Persistence of Different-sized Populations: An Empirical Assessment of Rapid Extinctions in Bighorn Sheep JOEL BERGER Department of Range, Wildlife, and Forestry and Department of Biology University of Nevada Reno, NV 89512, U.S.A. and Conservation and Research Center Smithsonian Institution Front Royal, VA 22630, U.S.A. Abstract: Theory and simulation models suggest that small populations are more susceptible to extinction than large populations, yet assessment of this idea has been hampered by lack of an empirical base. I address the problem by asking how long different-sized populations persist and present de- mographic and weather data spanning up to 70 years for 122 bighorn sheep ('Ovis canadensisj populations in south- western North America Analyses reveal that: (1) 100 percent of the populations with fewer than 50 individuals went ex- tinct within 50 years; (2) populations with greater than 100 individuals persisted for up to 70 years; and (3) the rapid loss of populations was not likely to be caused by food short- ages, severe weather, pr?dation, or interspecific competition. These data suggest that population size is a marker of per- sistence trajectories, and they indicate that local extinction cannot be overcome because 50 individuals, even in the short term, are not a minimum, viable population size for bighorn sheep. Resumen: La teor?a y los modelos de simulaci?n sugieren que las poblaciones peque?as son m?s suceptibles a la ex- tinci?n que las poblaciones grandes, pero la evaluaci?n de esto se ha visto obstaculizada por falta de una base emp?r- ica. Me refiero a este problema aqu?, preguntando por cu?nto tiempo persisten las poblaciones de diferentes tama?os y presentando datos demogr?ficos y clim?ticos de un per?odo que alcanza hasta 70 a?os para 122 probla- ciones de ovejas Bighorn ('Ovis canadensisj en el sudoeste de Norte Am?rica Los an?lisis revelan que: 1) 100% de la po- blaciones con menos de 50 individuos se extinguieron en 50 a?os. 2) Poblaciones con m?s de 100 individuos persisti- eron hasta los 70 a?os. 3) La r?pida p?rdida de poblaciones probablemente se ha debido a falta de alimento, clima severo, predaci?n, o competencia interespec?fica Estos datos proponen que el tama?o de una poblaci?n es un marcador de trayectorias de persistencia, e indican que una extinci?n a nivel local no puede ser impedida, ya que 50 individuos no representan un tama?o de poblaci?n m?nima viable para las ovejas bighorn, a?n en el corto plazo. Paper submitted 1219188; revised manuscript accepted 4/28189. 91 Conservation Biology Volume 4, No. 1, March 1990 92 Rapid Extinctions in Bighorn Sheep Berger Introduction Methods, Sources of Data, and Limitations Concern about the long-term persistence of populations (Smith 1974; Geist 1975; Shaffer & Sampson 1985; Goodman 1987; Newmark 1987) has led to questions about the size a population should be to minimize its chances of extinction (Gilpin & Diamond 1980; Wilcox & Murphy 1985). Until now, only evidence from simu- lation models (Soul? et al. 1979; Diamond 1984; Harris et al. 1987; Iwasa & Mochhizuki 1988), from avian turn- over rates (Pimm et al. 1988), and of the historical loss of species of unknown population sizes (Brown 1971; Patterson 1984) has been available to suggest how long isolated mammalian populations persist, and it has not been possible to assess the generality of the models or conservation tactics (Lande 1988). Such assessments are important because, as ecosystems continue to be fragmented, questions arise about the spatial requisites needed to assure the sustenance of many species, and empirical data are necessary to judge the validity of ex- tinction and viability models. Historical data offer a promising approach to refining knowledge in this area. Prior use of such data was helpful in forming and testing island biogeographic theory, but the data have not been amenable to projections of persistence by population size since they usually exist in the form of records of species' or populations' occurrences where data on pop- ulation size are unavailable. Here, I use existing data on multiple, small, insular bighorn sheep populations, primarily in the deserts of southwestern North America, to examine how long lo- cal extinctions may be resisted. Although Soul? (1987) suggested that small populations are more vulnerable to extinction than large ones, neither the time frame of persistence in relation to population size nor the effects of various factors are well known for mammals. Native sheep in xeric environments are well suited for exami- nation of such issues for two principal reasons. First, they occcur