North American Journal of Fisheries Management 21:756±764, 2001 ᭧ Copyright by the American Fisheries Society 2001

Effective Population Size and Genetic Conservation Criteria for Bull Trout

B. E. RIEMAN* U.S. Department of Agriculture Forest Service, Rocky Mountain Research Station, 316 East Myrtle, Boise, Idaho 83702, USA

F. W. A LLENDORF Division of Biological Sciences, University of Montana, Missoula, Montana 59812, USA

Abstract.ÐEffective population size (Ne) is an important concept in the management of threatened species like bull trout Salvelinus con¯uentus. General guidelines suggest that effective population sizes of 50 or 500 are essential to minimize inbreeding effects or maintain adaptive genetic

variation, respectively. Although Ne strongly depends on census population size, it also depends on demographic and life history characteristics that complicate any estimates. This is an especially dif®cult problem for species like bull trout, which have overlapping generations; biologists may monitor annual population number but lack more detailed information on demographic population

structure or life history. We used a generalized, age-structured simulation model to relate Ne to adult numbers under a range of life histories and other conditions characteristic of bull trout populations. Effective population size varied strongly with the effects of the demographic and

environmental variation included in our simulations. Our most realistic estimates of Ne were between about 0.5 and 1.0 times the mean number of adults spawning annually. We conclude that cautious long-term management goals for bull trout populations should include an average of at least 1,000 adults spawning each year. Where local populations are too small, managers should seek to conserve a collection of interconnected populations that is at least large enough in total to meet this minimum. It will also be important to provide for the full expression of life history variation and the natural processes of dispersal and gene ¯ow.

The concept of effective population size (Ne) netic variation in populations with small Ne may plays an important role in conservation manage- reduce ®tness through the so-called inbreeding ef- ment of ®shes (Waples in press). The Ne is a mea- fect of small populations and lead to an acceler- sure of the rate of genetic drift and is directly ating decline toward extinction in a process termed related to the rate of loss of genetic diversity and an extinction vortex (Soule and Mills 1998). the rate of increase in inbreeding within a popu- Because of the importance of Ne, the so called lation (Wright 1969). Conservation of populations ``50/500'' rule has emerged as general guidance large enough to minimize such effects has become in conservation management (Franklin 1980; Sou- an important goal in the management of threatened le 1980; Nelson and Soule 1987; see Allendorf and or endangered salmonids, including Paci®c salmon Ryman [in press] for a recent consideration of Oncorhynchus sp. (McElhaney et al. 2000) and bull these criteria). The generally accepted view is that trout Salvelinus con¯uentus (USFWS 1998). an N of less than about 50 is vulnerable to the The ongoing fragmentation and isolation of hab- e immediate effects of inbreeding depression. Al- itat of species like bull trout have led to reductions though populations might occasionally decline to in population size (Rieman and McIntyre 1993; numbers on this order without adverse effects, Rieman et al. 1997) and presumably in N for many e maintenance of adaptive genetic variation over populations. A resulting loss of genetic variation longer periods of time (e.g., centuries) probably can in¯uence the dynamics and persistence of pop- ulations through at least three mechanisms: in- will require an Ne averaging more than 500 (Al- breeding depression, loss of phenotypic variation lendorf and Ryman in press). These numbers have and plasticity, and loss of evolutionary potential been generally applied as criteria for determination (Allendorf and Ryman in press). The loss of ge- of conservation status among taxa (Mace and Lande 1991) and within the salmonids in particular (e.g., Allendorf et al. 1997; Hilderbrand and Ker- * Corresponding author: [email protected] shner 2000).

Received September 12, 2000; accepted February 19, 2001 The problem in application is that Ne and the 756 POPULATION SIZE AND CONSERVATION OF BULL TROUT 757 number of adult ®sh usually represented in pop- of population sizes and life history conditions ulation estimates (N) are not equal. Estimation of characteristic of species like bull trout. We were

