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Erosion of Heterozygosity in Fluctuating Populations Society for Conservation Biology (URVLRQRI+HWHUR]\JRVLW\LQ)OXFWXDWLQJ3RSXODWLRQV $XWKRU V -RKQ$9XFHWLFKDQG7KRPDV$:DLWH 5HYLHZHGZRUN V 6RXUFH&RQVHUYDWLRQ%LRORJ\9RO1R $XJ SS 3XEOLVKHGE\Blackwell PublishingIRUSociety for Conservation Biology 6WDEOH85/http://www.jstor.org/stable/2641700 . $FFHVVHG Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. Blackwell Publishing and Society for Conservation Biology are collaborating with JSTOR to digitize, preserve and extend access to Conservation Biology. http://www.jstor.org Erosion of Heterozygosity in Fluctuating Populations JOHN A. VUCETICH*AND THOMAS A. WAITEt *School of Forestry, Michigan Technological University, Houghton, MI 49931, U.S.A., email [email protected] tDepartment of Evolution, Ecology, and OrganismalBiology, Ohio State University, Columbus, OH 43210, U.S.A., email waite. [email protected] Abstract: Demographic, environmental, and genetic stochasticity threaten the persistence of isolated popula- tions. The relative importance of these intertwining factors remains unresolved, but a common view is that random demographic and environmental events will usually drive small populations to the brink of extinc- tion before genetic deterioration poses a serious threat. To evaluate the potential importance of genetic fac- tors, we analyzed a model linking demographic and environmental conditions to the loss of genetic diversity in isolated populations undergoing natural levels of fluctuation. Nongenetic processes-environmental sto- chasticity and population demography-were modeled according to a bounded diffusion process. Genetic processes were modeled by quantifying the rate of drift according to the effective population size, which was predictedfrom the same parameters used to describe the nongenetic processes. We combined these models to predict the beterozygosity remaining at the time of extinction, as predicted by the nongenetic portion of the model. Our modelpredicts that many populations will lose most or all of their neutral genetic diversity before nongenetic random events lead to extinction. Given the abundant evidence for inbreeding depression and re- cent evidence for elevated extinction rates of inbred populations, our findings suggest that inbreeding may be a greater general threat to population persistence than is generally recognized. Therefore, conservation biolo- gists should not ignore the genetic component of extinction risk when assessing species endangerment and developing recovery plans. Erosi6n de la Heterocigosidad en Poblacione Fluctuantes Resumen: La estocasticidad demogrdfica, ambiental y genetica amenaza la persistencia de poblaciones ais- ladas. La importancia relativa de estos factores interconectados permanece sin resolverse, pero una visi6n comun es que los eventos demogrdficos y ambientales al azar usualmente conducen a poblaciones pequenas al borde de la extinci6n cuando el deterioro gene'tico representa una amenaza seria. Para evaluar la impor- tancia potencial de los factores geneticos, analizamos un modelo conectando condiciones demogrdficas y ambientales a la perdida de diversidad genetica en poblaciones aisladas bajo niveles defluctuaci6n natural. Losprocesos no geneticos- estocasticidad ambientaly demografia poblacional-faeron modelados de acuerdo a procesos de difusi6n aniadidos. Los procesos geneticos fueron modelados cuantificando la tasa de deriva de acuerdo al tamafnopoblacional efectivo, el cual sepredijo de lospardmetros utilizadospara describir los pro- cesos no geneticos. Combinamos estos modelos para predecir la heterocigocidad remanente al tiempo de ex- tinci6n, predecido por la porci6n no genetica del modelo. Nuestro modelo predice que muchas de las pobla- cions perderian la mayoria de su diversidad gene'tica neutral antes de que los evenos no gene'ticos las conduzcan a la extinci6n. Dada la abundante evidencia de la depresi6n por intracruza y la evidencia re- ciente de la elevada tasa de intracruza poblacional, nuestros resultados sugieren que la intracrtza podria ser una amenaza general para la persistencia de poblaciones atn mayor de lo que se ha reconocido. Por lo tanto, los conservacionistas no deberfan ignorar el componente genetico del riesgo de extinci6n cuando se evaluian planes de amenaza de especies y de recuperaci6n. Papersubmitted May 26, 1998; revisedmanluscript accepted December 9, 1998. 