in small, isolated populations and in larger metapopulations (Geist 1971) inhabiting almost contin- uous mountain chains from which historical data on population size are available. And, although "popula- tion" is defined in terms of scale and dimensionality (Soul? 1987), bighorn biologists use the word to refer to sheep confined naturally to a discrete mountainous area (which may vary from several km^ to more than 1,000 km^); I adopt this usage here. Second, food abun- dance and its changes over time can be estimated for each population because plant primary productivity is predicted by rainfall (Rosenzweig 1968; Coe et al. 1976). By using historical information it is possible to generate the data set needed to examine how long dif- ferent-sized populations persist and possible causes of extinction. I collated information on 129 native populations from five states ? California, Colorado, Nevada, New Mexico, and Texas (Table 1 ). Excluded were states where sheep now occur solely because of reintroductions by humans (Oregon and Washington), states that did not respond to my queries (Arizona), and states whose data span less than two decades (Utah). Also excluded were popula- tions for which only one size estimate was available. Populations were included only when estimates were published or provided by respective management agen- cies or university biologists who had made multiple ground or aerial censuses. Since the focus of my analyses was on persistence of native populations, I did not in- clude extant native populations for time periods after sheep had been reintroduced to them; only two Nevada populations and one New Mexico population were in this category. The sources I used were Bear & Jones (1973), Berbach (1987), Buechner (I960), Campbell (1984), Davis & Taylor (1939), Deforge et al. (1981), Dunaway ( 1970 ), Goodson ( 1982 ), Gross ( 1960 ), Jones (1950), Lenarz (1979), McQuivey (1978), Moser (1962), Ober (1931), Sands (1964), Weaver (1972), Weaver (unpublished). Weaver & Mensch (unpub- lished), Wehausen (1980, 1985), Welles & Welles (1961), California Fish and Game (unpublished), Colo- rado Division of Wildlife (unpublished). National Park Service (Death Valley), Nevada Department of Wildlife (unpublished), and New Mexico Fish and Game (un- published). To be conservative, I omitted data from an additional 94 populations since past estimates of population size were not available, even though it was known that these populations had undergone recent extinctions (We- hausen et al. 1987?). Because my goal was to estimate persistence by population size, I relied on data sources that provided actual estimates rather than those that merely noted the presence or absence of sheep. Persis- tence was estimated for each decade up to 70 years, the maximum period for which data were available. To min- imize the confounding influence of sampling intervals, only the latest annual census per decade was used. I considered a population to be extinct only after two or more censuses failed to provide evidence of its exist- ence. To estimate primary plant productivity, I used precip- itation records from CUmatography of the United States and based estimates on the stations closest to each big- horn population. Data were unavailable for 7 of the 129 populations. For each of the remaining 122 sites, rank- related correlations were used to examine the relation- ships between precipitation and time (years) (Table 1 ). Extinction frequencies for five classes of population sizes (Si) (i = 1-5: of 1-15, 16-30, 31-50, 51-100; Conservation Biology Volume 4, No. 1, March 1990 Berger Rapid Extinctions in Bighorn Sheep 93 100 + ) were estimated by asking whether each popula- tion was present (P) or extinct (E) at and over time (Tj) where j = 1?7 and refers to decades of possible persis- tence. Put simply, the probability of persistence was calculated by categorizing the presence or absence ( = extinctions) of populations by size and time as fol- lows. If S = 0 @ Tj and @ Tj + 1, then SPij = SPij + 1 and SEi = SEjj + 1. However, ifS = 0@TorT+l, then SEjj = SEjj + 1. SPij refers to the frequency of populations present, and SEjj to the frequency of extinc- tions for size i and time j. This procedure applied to N populations yields a binomial for incremental periods (in this case 10 years), but because of uneven censusing by management agencies or researchers, sample sizes differed among decades. For example, if hypothetical population X consisted of 20 animals in 1938 and was extinct in 1958 when recensused twice, then a maxi- mum persistence time of 20 years was assigned. When dealing with census