Ne and even N can be complicated. Direct esti- primarily interested in estimating the ratio of Ne mation of Ne is possible but requires either detailed to the number of adults that might be observed in information on population demographics and typical monitoring efforts concerned with conser- breeding structure (Harris and Allendorf 1989; Ca- vation and the application of population size cri- ballero 1994) or extensive information on genetic teria. We use our results to show how managers population structure (Waples 1991; Laikre et al. can interpret annual estimates of adult abundance 1998; Schwartz et al. 1998). Limitations of sample or spawning escapements in light of existing con- size requirements, the resolution possible for all servation genetic theory and general knowledge of but very small populations, and time and analytical bull trout life history. costs may restrict the utility of these methods. As a result, application of population size criteria of- Methods ten relies on approximations of Ne based on ex- isting estimates of N and population simulation Estimation of Ne.ÐIn an ``ideal'' population, the expected loss of genetic variation (represented as methods (Harris and Allendorf 1989). Even if Ne is assumed to be some fraction of N based on other heterozygosity) per generation is ⌬H ϭϪ1/2N, work, the estimation of N can still be unclear. where N is the size of the adult population (Wright The life history patterns of most salmonids are 1969). For example, an ideal population of 10 complex. Paci®c salmon adults spawn and die, but adults would be expected to lose 1/(2 ϫ 10), or except for pink salmon Oncorhynchus gorbuscha, 5%, of its heterozygosity in one generation. An there is overlap among cohorts that mature at var- ideal population is one with discrete generations iable ages. The adult population is replaced each (all adults reproduce once and at the same age), year, but a single generation will encompass mul- random mating, equal sex ratio, constant popula- tiple spawning years. Trout and char, including tion size, and an equal probability for all adults to bull trout, may spawn several times. Age at ma- contribute offspring to the next generation (Ca- turity varies among individuals, and once mature, ballero 1994; Frankham 1995). Most populations not all surviving individuals will spawn in all do not ®t the ideal. years. Although new adults are recruited each year, To address this reality, effective population size the adult population as a whole is replaced grad- is de®ned as the size of the ideal population that ually through time (Laikre et al. 1998). will result in the same amount of genetic drift as Waples (1990) has shown for Paci®c salmon, in the actual population being considered (Wright 1969). Natural populations can deviate strongly which die after spawning, that Ne ϭ g ϫ Nb, where g is the average age of spawning or generation from conditions of the ideal. Family size (some adults produce more offspring than others), for ex- length, and Nb is the mean effective number of spawners per year. An appropriate estimate of N ample, is likely to vary substantially in salmonid would be the mean number of adults observed ®shes (e.g., Geiger et al. 1997). Strong temporal variation in population size can have a particularly across years times g. Hill (1972) showed that Ne in iteroparous species can be approximated by the important in¯uence as well (Crow and Denniston number of ®rst-time spawners entering the popu- 1988; Frankham 1995; Ray 2001). As a result Ne lation each generation (i.e., the mean number of is expected to be smaller than the actual census ®rst time spawners times g). For managers the in- number for most cases. terpretation of N may still remain obscure for spe- We used a simulation approach to track the loss cies that spawn multiple times. Even detailed in- of genetic variation in relation to total adult num- ventory and monitoring projects cannot routinely ber for a series of hypothetical bull trout popu- discriminate between ®rst-time and repeat spawn- lations. Our results provided an estimate of the ing individuals. ratio of Ne to the number of adults that might ac- In our work with bull trout, a recent addition to tually be observed or estimated in annual popu- the threatened species list under the Endangered lation monitoring. We used a range of simulations Species Act of the United States (USFWS 1998), representative of the range of life history char- application of population conservation criteria acteristics believed to exist in bull trout popula- (i.e., 50/500) was limited by these problems. Our tions (Pratt 1985, 1992; Fraley and Shepard 1989). objective was to describe the expected loss of ge- We used the observed rate of loss of heterozygosity netic variation and to approximate Ne for a range and the generation length to estimate the inbreed- 758 RIEMAN AND ALLENDORF ing effective population size (Crow and Kimura TABLE 1.