860 Conservation Biology, P'ages860-868 Volume 13, No. 4, Aulgust 1999 Vucetich& Waite PopulationVariability and GeneticErosion 861 Introduction mographic and environmental conditions cause all pop- ulations to fluctuate, we ask whether realistic levels of How important is genetic deterioration as a contributor fluctuation could substantially erode heterozygosity be- to the extinction risk of conserved populations? This fore demographic and environmental conditions cause fundamental question remains unresolved and conten- extinction. tious. Many empirical findings have indirectly suggested that genetic factors could contribute to extinction risk (e.g., reviews by Allendorf & Leary 1986; O'Brien & Ev- ermann 1988; Frankham 1995a; Lacy 1997), yet genetic Methods deterioration has been commonly viewed as a minor component of extinction risk. This perspective is re- Because heterozygosity is lost through genetic drift at flected in the low ranking of genetic factors (15 out of the rate of l/2Ne per generation, the proportion of ex- 18) among cited causes of species endangerment in the pected heterozygosity (hereafter, simply heterozygosity) continental United States (Czech & Krausman 1997). Un- remaining in a population after t generations, Ht, is (1 - til recently, no evidence directly supported the hypothe- 1/2Ne)t, where Ne is the average effective population sis that genetic deterioration contributes to the extinc- size, assuming neutrality and no mutation (Wright 1931). tion of wild populations (Frankham & Ralls 1998; We calculated the proportion of initial heterozygosity re- Saccheri et al. 1998). A compelling view in the absence maining at the expected (mean) time to extinction, of such evidence is that stochastic demographic and en- HE[TE](i.e., Ht when t = E[TE],where TE is the time to vironmental events are likely to drive small populations extinction and E[] indicates the expected value). Using to the brink of extinction before genetic deterioration diffusion theory applied to population dynamics, the ap- poses a serious threat (Lande 1988; Pimm et al. 1988, proximation for the expected time to extinction (in gen- 1989; Caro & Laurenson 1994). erations) of an isolated population is (Foley 1994) Here, we reevaluate this perspective using a model E[TE] = I (e2sln(K)(I -2esI (NO) ))-2sIn(NO)), that links demographic and environmental conditions [T]-2sE[r]G (1) with rates of inbreeding and genetic deterioration in iso- lated populations. If demographic and environmental where K is carryingcapacity; E[r] is the expected value of stochasticity usually lead to extinction before genetic di- r, the annual growth rate; s is expected growth rate di- versity is substantially reduced, then inbreeding is un- vided by variance in growth rate (Var[r]); G is generation likely to be an important component of extinction risk time in years; and No is initial population size. Consider- even for species thought to be vulnerable to inbreeding ations for estimating these parameters for naturalpopula- depression. However, if inbreeding is predicted to elimi- tions and assumptions underlying diffusion models (e.g., nate most or all of the genetic diversity before demo- stationarityof demographic processes) are discussed else- graphic and environmental factors cause extinction, then where (Dennis et al. 1991; Foley 1994, 1997). the contribution of inbreeding to extinction risk should Calculating HE[TE]also requires an estimate of the aver- be reconsidered. Although extinction is typically caused age effective size of a population over its life span, by multiple, only partially separable factors (Gilpin & which can be expressed as a function of SD[log(N)], a Soule 1986), an improved understanding of these factors measure of temporal fluctuation in population size (Vu- and the time scales on which they operate would allow cetich et al. 1997a; also see Vucetich & Waite 1998): us to devise better conservation strategies. Environmental stochasticity by itself represents an im- portant category of extinction risk even for large popula- Ne =LE[N]]Ll+In(lO) SD[log(N)]]l (2) tions (Lande 1993; Caughley 1994; Foley 1994). In addi- tion, environmental stochasticity causes fluctuation in where E[N] is the expected size of N, the population, population size, which accelerates genetic deterioration over its life span, and SD[log(N)] is the standard devia- (Vucetich et al. 1997a) and potentially increases extinc- tion of log-transformed population size. Based on the tion risk due to inbreeding depression. To evaluate this properties of the diffusion model, E[N1 may be ex- process, we modeled the loss of neutral genetic diversity pressed as through inbreeding in isolated populations. Using the I [K2s+ -1][-2s(e ?-1 )] term
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