data from different man- agement agencies and techniques that vary among years and habitats, it is difficult to remove potential biases and to standardize data sets. Clearly, methods used four or five decades ago will be less precise than those used today, and there is no straightforward way to deal with this problem. Therefore, 1 must assume that larger pop- ulations were more detectable than smaller ones and that any biases reported in the overestimation of popu- lations of large size should be cancelled by the effects of underestimation of populations of smaller sizes. How- ever, it is also possible to contrast data on persistence in relation to population size at different time periods. As- suming that the persistence trajectories of different- sized populations are real, then analyses based on recent and older population estimates should not differ. If this were the case, it would bolster support for the idea that population estimates, while being biased to an unlmown extent, do not alter the interpretations since patterns detected from the more recent data would be consistent with those found during censusing periods from de- cades ago. Persistence and Population Size Populations of 100 + sheep persisted for up to 70 years; those with fewer than 50 individuals went extinct in less than 50 years, while those with between 51?100 sheep existed for about 60 years (Fig. 1 ). Because, at year 60, the sample is so small (of two historic populations, none persisted), it is not possible to ascertain whether sheep in the 51?100 category fit closer to the persistence tra- jectories of the smaller or larger populations. The extinctions were related to initial population size and the number of years over which data were available (three-dimensional contingency analysis: X^ = 134.87; df = 46; p < 0.001), but except for populations of 100 + , initial population size was not independent of year (X^ = 22.10; df = 16; NS). It is also possible to test further for partial dependence (Zar 1984), not by rely- ing on the entire data set, but by using only those data for the last two decades, the time frame when census methods have presumably become more refined. While time period (in this case, two decades; Tj = 2) had otily a slight effect on persistence (X^ = 20.48; df = 12; 0.05 < p < 0.10), extinctions were not independent of initial population size (X^ = 39.87; df = 4; p < 0.001), reaf- firming that population size by itself is a reasonable marker of persistence. When data over all time periods are considered, a positive relationship between popula- tion size and persistence time existed (Fig. 1; r^ = + 0.54; p < 0.0005). Hence, these data offer the strong- est evidence yet that native populations below a thresh- old size (N = 50) are unable to resist rapid extinction. Tests of Potential Causes of Rapid Population Losses To what extent do the persistence times reflect recol- onization rather than extinction? Undoubtedly, preci- sion is lost by lack of knowledge of recolonization fre- quency. However, the persistence estimates are conservative and underestimate population losses be- cause any recolonization would result in increased per- sistence rather than local extinction. Furthermore, the available data indicate that extinction has far out- stripped recolonization, 34 to 2 (one-tailed binomial test; p < 0.001), although recolonizations often go un- detected (Bleich et al. 1990). Four variables that may mediate the rapid demise of these small populations may be examined: ( 1 ) climatic severity, (2) food shortages, (3) pr?dation, and (4) in- terspecific competition. None of these appears to be causally related to the rapid extinctions. If the demises were a consequence of severe weather, then popula- tions in areas of extreme conditions should be in greater jeopardy than those where conditions are more benign. I examined this possibility by contrasting environmental severity (as measured by the mean number of annual days in which mean maximum daily temperature was below or above 0? C) between populations greater and less than 50 sheep. Since 10 percent (N = 50) of the small populations occupied areas where temperatures fell below 0? C for more than one month on average (in contrast to 44 percent [N = 62] of the larger popula- tions: Z = 3.97; p < 0.0001 ), it is unlikely that climatic factors were the primary reason for the rapid loss of small populations. Perhaps declining food supplies were responsible, es- pecially because evidence from one desert population indicates that few lambs are recruited when precipita- tion is low (Douglas & Leslie 1986). If this were the case