ÐSpawning ages, adult survival, and resulting 1970:345) based on the following formula: mean generation time used to estimate effective population size for bull trout in simulations with and without envi- H ϭ H ´[1 Ϫ (1/2N )]t (1) ronmental variation. All simulations were initiated with a t 0 e starting population of half the carrying capacity except for where H is the heterozygosity after t generations, S2, which was initiated at carrying capacity. S2 was not t included in the second set of simulations, which incorpo- and H0 is the initial heterozygosity (standardized rated environmental variation, reduced frequency of fe- at 1.0). In our analyses, t was the total length of male spawning, and reduced spawning success in males. the simulated period divided by the average gen- All other parameter values used in the simulations are ex- eration time. plained in the text. The model.ÐVORTEX is a stochastic, age- Annual Mean structured, population simulation model that tracks Simu- Spawn- adult generation the genetic structure of an entire population by lation ing ages survival time following the history of each individual (Miller S1 4±7 0.50 4.73 and Lacy 1999). This ¯exible simulation program S2 4±7 0.50 4.73 incorporates demographic stochasticity at each in- S3 7±10 0.50 7.73 S4 5±8 0.50 5.73 dividual life history event and user-de®ned levels S5 5±8 0.20 5.32 of variation in age- and sex-speci®c mortality, mat- S6 5±12 0.50 5.97 uration schedule, and population carrying capac- S7 5 0.00 5.00 ity. The genetic composition of a population is tracked at a single locus in each simulation. At the spawn every year or in alternate years after ®rst initiation of a simulation, each individual in the maturity (Rieman and McIntyre 1993). In our anal- population is assigned two unique alleles. Matings ysis we used combinations of maturity and lon- are random, but the relative contribution of males gevity that included ®rst maturity at 4, 5, and 7 and females can vary with age. Alleles are trans- years of age, with the ®sh spawning only once or, mitted in random Mendelian fashion, and the fate alternatively, for as many as ®ve subsequent years. of each allele is tracked through the pedigree of In simulations with only demographic stochastic- surviving individuals. Summary results include ity, we assumed that 100% of females spawned mean population size and growth rate (and their each year once mature. In a second series of sim- standard deviations [SDs]), mean number of ulations used to characterize the variation possible adults, expected and observed heterozygosity as a in family size and adult number (see section on proportion of initial condition, and a variety of simulation approach), we assumed that 50% of fe- statistics related to population extinctions. More males were expected to spawn in any year, equiv- detail on VORTEX is available from Lindemayer alent to every-other-year spawning cycles. All et al. (1995) and Miller and Lacy (1999). males were assumed to contribute to spawning in Parameter estimates and simulation approach.Ð the ®rst series, but only 50% of males were ex- We did not conduct an exhaustive study of all pos- pected to be successful in the second. Although sible population conditions or produce a precise males may actually return every year, it would not characterization of any particular population. be unusual to ®nd that not all compete successfully Rather we used the simulations to generate a range for mates. We assumed a sex ratio in all simula- of results that would span those most likely for tions of 1:1, with males and females maturing at bull trout populations. We parameterized the mod- the same age. el to represent the range of life histories that are Survival.ÐAnnual survival of bull trout popu- reasonable, given existing knowledge (Table 1). lations has rarely been estimated, but data from Our rationale is explained below. Pratt (1985) suggest that survival ranges between Maturity and longevity.ÐBull trout are thought 0.30 and 0.70 for subadult ®sh. We assumed that to live at least 7 or 8 years and to begin maturing survival improved from the low to high end of this between ages 4 and 7 years (Fraley and Shepard range as ®sh progressed from age 1 to maturity. 1989; Pratt 1992; Rieman and McIntyre 1993). In From our own work with population estimates of our own work on Pend Oreille Lake, Idaho, we spawning adults, immediate postspawning mor- observed adults between ages 5 and 7 years tality appears to be about 0.50 (B.E.R. unpublished (B.E.R. unpublished data), but anecdotal accounts data). Because additional mortality may be asso- from ongoing tagging studies suggest that some ciated with the year(s) of life between spawnings, ®sh may live 12 years or more. Bull trout may we estimated adult survival rates at 0.50 and 0.25. POPULATION SIZE AND CONSERVATION OF BULL TROUT 759

