex-ratio, minimum viable population size (Nunney & Campbell, variance in family size and fluctuation in population 1993). Unequal sex-ratios, variance in family sizes, size (comprehensive estimates). A range of genetic and and fluctuations in population size over generations demographic methods have been used to estimate Ne are all predicted to affect NJN (Wright, 1969; (see below). Typically genetic estimates have included Falconer, 1989). Experimental tests have validated all three relevant variables, while most demographic R. Frankham 96 estimates have not included the effects of fluctuations variance in gametic contributions (Gowe, Robertson in population size. Consequently, many available & Latter, 1959). estimates of NJN, particularly demographic ones, 1 /Ne = [1 /Ne, +1 /Ne2 + 1 /Ne3 + ...1 /Net... 1 /Net]/t, may be overestimates. (4) Wildlife species differ in life history characteristics, where N is the effective population size in the rth so they may differ in NJN ratios. High fecundity ei generation. species might be expected to have lower ratios due to Equations to accommodate overlapping gener- high variance in family sizes, and perhaps greater ations have been developed by Hill and others (see fluctuations in population size over generations. Caballero 1994; Nunney & Elam, 1994), and one Species exhibiting polygamy would be expected to to include the effects of selfing by Heywood (1986). have lower ratios than monogamous species due to Demographic estimates of N have relied on one or unequal sex-ratio and high variance of male gametic e more of equations 2-4. Very few such estimates have contributions. included all these variables. Genetic estimates have The objectives of this contribution were to review been made from changes in allozyme heterozygosity estimates of NJN in order to identify the major (or quantitative genetic variation) over time using variables affecting the ratio, and to obtain a reliable equation 1 (Briscoe et al. 1992), from drift variances comprehensive estimate of the ratio. In particular, among populations for allozymes (Easteal & Floyd, they were to test the hypotheses that (i) sex-ratio, 1986), from linkage disequilibrium (Hill, 1981; Bartley variance in family size, and fluctuating population size et al. 1992), lethal allelism (Malpica & Briscoe, 1981), affect the ratio; (ii) taxonomic groups differ in ratio; and from changes in pedigree inbreeding over time (iii) life history characteristics affect the ratio and (iv) (Tomlinson et al. 1991). Typically genetic estimates different methods yield different estimates. Estimates were comprehensive estimates. were compared with the 0-5 and 0-25 values predicted The time frame of interest in conservation biology above. Means for comprehensive estimates were is several generations to a few hundred generations. computed by two methods. NJN averaged only The genetic estimates reviewed here reflect this time O10-0-11, much smaller than previously recognized. frame. Long-term species estimates of Ne, based on either a neutral interpretation of allozyme variation 2. Methods of estimating Ne (Nei & Graur, 1984; Schoen & Brown, 1991), a drift- heterokaryotype disadvantage model of karyotype The concept of effective population size was intro- evolution (Lande, 1979; Barrowclough & Shields, duced by Wright (1931, 1938, 1939) and has been 1984), or DNA sequence divergence (Avise, Ball & refined by others, especially Crow and co-workers (see Arnold, 1988) operate over hundreds of thousands to Crow & Kimura, 1970; Caballero, 1994). N is defined e millions of generations, and require additional as the size of an idealized population that would give assumptions, so they have not been included in the rise to the same variance of gene frequency, or rate of survey in the Appendix. However, the mean of the Nei inbreeding as in the actual population under con- & Graur (1984) estimates has been computed to sideration (see Falconer, 1989; Caballero, 1994). compare with estimates from the data in the Appendix. Three effective sizes have been denned: inbreeding, variance and eigenvalue. Estimates from the former two are the same under random mating and constant 3. Data size over generations, but can differ when population There are 192 published estimates of the NJN ratio sizes are changing, and also differ from the eigenvalue from 102 species of insects, molluscs, amphibians, estimate (see Caballero, 1994; Templeton & Read, reptiles, birds, mammals and plants listed in the 1994). Appendix along with estimation methods, the Unequal sex-ratio (SR), variance in family size variables they include, and the N value used. The (VFS), and fluctuations in population size (FPS) are values reported for the Japanese human population the major variables predicted to affect Ne (Wright, (Imaizumi, Nei & Furusho, 1970) were restricted to 1969; Lande & Barrowclough, 1987; Falconer, 1989). mothers' birth dates prior to 1910 as birth control Their effects are given by equations 2-4 below. affected values after that. Estimates based on the use of segregating mutations (Nozawa, 1963, 1970; = 4N,N /[N,+ N m m (2) Wright, 1977, 1978; Wade, 1980; Pray et al. 1995) are where Nf and Nm are the number of female and male given for comparative purposes, but were not included parents of the next generation. in statistical analyses as they may have been influenced by natural selection, and such estimates were not Ne = N/[\+{Vk-mk)/mk], (3) available outside insects. NJN estimates for white where N is the number of sexually mature, non- spruce and black spruce that included only the effects senescent adults, mk is the mean number of gametes of maternal-to-seed sampling, rather than seedling per individual contributing to production of mature establishment, were not included (Cheliak, Pitel & individuals in the next generation, and Vk is the Murray, 1985; Barrett, Knowles & Cheliak, 1987). Ne/N in wildlife 97 Values for domestic animal populations and mutant 1993 and Blackwell et al. 1995; Crow & Morton, 1955 stocks were excluded. The estimate for Rana pipiens and Nei & Murata, 1966; Imaizumi et al. 1970; from Merrell (1968) was not used in the statistical MacCluer & Shull, 1970 and Nei, 1970; Felsenstein, analyses as it was only an estimate of the ratio of 1971, Emigh & Pollak, 1979 and Charlesworth, 1980; breeding adults to all adults. Taylor et al. 1994 and Taylor pers. comm.; Husband Estimates varied widely in methods used, variables & Barrett, 1992). Analyses were generally done on included, precision, and in the value of N used. Few both the full data set and on the data set where repeat demographic estimates were based on paternities that estimates on the same population were pooled. had been verified with genetic markers.
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