Conservation Biology Volume 4, No. 1, March 1990 94 Rapid Extinctions in Bighorn Stieep Berger Table 1. Summary of location, year of first population census, and number of years of precipitation data (N), r, values, and probability tliat precipitation changes over time were significant; NS = not significant; *p < 0.05; **p < 0.02; ***p < 0.001. Site Year A' ^s P Site Year N fs P California 62 Santa Rosa 1957 0 1 Argus Ra 1957 24 -.02 NS 63 Shadow Mts 1938 20 + .43 * 2 Avawatz Ra 1957 26 + .30 NS 64 Sheep Hole 1957 30 + .34 NS 3 Baxter Cr 1915 40 + .01 NS 65 Slate Ra 1957 14 -.11 NS 4 Big Maria Mts 1946 23 + .05 NS 66 Stepladder 1957 13 -.20 NS 5 Birch Mtn 1911 50 -.21 NS 67 Taboose Cr 1948 24 -.02 NS 6 Black Mts 1957 26 + .18 NS 68 Tierra Bine 1957 0 7 Bristol Mts 1957 30 + .34 NS 69 Turtle Mts 1957 24 + .29 NS 8 Bullion Mts 1957 30 + .34 NS 70 Vallecito 1957 30 + .42 * 9 Cache Pk 1933 16 -.11 NS 71 Wheeler Ri 1921 20 -.09 NS 10 Cady Mts 1957 23 + .13 NS 72 Whipple Mts 1946 41 + .29 NS 11 Castle Pk 1957 27 + .40 ** 73 White Mts 1970 17 + .35 NS 12Chemehuevi Mt 1957 30 + .37 * 74 Woods Mtn 1974 12 + .31 NS 13 Chocolate Mts 1957 30 + .42 * 14 Chuckwalla Mt 1957 30 + .21 NS Colorado 15 Clark Mts 1957 29 + .17 NS 16 Clipper Mts 1957 29 + .37 ? 1 Arkansas R 1954 30 -.01 NS 17 Coso Ra 1957 24 -.02 NS 2 Battlement 1956 31 + .23 NS ISCottonwood Mt 1957 26 + .18 NS 3 Black Cyn 1953 29 -.06 NS 19 Coxcomb Mts 1974 12 + .37 NS 4 Brush Cr 1947 21 + .50 ? 20 Dead Mts 1957 30 + .37 * 5 Buffalo Pks 1956 24 + .16 NS 21 Deep Springs 1946 35 + .04 NS 6 Cimarr?n Pk 1956 31 + .23 NS 22 Eagle Crags 1957 24 -.02 NS 7 Clinetop 1955 30 + .51 *?* 23 Eagle Mts 1974 12 + .39 NS 8 Elkshead Mt 1955 0 ? 24 Funeral Mts 1957 26 + .18 NS 9 Gore Ra 1955 24 + .16 NS 25 Granite Mts 1957 22 + .28 NS 10 Lake City 1969 17 + .33 NS 26 Granite Mts 1946 20 + .43 NS 11 Mt Zirkel 1956 15 -.03 NS 27 Grapevine Mts 1957 26 + .18 NS 12 Pikes Peak 1954 30 -.01 NS 28 Hackberry Ra 1969 16 + .58 ** 13 Pole Mtn 1941 37 + .33 * 29 Inkopah 1974 13 + .35 NS 14 Redstone 1962 18 + .07 NS 30 Inyo Mts 1957 29 + .04 NS 15 Roan Plateau 1954 17 + .32 NS 31 Iron Mts 1957 29 + .34 NS 16 Rocky Mtn NP 1955 30 + .11 NS 32 Ivanpah 1974 12 + .31 NS 17 San Luis Peak 1970 17 -.10 NS 33 Kelso Ra 1957 26 + .30 NS 18 Sangre d Crst 1956 31 + .23 NS 34 Kingston Ra 1957 26 + .30 NS 19 Sheep Mtn 1961 26 -.04 NS 35 Laguna Mts 1957 18 -.33 NS 20 Snowmass 1955 24 + .16 NS 36 Last Chance 1957 29 + .04 NS 21St. Vrain 1958 13 -.02 NS 37 Ut?e Maria 1946 23 + .05 NS 22 Vallecito 1968 19 -.38 NS 38 Littie San B 1974 12 + .37 NS 23 Waterton Cyn 1956 0 ? 39 McCoy Mts 1946 23 + .05 NS 24 West Elk Mts 1958 25 + .12 NS 40 Mt Langley 1947 32 + .04 NS 41 Mt Tom 1920 21 -.24 NS Nevada 42 Mt Williamson 1947 40 + .01 NS 43 New York Mts 1957 27 + .40 ? ? 1 Black Mts 1976 10 -.08 NS 44 Nopah Ra 1957 29 + .17 NS 2 Delamar Ra 1976 10 -.32 NS 45 Olancha Pk 1926 14 + .10 NS 3 Desert Ra 1976 10 -.32 NS A6 Old Dad Mts 1957 30 + .34 NS 4 East Desert 1976 10 -.32 NS 47 Old Women 1957 30 + .34 NS 5 El Dorado Ra 1976 10 -.08 NS 48 Orcopia Mts 1957 30 + .21 NS 6 Grant Ra I960 26 + .53 *? 49 Owlshead Mt 1957 23 + .13 NS 7 Highland Ra 1976 10 -.08 NS 50 Palen Mts 1946 40 + .38 ** 8 Lone Mtn 1976 10 -.20 NS 51 Panamint Ra 1957 26 + .18 NS 9 Las Vegas Ra 1976 10 -.32 NS 52 Pichacho Mt 1957 17 -.33 NS 10 McCuUough Ra 1976 10 -.08 NS 53 Pinto Ra 1974 12 + .37 NS 11 Meadow Valley 1976 10 -.32 NS 54 Piute Ra 1957 27 + .40 m? 12 Monte Carlo 1976 10 -.20 NS 55 Providence 1957 30 + .37 * 13 Mormon Mts 1974 12 -.12 NS 56 QuaU Mts 1957 18 -.12 NS 14 Muddy Mts 1976 10 -.32 NS 57 Queen Mts 1974 0 ? 15 Newberry Ra 1976 10 -.32 NS 58 Sacramento 1957 29 + .01 NS 16 Pintwater Ra 1976 10 -.32 NS 59 San Brnadno 1957 30 + .34 NS 17SUver Peak 1955 30 + .62 *** 60 San Gabriel 1957 0 ? 18 Spring Ra 1976 10 -.32 NS 61 San Ysidro 1957 30 + .42 * 19 Toiyabe Ra 1958 26 + .53 *? Conservation Biology Volume 4, No. 1, March 1990 Berger Rapid Extinctions in Bighorn Sheep 95 Table 1. Continued. Site Year N rs P Site Year N rs P Texas 8 Glass Mts 1937 21 + .19 NS 9 Guadalupe 1937 25 + .08 NS 1 Apache 1937 25 + .08 NS 10 Sierra Diab 1937 25 + .08 NS 2 Baylor Mts 1937 25 + .08 NS 3 Beach Mts 1937 25 + .08 NS 4 Carrizo 1937 25 + .08 NS New Mexico 5 Chinatic 1937 21 + .19 NS 6 Delaware 1937 25 + .08 NS 1 Big Hatchet 1953 28 + .37 ? 