Survival to age 1 was used to produce a stable we included a single simulation in which the pop- population (a mean instantaneous population ulation was initiated at carrying capacity (S2) (i.e., growth rate of 0) in all simulations. We increased carrying capacity equaled the initial population ®rst-year survival with spawning age to produce size, regardless of what that size was). All other equivalent numbers of adults for all scenarios be- simulations used carrying capacities that were cause the number of adults declined with stable twice the initial population size, regardless of what survival and increasing age at maturity. Our results that was. are representative of populations that are in dy- Simulation approach.ÐAs noted above, we used namic equilibrium (not growing or declining on two series of simulations to capture the potential average). range of conditions possible for bull trout. In the We are not aware of any estimates of the vari- ®rst, we included only the demographic variation ation in survival attributable to the in¯uence of in life history processes inherent in VORTEX. We environmental variation on these populations. To used a range of values in age at maturity, longevity, consider a range of possibilities, we included one survival, and initial population size in relation to series of simulations with only demographic sto- carrying capacity, to explore the in¯uence of var- chasticity in mortality based on the binomial sam- iation in general life history and generation time pling error incorporated in the model. In a second on Ne and the loss of genetic variation (S1±S7; series we included variation in mortality after age Table 1). Being based on a stable age structure and 1 equivalent to a standard error of about 0.10. We no variation in fecundity, these simulations rep- included greater variation in ®rst-year survival. resent the most optimistic scenarios possible for Because we have no empirical estimates, we chose the retention of genetic variation. a SD in ®rst-year survival that produced a SD in To generate a more realistic view of the potential population growth rates between about 0.30 and loss of genetic variation, we included a second set 0.50, values characteristic of those observed from of simulations that incorporated variations in pa- long-term monitoring of bull trout populations in rameters that might result from environmental var- Idaho and Montana (Rieman and McIntyre 1993). iation and breeding structure. All of these simu- Fecundity.ÐTwo attributes of VORTEX limit lations were reiterations of those in the ®rst set its utility for ®sh populations. One is the limited (except for S2), but with additional variation in range of fecundities that can be assigned to adult fecundity and survival, spawning frequency in fe- females. Another is an inability to specify an age± males, and spawning success in males (S1 ±S7 ). size relationship in fecundity that correlates with v v We refer to the additional variation as ``environ- growth in iteroparous ®sh like bull trout. To com- mental variation'' in the remainder of the paper. pensate for the reduced fecundities in VORTEX, In all, we simulated 13 life history scenarios. Each we collapsed two life stages (e.g., between egg to fry and fry to age-1) as suggested in the users' scenario included ®ve different average population manual. We varied fecundity expected for any fe- sizes that ranged from about 50 to 550 adults. The male in direct proportion to the distribution of fe- initial population size was varied to produce av- cundity predicted from the bull trout growth, sur- erage adult numbers distributed at ®ve levels vival, and fecundity models reported by Rieman across this range (i.e., 50±75, 100±150, 200±250, and McIntyre (1993) to simulate the variation in 300±375, 450±550). The actual averages varied fecundity expected with females of different ages slightly because of the stochastic process inherent and sizes. in the model. We chose the upper bound because Density dependence.ÐAlthough VORTEX al- we anticipated that loss of genetic variation would lows density dependence in some life history pro- accelerate as numbers decreased to somewhere be- cesses, we did not include it in the model. The low about 500 adults. We restricted the lower model imposes a re¯ecting boundary as a carrying bound because simulated populations much small- capacity that we did use. In essence, our popula- er than this frequently went extinct within the pe- tions grew or declined in size only as a function riod of simulation as a result of demographic pro- of random variation in mortality and reproduction. cesses alone. Each simulation was for 200 years. If a population reached carrying capacity, further Simulations for each scenario and population size reproduction was preempted, thereby representing were replicated 500 times. an ``all or nothing'' form of density dependence. We summarized the proportion of expected het- To consider the effect that a re¯ecting boundary erozygosity retained at the completion of each sim- might have on estimated loss of genetic variation, ulation. We estimated a mean for the replicated 760 RIEMAN AND ALLENDORF