7 Eagle Mts 1937 25 + .08 NS 2 San Andreas 1941 31 + .47 ** Weatherstations used in the above were located at: (California) Baker, Barstow, Bishop, Bishop Creek, Blythe, Death Valley, El Centro, Lone Pine, Needles, Twentynine Palms; (Colorado) Alamosa, Aspen, Canon City, Delta, Estes Park, Grand Junction, Lake City, Montrose, Rifle; (Nevada) Austin, Las Vegas, Searchlight, Tonopah; (New Mexico) Jornada Experiment Station; (Texas) Pecos, Van Horn. for the populations that I examined, then a negative relationship between food abundance at each site and time should be characteristic of populations experienc- ing extinctions. Also, larger populations should not be associated with declining food abundance because it is the smaller populations that are more susceptible to extinction (Fig. 1). Annual precipitation was used as an indicator of food abundance since it is a good predictor of primary productivity in xeric environments (Rosen- zweig 1968; Coe et al. 1976), and data on precipitation were available as far back as 1915. At none of the 122 sites was the relationship between estimated primary productivity and time negative, suggesting that declin- ing food was not responsible for the extinctions (Table 1). In contrast, 17 percent of the 122 sites had increas- ing estimated plant productivity and 5 (all with fewer than 50 sheep) experienced extinction (Table 2). No association occurred between the size of extinct popu- lations and estimated plant productivity (G^^j = 0.12; df = 1; NS; Table 2). This nonsignificant relationship re- mains unaltered by exclusion of populations from Col- orado where precipitation is often in the form of snow. A^ile numerous factors may account for the demises of small populations, neither food nor weather appears to be among them. The last two potential factors responsible for the rapid extinctions, pr?dation and interspecific competi- tion, appear to have played minor roles, if any. Though accounts of pr?dation on sheep are available (Murie 1944; Geist 1971; Kelly 1980), carnivore densities are linked to prey biomass (Hornocker 1970; Sunquist & Sunquist 1989). Where sheep densities are low, as in the Mohave desert, and populations are declining, no evi- dence indicates that pr?dation effectively reduces pop- ulation size, especially because prey items vary with availability (Stephens & Krebs 1986). And, while moun- tain lions {Felis concolor) are thought to be more effi- cient predators of sheep than are coyotes {Cams la- trans) (McCutchen 1982; Berger 1990), lions do not occur in many of the desert ranges where sheep are found (SmaUwood & Fitzbugh 1987). Finally, if inter- specific food competition were responsible for demises of native sheep, cattle or other herbivores should cooc- cupy sheep habitat and share the same food. Although cattle (and wild horses) prefer grasses, as do native sheep (Bailey 1980; Hanley & Hanley 1982), these spe- cies occupy different habitats, and interspecific effects on sheep population size have yet to be demonstrated (Berger 1986). Potential Genetic and Etiological Effects In contrast to the negative evidence given above, some data suggest that both genetic (Schwartz et al. 1986) 30 40 50 TIME (YRS) Figure 1. Relationships between time and the per- centage of populations persisting according to five population size categories. Sample sizes for each cat- egory at 10-year intervals as follows: 1?15 individu- als: 53, 54, 40, 19, 7, 4, 0; 16-30 individuals: 32, 30, 20, 8, 5, 4, 1; 31-50 individuals: 41, 34, 18, 14, 8, 4, 1; 51-100 individuals: 43, 26, 16, 8, 4, 2, 0; 100 + individuals: 67, 44, 20, 11, 2, 1, 1. Dotted lines re- flect samples based on less than four populations. Conservation Biology Volume 4, No. 1, March 1990 96 Rapid Extinctions in Bighorn Sheep Berger Table 2. Summary of effects of significant (p < 0.05) trends in estimated plant productivity (PP) over periotk of demographic censuses for 122 bighorn sheep populations. Small < 50 sheep; lai^e > 50 sheep. (See Table 1 for locations and relationships between estimated PP and time.) Percentage of total sample Number of extinctions Small Large PP increasing (N = 21) PP decreasing (N = 0) No relationship (N = 101) 17.2 0 82.8 5 0 24 0 0 5 G^j = . 12; NS, for comparison of population extinctions in relation to increasing PP versus all populations with no relationship to PP. and etiological (Foreyt & Jessup 1982; Clark et al. 1985; Wehausen et al. 1987?) factors influence bighorn repro- duction and survival, and, presumably, these affect per- sistence. In captivity, inbred bighorns suffer higher ju- venile mortality than those from less inbred lines (Sausman 1984). Whether this occurs in field popula- tions is unknown, but questions about population size and potential genetic effects can be examined because small founding populations are reintroduced (by wi\?- life managers) back into the same locations where na- tive sheep become extinct (Leslie 1980; Gray 1986). If population size per se were responsible for the lack of persistence, then both native and reintroduced small populations should persist for similar time frames. I ex- amined this prediction by contrasting minimum persis- tence times of 57 reintroduced populations (from Cal- ifornia, Colorado, Nevada, Oregon, and South Dakota) with native ones matched for Sj of 8-15 and 16-30. Reintroduced populations succeeded better at 10 and 20 years (G = 16.79; df = 3; p < 0.05 and 5.03; 0.05 < p < 0.10). These differences cannot be explained solely by habitat variation or by reintroduction of sheep into areas where cattle grazing is not permitted: in Nevada alone, 11 of 14 reintroductions into areas of historical bighorn occupation were successful despite cattle graz- ing during both population declines of native sheep and reintroductions. However, two unsuccessful transplants occurred in areas of domestic sheep use. Because founders are often from larger and presumably more heterozygous populations, genetic factors may indeed underlie the differences in success between populations founded by humans and declining native populations. If this view is correct, then greater genetic diversity may buffer against rapid extinction, a hypothesis that can only be tested rigorously when habitat conditions are controUed (Wakelyn 1987). Evidence that indirectly implicates etiological factors is diverse, including examples of widespread extirpa- tions when native sheep were exposed to domestic sheep (Goodson 1982; Foreyt & Jessup 1982) and to avenues of viral infection promoted by cattle (We- hausen et al. 1987?). Unfortunately, such evidence re- mains indirect and in need of rigorous testing (but see Onderka & Wishart 1988; Onderka et al. 1988). Conclusions The data presented here illustrate that population size can be used to gauge the persistence of populations, especially when factors such as inclement weather, food shortages, pr?dation, or interspecific competition fail to exacerbate extirpation. Nevertheless, it is clear that small (and especially single) mammalian populations are in imminent need of enhanced management to max- imize their persistence. Data for numerous species, in- cluding bighorn sheep and the sole deme of black- footed ferrets {Mustela nigripes) (Clark 1987; Thorne & Williams 1988), confirm that exposure to extrinsic factors, notably epizootics, precipitates sweeping local- ized and rapid extirpation. If small, fragmented populations are to be conserved, then it no longer seems wise to await the accumulation of additional demises to determine whether such pop- ulations of other species become extinct as rapidly as native sheep. Nevertheless, it is important to recognize that species differing from sheep in body size, genera- tion times, fecundity, trophic levels (Belovsky 1987), and perhaps economic status should differ in persis- tence times. Presently, data for other mammals are lack- ing, but historical approaches may prove to be one way to evaluate the generality of persistence models, per- haps through use of information on widely fluctuating population sizes in species such as voles, lagomorphs, and mice. Acknowledgments I thank the following people and agencies for graciously offering advice, support, and access to their data: Cali- fornia Department of Fish and Game (V. Bleich, R. Weaver), Colorado Division of Wildlife (M. Elkins, J. EUenberger, R. Hernbrode, J. Olterman), Nevada De- partment of Wildlife (D. Delaney, M. Hess, G. Tsuku- moto), and New Mexico Fish and Game (B. Morrison). I benefited greatly from the critical advice or manu- script reviews offered by Carol Cunningham, Charles Douglas (National Park Service), David Ehrenfeld, Marco Festa-Bianchet, Valerius Geist, Stephen Jenkins, Linda Kerley, Hal Kleiforth, Craig Packer, Ann Pusey, Robin Tausch, John Wehausen, and an anonymous re- viewer, and I wish to say thank you! Literature Cited Bailey, J. A. 1980. Desert bighorn, forage competition and zoo- geography. Wildlife Society Bulletin 8:208-216. Conservation Biology Volume 4, No. 1, March 1990 Berger Rapid Extinctions in Bighorn Sheep 97 Bear, G. D., and G. W. Jones. 