FIGURE 2.ÐMean expected heterozygosity retained over 200 years in 500 simulations of bull trout popu-

lations with a single life history pattern (S5v) and varied mean number of adults. The vertical lines indicate Ϯ1 SD.

(i.e., S1v±S7v). Nspawn was used as an approxi- mation of population size that would be consistent with typical escapement monitoring. The third

measure was ideal population (Nideal), de®ned as the population size estimated by assuming the

characteristics of an ideal population as Nnew ϫ g (Hill 1972), where Nnew is the mean number of individuals entering the adult population each year FIGURE 1.ÐMean expected heterozygosity, as a pro- and the g is mean generation time in years; we portion of the original, retained over 200 years in 500 used this estimate to compare our results with es- simulations of bull trout populations with varied life history patterns and mean number of adults. Panel A timates of Ne/N ratios in the literature (e.g., Frank- includes simulations with demographic variation only, ham 1995; Allendorf et al. 1997). panel B simulations with both demographic and envi- ronmental variation. Simulations are as de®ned in the Results text and Table 1. In simulations that did not include environmen- tal variation (S1±S7), the loss of heterozygosity differed among life histories and increased sharply scenario±population size combinations with effec- with fewer numbers of adults (Figure 1A). Dif- tive population size calculated as follows: ferences in heterozygosity were greatest between

logetH /t simulations with delayed (S3) and early (S1) mat- Ne ϭ (1/2)´(1 Ϫ e ) (2) uration, but the differences were relatively minor where all terms are as de®ned in equation (1). To among other life histories. contrast Ne and the N that might actually result In simulations that included environmental var- from population inventory and monitoring, we iation (S1v±S7v), the losses of heterozygosity and summarized adult populations in several ways. The differences among the extremes in life histories ®rst measure of population was mean number of were more pronounced (Figure 1B). The rate of adults (Nadult), de®ned as the mean number of in- loss of genetic variation increased noticeably with dividuals of spawning age in the population wheth- simulations involving fewer than about 250±400 er they spawn or not. The second measure was adults. mean number of spawners (Nspawn), de®ned as the Although loss of heterozygosity differed among mean number of ®sh that return to spawn in a given life histories, the variation within any scenario that year. This number is identical to Nadult in simula- included environmental variation was also sub- tions where spawning frequency is 1 (i.e., S1±S7; stantial (Figure 2). The SD in the loss of genetic