1973. History and distribution of bighorn sheep in Colorado. Colorado Division of Wildlife, Denver. Belovsky, G. E. 1987. Extinction models and mammalian per- sistence. Pages 35?57 in M. E. Soul?, editor. Viable popula- tions for conservation. Cambridge University Press, New York. Berbach, M. W. 1987. The behavior, nutrition, and ecology of a population of reintroduced desert mountain sheep in the Whipple Mountains, San Bernadino County, California. M.S. thesis. California State University, Pomona. Berger, J. 1986. Wild horses of the Great Basin: social compe- tition and population size. University of Chicago Press, Chi- cago, Illinois. Berger, J. 1990. Pregnancy incentives and pr?dation con- straints in habitat shifts: experimental and field evidence for wild bighorn sheep. Submitted for publication. Bleich, V. C, J. D. Wehausen, and S.A. Holl. 1990. Desert- dwelling mountain sheep: conservation implications of a nat- urally fragmented distribution. Submitted for publication. Brown, J. H. 1971. Mammals on mountaintops: nonequilibrium insular biogeography. American Naturalist 105:467-478. Buechner, H. K. I960. The bighorn sheep in the United States, its past, present, and future. Wildlife Monographs 4:1-174. Campbell, T. G. 1984. A report on the reintroduction of big- horn sheep onto the Naval Weapons Center, China Lake, Cal- ifornia. Desert Bighorn Council Transactions 28:55?56. Clark, T. W. 1987. The black-footed ferret recovery: a progress report. Conservation Biology 1:8-11. Coe, M.J., D.H. Cummings, and J. Phillipson. 1976. Biomass and production of large African herbivores in relation to rain- fall and primary production. Oecologia 22:341-354. Davis, W. B., and W. P. Taylor. 1939. The bighorn sheep of Texas. Journal of Mammalogy 20:440-455. Deforge, J. R., J. Scott, G. W. Sudmeier, R. L. Graham, and S. V. Segreto. 1981. The loss of two populations of desert bighorn sheep in California. Desert Bighorn Council Transactions 25:36-38. Diamond, J. M. 1984. "Normal" extinctions of isolated popu- lations. Pages 191-246 in M. H. Nitecki, editor. Extinctions. University of Chicago Press, Chicago, Illinois. Douglas, C. L., and D. M. Leslie, Jr. 1986. Influences of weather and density on lamb survival of desert mountain sheep. Journal of W?dUfe Management 50:153-156. Dunaway, D.J. 1970. Status of bighorn sheep populations and habitat studies on the Inyo National Forest. Desert Bighorn Council Transactions 14:127?146. Foreyt, W.J., and D. A. Jessup. 1982. Fatal pneumonia of big- horn sheep following association with domestic sheep. Journal of WUdlife Diseases 18:163-168. Geist, V. 1971. Mountain sheep. University of Chicago Press, Chicago, Illinois. Geist, V. 1975. On the management of mountain sheep; theo- retical considerations. Pages 77?98 in J. B. Trefethen, editor. The wild sheep in modern North America. Boone and Crocket Club, Alexandria, Virginia. Gilpin, M. E., and J. M. Diamond. 1980. Subdivision of nature reserves and the maintenance of species diversity. Nature 285:567-568. Goodman, D. 1987. How do any species persist? Lessons for conservation biology. Conservation Biology 1:59?62. Goodson, N.J. 1982. Effects of domestic sheep grazing on big- horn sheep: a review. Biennial Symposium of the North Amer- ican Wild Sheep and Goat Council 3:287-313. Gray, J. 1986. Status of bighorn sheep in Colorado, 1985. Des- ert Bighorn Council Transactions 30:22. Gross, J. E. i960. History, present and fiiture status of the des- ert bighorn sheep {Ovis canadensis mexicana) in the Gua- dalupe Mountains of southwestern New Mexico and north- western Texas. Desert Bighorn Council Transactions 4:66-71. Hanley, T. A., and K. A. Hanley. 1982. Food resource partition- ing by sympatric ungulates on Great Basin rangeland. Journal of Range Management 35:152-158. Harris, R. B., L. A. Maguire, and M. L. Shaffer. 1987. Sample sizes for minimum viable population estimation. Conservation Biol- ogy 1:72-76. Hornocker, M. E. 1970. An analysis of mountain lion pr?dation upon mule deer and elk in the Idaho Primitive area. Wildlife Monographs 21:1?39. Iwasa, Y., and H. Mochizuki. 1988. Probability of population extinction accompanying a temporary decrease of population size. Researches on Population Ecology 30:145-164. Jones, F. L. 1950. A survey of the Sierra Nevada bighorn. Sierra Club Bulletin 35:29-76. Kelly, W. E. 1980. Predator relationships. Pages 186-196 in G. Monson and L. Sumner, editors. The desert bighorn. University of Arizona Press, Tucson. Lande, R. 1988. Genetics and demography in biological con- servation. Science 24:1455-1460. Lenarz, M. S. 1979. Social structure and reproductive strategies in desert bighorn sheep {Ovis canadensis mexicana). Journal of Mammalogy 60:671-678. Leslie, D. M., Jr. 1980. Remnant populations of desert bighorn sheep as a source for transplantation. Desert Bighorn CouncU Transactions 24:36-43. McCutchen, H. E. 1982. Behavioral ecology of reintroduced desert bighorns, Zion National Park, Utah. Ph.D. dissertation. Colorado State University, Fort Collins. McQuivey, R. P. 1978. The desert bighorn sheep of Nevada. Nevada Fish and Game Biological Bulletin 6:1?81. Conservation Biology Volume 4, No. 1, March 1990 98 Rapid Extinctions in Bigborn Sheep Berger Moser, CA. 1962. The bighorn sheep of Colorado. Colorado Department of Fish and Game Technical Publication 10:1?48. M?rie, A. 1944. The wolves of Mount McKinley. U.S. National Park Fauna Series 5:1-238. Newmark, W. D. 1987. A land-bridge island perspective on mammalian extinctions in western North American parks. Na- ture 325:430-432. Ober, E. 1931- The mountain sheep of California. California Fish and Game Bulletin 17:27-39. Onderka, D. K., and W. D. Wishart. 