Table 1) but is approximately 0.75 Nadult when fe- variation in the series of simulations for a single males are expected to spawn only half of the time life history (Figure 2) was similar to or greater POPULATION SIZE AND CONSERVATION OF BULL TROUT 761

the total number of adults under the assumptions associated with environmental variation. Estimates

of Ne relative to the Nideal ranged between about 0.38 and 0.68 without environmental variation and between about 0.15 and 0.27 with variation (Figure

3C). The ratio of Ne to the different estimates of N varied with life history scenario (e.g., S1 versus

S3 or S1v versus S3v; Figure 3), but the largest differences were clearly between those simulations with and without environmental variation (e.g., S1

versus S1v). There was no apparent pattern in the ratios of Ne to the different N values associated with varied mean number of adults within each scenario; that is, the smallest or largest means were not associated consistently with the smallest or largest ratios (Figure 3).

Discussion Genetic variation will be lost through time in isolated populations and this loss will occur more quickly in small populations than in large ones (Allendorf and Ryman in press). Our simulations show that even populations averaging approxi- mately 500 adults annually can lose more than 10% of original heterozygosity in 200 years; this loss is expected to accelerate dramatically as popula- tion sizes fall. A population of fewer than 100 may FIGURE 3.ÐRatios of estimated effective population lose ®ve or more times that much in the same size (Ne)to(A) the mean number of adults, (B) spawners, period. and (C) the ideal population in 500 simulations of bull Our results also show that the variation in life trout populations with varied life history patterns and history and demographic characteristics among mean number of adults. The different bars associated bull trout populations will almost certainly in¯u- with each life history scenario represent the simulations with means for the number of adults ranging from ap- ence the loss of genetic variation that can be ex- proximately 500 (leftmost bar) to 50 (rightmost bar). pected in those populations. Some populations will face greater risks than others. In our simulations the most extreme differences in life history pro- than the range in the average loss of variation duced a two- to threefold range in the relative dif- among all life histories (Figure 1). The SD also ference between Ne and the number of adults or increased with fewer numbers of adults. Thus, not spawners in simulations including environmental all populations will experience a loss of genetic variation. The difference was between four- and variation, but some may lose far more than ex- ®vefold if we contrast simulations with and with- pected. The potential for substantial loss of het- out environmental variation. Clearly, population erozygosity also increased dramatically as popu- characteristics that we know relatively little about lation size fell. in many populations can strongly in¯uence the loss Simulations without environmental variation of genetic variation and the relationship between produced estimates of Ne that ranged between Ne and the numbers we might observe in those about 1.50 Nadult and 2.40 times Nadult compared populations. with estimates between 0.5 and 1.2 when environ- The interaction of life history and environmen- mental variation was included (Figure 3A). Esti- tal variation and their in¯uence on Ne can be com- mates of Ne relative to Nspawn were identical to plex but, in some cases, predictable (e.g., Gaggiotti those for total adults with no environmental var- and Vetter 1999). A detailed analysis based on a iation but were slightly higher with variation in- better understanding of the characteristics of any cluded (0.6±1.5; Figure 3B). The increase resulted real populations (e.g., Waples and Teel 1990) could because the number of ``spawners'' was less than produce a better understanding of the immediate 762 RIEMAN AND ALLENDORF threats to a population. Without that information, the risks of inbreeding in any population. An av- managers must simply be more conservative and erage of 1,000 (i.e., 1000 ϫ 0.5 ϭ 500) adults acknowledge a range of possible results. spawning annually would be necessary to maintain

Our range of estimates of Ne/Nideal (0.15±0.27) genetic variation inde®nitely. Those criteria might for the hypothetical bull trout populations are com- be relaxed if there were clear evidence that the parable with other work. Frankham (1995) sum- adult population is larger than the number of ®sh marized estimates that averaged about 0.10 for a spawning in any year (because all females do not wide variety of wildlife species. Existing estimates spawn in all years), or if more precise estimates for salmonids range widely (0.04±0.83) (Simon et of other life history parameters and variation were al. 1986; Bartley et al. 1992) and may be partic- available. ularly variable for hatchery populations (Bartley Few local bull trout populations are likely to et al. 1992), where mating structures are highly support spawner numbers averaging 1,000 or more arti®cial. Allendorf et al. (1997) concluded that per year. The largest local spawning aggregations