1988. Experimental contact transmission of Pasteurella haemolytica from clinically nor- mal domestic sheep causing pneumonia in Rocky Mountain bighorn sheep. Journal of Wildlife Diseases 24:663?667. Onderka, D. K., S. A. Rawluk, and W. D. Wishart. 1988. Suscep- tibility of Rocky Mountain bighorn sheep and domestic sheep to pneumonia induced by bighorn and domestic livestock strains o? Pasteurella haemolytica Canadian Journal of Veter- inary Research 52:439-444. Soul?, M.E. 1987. Introduction. Pages 1-10 in M. E. Soul?, editor. Viable populations for conservation. Cambridge Uni- versity Press, Cambridge, England. Soul?, M. E., B. A. Wilcox, and C. Holtby. 1979. Benign neglect: a model of faunal collapse in the game reserves of East Africa. Biological Conservation 15:259-272. Stephens, D. W., and J. R. Krebs. 1986. Foraging theory. Prince- ton University Press, Princeton, New Jersey. Sunquist, M. E., and F. C. Sunquist. 1989. Ecological constraints on pr?dation by large felids. Pages 283?301 in J. L. Gittleman, editor. Carnivore behavior, ecology, and evolution. Cornell University Press, Ithaca, New York. Thorne, E. T., and E. S. Williams. 1988. Disease and endangered species; the black-footed ferret as a recent example. Conser- vation Biology 2:66-74. Wakelyn, L. A. 1987. Changing habitat conditions on bighorn sheep ranges in Colorado. Journal of Wildlife Management 51:904-912. Patterson, B. D. 1984. Mammalian extinction and biogeogra- phy in the southern Rocky Mountains. Pages 247-293 in M. H. Nitecld, editor. University of Chicago Press, Chicago, Illinois. Weaver, R. A. 1972. Conclusions of the bighorn sheep inves- tigation in California. Desert Bighorn Councu Transactions 16:56-65. Pimm, S. L., H. L. Jones, and J. Diamond. 1988. On the risk of extinction. American Naturalist 132:757?785. Rosenzweig, M. L. 1968. Net primary production of terrestrial communities: prediction from cUmatological data. American Naturalist 102:67-74. Sands, J. L. 1964. Current status of desert bighorn sheep in New Mexico. Desert Bighorn Council Transactions 8:123? 125. Wehausen, J. D. 1980. Sierra Nevada bighorn sheep: history and population ecology. Ph.D. dissertation. University of Mich- igan, Ann Arbor. Wehausen, J. D. 1985. Bighorn sheep in the White Mountains: past and recent history. Pages 180-182 in C. A. Hall, Jr., and D. J. Young, editors. Natural history of the White-Inyo Range, Eastern California and Western Nevada and High Altitude Physiology. University of California White Mountain Research Station Symposium, Volume 1, Bishop, California. Sausman, K. A. 1984. Survival of captive-born Ovis canadensis in North American zoos. Zoo Biology 3:111-121. Schwartz, O. A., V. C. Bleich, and S. A. HoU. 1986. Genetics and the conservation of mountain sheep Ovis canadensis nelsoni Biological Conservation 37:179-190. Shaffer, M. L, and F. B. Sampson. 1985. Population size and extinction: a note on determining critical population size. American Naturalist 125:144?152. Smallwood, K. S., and E. L. Fitzbugh. 1987. A statewide moun- tain lion index technique. Unpublished Final Report, California Fish and Game, Sacramento. Smith, A. T. 1974. The distribution and dispersal of pikas: con- sequences of insular population structure. Ecology 55:1112? 1119. Wehausen, J. D., V. C. Bleich, B. Blong, and T. L. Russi. 1987a Recruitment dynamics in a southern California mountain sheep population. Journal of Wildlife Management 51:86-98. Wehausen, J. D., V. C. Bleich, and R. A. Weaver. 1987fe Moun- tain sheep in California: a historical perspective on 100 years of full protection. Transactions of the Western Wildlife Society 23:65-74. Welles, R. E., and F. B. Welles. 1961. The bighorn sheep of Death Valley. U.S. National Parks Fauna Series 6:1?242. Wilcox, B. A., and D. D. Murphy. 1985. Conservation strategy: the effects of fragmentation on extinction. American Naturalist 125:879-887. Zar, J. H. 1984. Biostatistical analysis. Prentice-Hall, Engle- wood Cliffs, New Jersey. Conservation Biology Volume 4, No. 1, March 1990