Ne/Nideal ϭ 0.2 is a reasonable approximation for we are aware of contain between several hundred wild populations of Paci®c salmon. McElhaney et and several thousand adults (Rieman and McIntyre al. (2000) suggested 0.3 as an appropriate starting 1993; Dunham et al. 2001). Many populations may point. Our results suggest that natural bull trout be isolated and much smaller (Rieman et al. 1997). populations will fall in about this range. That does not mean the latter populations should In applying these models, it is useful to consider be written off as lost causes; rather, managers the ratio of Ne to the actual observations of pop- should recognize that those populations face great- ulation numbers likely to be made in the ®eld. er threats associated with small population size and Based on the range of conditions we included in may require more aggressive management and our analysis, estimates of Ne ranged between about more immediate attention to mitigate those threats. 0.5 and 1.5 times the number of adults that would Improved habitat capacity and mitigation of de- be observed in an annual spawning run of bull mographic threats (e.g., excessive mortality or trout. Thus, a population with an average of 100 competition) that may compound the effects of re- spawners per year would have an effective pop- duced genetic variation could be important objec- ulation size between 50 and 150. Although we did tives. not use an exhaustive combination of parameter Perhaps a more important point is that main- estimates, most of our simulations with environ- taining the natural connections and potential for mental variation produced ratios close to or less gene ¯ow among populations can be critical (Rie- than 1. In addition, our values may be overesti- man and Dunham 2000). Dispersal and the full mates because we did not account for all possible expression of life histories in salmonid populations sources of variability in reproductive success (e.g., require free movement of migratory ®sh. Meta- sexual selection). Therefore, in the absence of population theory has been a focus of growing more detailed local population and demographic attention in work with ®shes (Rieman and Dunham information, we believe the best estimate of Ne is 2000) and in our own work with bull trout (Dun- between 0.5 and 1.0 times the mean number of ham and Rieman 1999; Spruell et al. 1999). At adults observed annually. present, no simple rules guide consideration of the effective population size of a metapopulation Management Recommendations (Hedrick and Gilpin 1997), and simulating meta- In the process of developing recovery plans, population processes to generate estimates for bull managers of threatened or endangered species trout would be highly speculative. Clearly, how- must establish recovery criteria and goals for man- ever, the natural substructuring of populations as- agement of critical populations (W. Fredenberg, sociated with metapopulations can actually en- U.S. Fish and Wildlife Service, personal com- hance the maintenance of genetic diversity beyond munication). Managers may also prioritize limited that expected in the sum of the local populations resources for habitat conservation and restoration, (Ray 2001). Disruption of the natural structure based on some measure of risk (e.g., Allendorf et could also accelerate the loss well beyond that al. 1997). If we accept the general guidance of the expected from the composite of local populations 50/500 criteria (Allendorf and Ryman in press), a (Ray 2001). At present, where local populations cautious interpretation of our results would be that cannot support the minimum size necessary to approximately 100 (i.e., 100 ϫ 0.5 ϭ 50) adults maintain genetic variation, managers should seek spawning each year would be required to minimize to conserve a natural collection of populations that POPULATION SIZE AND CONSERVATION OF BULL TROUT 763 is at least large enough in total to meet the min- Acknowledgments imum. For example, 10 or more interconnected We thank R. Lacy for his advice on the use of populations that each support an average of at least VORTEX, D. Horan for help in preparation of the 100 spawners would be an appropriate objective. manuscript, and P. Spruell for constructive review, Managers should also seek to conserve the full food, and hours of entertainment. R. Remmick and expression of life history and processes in¯uenc- two anonymous reviewers provided helpful com- ing natural dispersal and gene ¯ow among those ments on an earlier draft. populations. Removal of barriers to migration, res- References toration of habitat conditions in migratory corri- Allendorf, F. W., D. W. Bayles, D. L. Bottom, K. P. dors, and the maintenance of at least some pop- Currens, C. A. Frissell, D. Hankin, J. A. Lichatow- ulations large enough to act as sources for dis- ich, W. Nehlsen, and T. H. Williams. 1997. Prior- persal could be important (Rieman and McIntyre itizing Paci®c salmon stocks for conservation. Con- 1993; Rieman and Dunham 2000). servation Biology 11:140±152. Managers must often make decisions with lim- Allendorf, F. W., and N. Ryman. In press. The role of genetics in population viability analysis. In D. R. ited information. Although population biology McCullough and S. R. Beissinger, editors. Popu- provides theory and sophisticated models relevant lation viability analysis. University of Chicago to many issues, management must often default to Press, Chicago. apparently simple rules-of-thumb, such as the 50/ Bartley, D., M. Bagley, G. Gall, and M. Bentley. 1992. 500 criteria for maintenance of genetic diversity. Use of linkage disequilibrium data to estimate ef- Unfortunately, that guidance is not so simple to fective size of hatchery and natural ®sh populations. Conservation Biology 6:365±375. apply; indeed, our analysis grew out of our own Caballero, A. 1994. Developments in the prediction of dif®culties in interpreting Ne for species like bull effective population size. Heredity 73:657±679. trout that have overlapping generations. Our re- Crow, J. F., and C. Denniston. 1988. Inbreeding and sults clarify that problem and allow a more direct variance effective population numbers. Evolution application of the existing guidance. We empha- 42:482±495. Crow, J. F., and M. Kimura. 1970. An introduction to size, however, that our analysis is simply an ap- population genetics theory. Burgess, Minneapolis, proximation, built on other approximations. With- Minnesota. out detailed information, managers should ac- Dunham, J. B., and B. E. Rieman. 1999. Metapopulation knowledge this uncertainty and recognize that the structure of bull trout: in¯uences of physical, biotic, guidelines we have provided are conservative min- and geometrical landscape characteristics. Ecolog- ical Applications 9:642±655. imums and not goals that will assure the viability Dunham, J. B., B. E. Rieman, and K. Davis. 2001. of any population. Sources and magnitude of sampling error in redd Maintenance of genetic variation is only one counts for bull trout. North American Journal of issue in the challenge that faces managers charged Fisheries Management 21:343±352. with the conservation of species like bull trout. Fraley, J. J., and B. B. Shepard. 1989. Life history, Mitigation of extinction threats associated with de- ecology and population status of migratory bull trout (Salvelinus con¯uentus) in the Flathead mographic processes may require larger popula- LakeϪRiver system, Montana. Northwest Science tion sizes regardless of the genetic issues (Lande 63:133±143. 1988; Rieman and McIntyre 1993). Our work and Frankham, R. 1995. Effective population size/adult pop- other work with demographic and empirical mod- ulation size ratios in wildlife: a review. Genetical els, for example, indicate that many smaller pop- Research 66:95±107. Franklin, I. A. 1980. Evolutionary changes in small pop- ulations (e.g., less than 100 spawning adults) may ulations. Pages 135±150 in M. Soule and B. A. Wil- be prone to extinction if they are isolated (Rieman cox, editors. Conservation biology: an evolution- and McIntyre 1993; Dunham and Rieman 1999). aryϪecological perspective. Sinauer Associates, Maintenance of the full expression of life history, Sunderland, Massachusetts. dispersal, and the phenotypic diversity that can be Gaggiotti, O. E., and R. D. Vetter. 1999. Effect of life history strategy, environmental variability, and distributed among diverse habitats may be as im- overexploitation on the genetic diversity of pelagic portant as maintenance of genetic variation if pop- ®sh populations. Canadian Journal of Fisheries and ulations are to remain resilient and productive in Aquatic Sciences 56:1376±1388. the face of natural disturbances (Healey 1994; Geiger, H. J., W. W. Smoker, L. A. Zhivotovsky, and A. Healey and Prince 1995; Rieman and Dunham J. Gharrett. 1997. Variability of family size and marine survival in pink salmon (Oncorhynchus gor- 2000). Maintenance of genetic diversity is essen- buscha) has implications for conservation biology tial, but not necessarily suf®cient, for effective and human use. Canadian Journal of Fisheries and conservation. Aquatic Sciences 54:2684±2690. 764 RIEMAN AND ALLENDORF

Harris, R. B., and F. W. Allendorf. 1989. Genetically Ray, C. 2001. Maintaining genetic diversity despite lo- effective population size of large mammals: an as- cal extinctions: a spatial scaling problem. Biological sessment of estimators. Conservation Biology 3: Conservation 100:3±14. 181±191. Rieman, B. E., and J. B. Dunham. 2000. Metapopula- Healey, M. C. 1994. Variation in the life history char- tions and salmonids: a synthesis of life history pat- acteristics of chinook salmon and its relevance to terns and empirical observations. Ecology of Fresh- conservation of the Sacramento winter run of chi- water Fish 9:51±64. nook salmon. Conservation Biology 8:876±877. Rieman, B. E., and J. D. McIntyre. 1993. Demographic Healey, M. C., and A. Prince. 1995. Scales of variation and habitat requirements for the conservation of bull in life history tactics of Paci®c salmon and the con- trout Salvelinus con¯uentus. U.S. Forest Service In- servation of phenotype and genotype. Pages 176± termountain Research Station, General Technical 184 in J. A. Nielsen, editor. Evolution and the aquat- Report INT-302, Ogden, Utah. ic ecosystem: de®ning unique units in population Rieman, B. E., D. C. Lee, and R. F. Thurow. 1997. Dis- conservation. American Fisheries Society, Sympo- tribution, status, and likely future trends of bull sium 17, Bethesda, Maryland. trout within the Columbia River and Klamath ba- Hedrick, P.W., and M. E. Gilpin. 1997. Genetic effective sins. North American Journal of Fisheries Manage- size of a metapopulation. Pages 165±181 in I. Han- ment 17:1111±1125. ski and M. E. Gilpin, editors. Metapopulation bi- Schwartz, M. K., D. A. Tallmon, and G. Luikart. 1998. ology. Academic Press, San Diego, California. Review of DNA-based census and effective popu- Hilderbrand, R. H., and J. L. Kershner. 2000. Conserv- lation size estimators. Animal Conservation 1:293± ing inland cutthroat trout in small streams: how 299. much stream is enough? North American Journal of Simon, R. C., J. D. McIntyre, and A. R. Hemmingsen. Fisheries Management 20:513±520. 1986. Family size and effective population size in Hill, W. G. 1972. Effective size of populations with a hatchery stock of coho salmon (Oncorhynchus kis- overlapping generations. Theoretical Population Bi- utch). Canadian Journal of Fisheries and Aquatic ology 3:278±289. Sciences 43:2434±2442. Laikre, L., P. E. Jorde, and N. Ryman. 1998. Temporal SouleÂ, M. E. 1980. Thresholds for survival: maintaining change of mitochondrial DNA haplotype frequen- ®tness and evolutionary potential. Pages 151±169 cies and female effective size in a brown trout (Sal- in M. E. Soule and B. A. Wilcox, editors. Conser- mo trutta) population. Evolution 52:910±915. vation biology: an evolutionaryϪecological per- Lande, R. 1988. Genetics and demography in biological spective. Sinauer, Sunderland, Massachusetts. conservation. Science 241:1455±1460. SouleÂ, M. E., and L. S. Mills. 1998. No need to isolate Lindemayer, D. B., M. A. Burgman, H. R. AkcËakaya, genetics. Science 282:1658±1659. R. C. Lacy, and H. P. Possingham. 1995. A review Spruell, P., B. E. Rieman, K. L. Knudsen, F. M. Utter, of the generic computer programs ALEX, RAMAS/ and F. W. Allendorf. 1999. Genetic population structure within streams: microsatellite analysis of space and VORTEX for modeling the viability of bull trout populations. Ecology of Freshwater Fish wildlife metapopulations. Ecological Modeling 82: 8:114±121. 161±174. USFWS (U.S. Fish and Wildlife Service). 1998. Deter- Mace, G. M., and R. Lande. 1991. Assessing extinction mination of threatened status for the Klamath River threats: toward a reevaluation of IUCN threatened and Columbia River distinct population segments species categories. Conservation Biology 5:148±157. of bull trout. Federal Register (10 June 1998) 63: McElhaney, P., M. H. Ruckleshaus, M. J. Ford, T. C. 31647±31674. Wainright, and E. P. Bjorkstedt. 2000. Viable sal- Waples, R. S. 1990. Conservation genetics of Paci®c monid populations and the recovery of evolutionarily salmon II. Effective population size and the rate of signi®cant units. NOAA Technical Memorandum loss of genetic variability. Journal of Heredity 81: NMFS-NWFSC-42. 267±276. Miller, P.S., and R. C. Lacy. 1999. VORTEX: a stochastic Waples, R. S. 1991. Genetic methods for estimating the simulation of the extinction process. User's manual, effective size of cetacean populations. Pages 279± version 8. Conservation Breeding Specialists Group 300 in R. Hoelzel, editor. Genetic ecology of whales (SSC/IUCN), Apple Valley, Minnesota. and dolphins. International Whaling Commission, Nelson, K., and M. SouleÂ. 1987. Genetical conservation Cambridge, UK. of exploited ®shes. Pages 345±368 in N. Ryman and Waples, R. S. In press. De®nition, and estimation of F.Utter, editors. Population genetics and ®shery man- effective population size in the conservation of en- agement. University of Washington Press, Seattle. dangered species. In D. R. McCullough and S. R. Pratt, K. L. 1985. Pend Oreille trout and char life history Beissinger, editors. Population viability analysis. study. Idaho Department of Fish and Game, Final University of Chicago Press, Chicago. Report, Boise. Waples, R. S., and D. J. Teel. 1990. Conservation ge- Pratt, K. L. 1992. A review of bull trout life history. netics of Paci®c salmon I. Temporal changes in al- Pages 5±9 in P. J. Howell and D. V. Buchanan, ed- lele frequency. Conservation Biology 4:144±156. itors. Proceedings of the Gearhart Mountain bull Wright, S. 1969. Evolution and the genetics of popu- trout workshop. American Fisheries Society, lations, volume 2. The theory of gene frequencies. Oregon Chapter, Corvallis. University of Chicago Press, Chicago. The paper by Rieman and Allendorf published in the North American Journal of Fisheries Management 21:756-764, 2001 contains an error. On page 760 the following correction is necessary:

The current equation 2 is

logeHt/t Ne = (1/2) (1-e )

The correct equation 2 should be

Ne = 1 _ 2(1-e(logeHt)/t )