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

Effective Population Size and Genetic Conservation Criteria forBull Trout

B. E. RIEMAN*U.S. Department of Agriculture Forest Service, Rocky Mountain Research Station,

316 East Myrtle, Boise, Idaho 83702, USA

F. W. ALLENDORF

Division of Biological Sciences,University of Montana, Missoula, Montana 59812, USA

Abstract.—Effective population size (Ne) is an important concept in the management of threatenedspecies like bull trout Salvelinus confluentus. General guidelines suggest that effective populationsizes of 50 or 500 are essential to minimize inbreeding effects or maintain adaptive geneticvariation, respectively. Although Ne strongly depends on census population size, it also dependson demographic and life history characteristics that complicate any estimates. This is an especiallydifficult problem for species like bull trout, which have overlapping generations; biologists maymonitor annual population number but lack more detailed information on demographic populationstructure or life history. We used a generalized, age-structured simulation model to relate Ne toadult numbers under a range of life histories and other conditions characteristic of bull troutpopulations. Effective population size varied strongly with the effects of the demographic andenvironmental variation included in our simulations. Our most realistic estimates of Ne werebetween about 0.5 and 1.0 times the mean number of adults spawning annually. We conclude thatcautious long-term management goals for bull trout populations should include an average of atleast 1,000 adults spawning each year. Where local populations are too small, managers shouldseek to conserve a collection of interconnected populations that is at least large enough in totalto meet this minimum. It will also be important to provide for the full expression of life historyvariation and the natural processes of dispersal and gene flow.

The concept of effective population size (Ne)plays an important role in conservation manage-ment of fishes (Waples in press). The Ne is a mea-sure of the rate of genetic drift and is directlyrelated to the rate of loss of genetic diversity andthe rate of increase in inbreeding within a popu-lation (Wright 1969). Conservation of populationslarge enough to minimize such effects has becomean important goal in the management of threatenedor endangered salmonids, including Pacific salmonOncorhynchus sp. (McElhaney et al. 2000) and bulltrout Salvelinus confluentus (USFWS 1998).

The ongoing fragmentation and isolation of hab-itat of species like bull trout have led to reductionsin population size (Rieman and McIntyre 1993;Rieman et al. 1997) and presumably in Ne for manypopulations. A resulting loss of genetic variationcan influence the dynamics and persistence of pop-ulations through at least three mechanisms: in-breeding depression, loss of phenotypic variationand plasticity, and loss of evolutionary potential(Allendorf and Ryman in press). The loss of ge-

* Corresponding author: brieman@fs.fed.us

Received September 12, 2000; accepted February 19, 2001

netic variation in populations with small Ne mayreduce fitness through the so-called inbreeding ef-fect of small populations and lead to an acceler-ating decline toward extinction in a process termedan extinction vortex (Soule and Mills 1998).

Because of the importance of Ne, the so called‘‘50/500’’ rule has emerged as general guidancein conservation management (Franklin 1980; Sou-le 1980; Nelson and Soule 1987; see Allendorf andRyman [in press] for a recent consideration ofthese criteria). The generally accepted view is thatan Ne of less than about 50 is vulnerable to theimmediate effects of inbreeding depression. Al-though populations might occasionally decline tonumbers on this order without adverse effects,maintenance of adaptive genetic variation overlonger periods of time (e.g., centuries) probablywill require an Ne averaging more than 500 (Al-lendorf and Ryman in press). These numbers havebeen generally applied as criteria for determinationof conservation status among taxa (Mace andLande 1991) and within the salmonids in particular(e.g., Allendorf et al. 1997; Hilderbrand and Ker-shner 2000).

The problem in application is that Ne and the

757POPULATION SIZE AND CONSERVATION OF BULL TROUT

number of adult fish usually represented in pop-ulation estimates (N) are not equal. Estimation ofNe and even N can be complicated. Direct esti-mation of Ne is possible but requires either detailedinformation on population demographics andbreeding structure (Harris and Allendorf 1989; Ca-ballero 1994) or extensive information on geneticpopulation structure (Waples 1991; Laikre et al.1998; Schwartz et al. 1998). Limitations of samplesize requirements, the resolution possible for allbut very small populations, and time and analyticalcosts may restrict the utility of these methods. Asa result, application of population size criteria of-ten relies on approximations of Ne based on ex-isting estimates of N and population simulationmethods (Harris and Allendorf 1989). Even if Ne

is assumed to be some fraction of N based on otherwork, the estimation of N can still be unclear.

The life history patterns of most salmonids arecomplex. Pacific salmon adults spawn and die, butexcept for pink salmon Oncorhynchus gorbuscha,there is overlap among cohorts that mature at var-iable ages. The adult population is replaced eachyear, but a single generation will encompass mul-tiple spawning years. Trout and char, includingbull trout, may spawn several times. Age at ma-turity varies among individuals, and once mature,not all surviving individuals will spawn in allyears. Although new adults are recruited each year,the adult population as a whole is replaced grad-ually through time (Laikre et al. 1998).

Waples (1990) has shown for Pacific salmon,which die after spawning, that Ne 5 g 3 Nb, whereg is the average age of spawning or generationlength, and Nb is the mean effective number ofspawners per year. An appropriate estimate of Nwould be the mean number of adults observedacross years times g. Hill (1972) showed that Ne

in iteroparous species can be approximated by thenumber of first-time spawners entering the popu-lation each generation (i.e., the mean number offirst time spawners times g). For managers the in-terpretation of N may still remain obscure for spe-cies that spawn multiple times. Even detailed in-ventory and monitoring projects cannot routinelydiscriminate between first-time and repeat spawn-ing individuals.

In our work with bull trout, a recent addition tothe threatened species list under the EndangeredSpecies Act of the United States (USFWS 1998),application of population conservation criteria(i.e., 50/500) was limited by these problems. Ourobjective was to describe the expected loss of ge-netic variation and to approximate Ne for a range

of population sizes and life history conditionscharacteristic of species like bull trout. We wereprimarily interested in estimating the ratio of Ne

to the number of adults that might be observed intypical monitoring efforts concerned with conser-vation and the application of population size cri-teria. We use our results to show how managerscan interpret annual estimates of adult abundanceor spawning escapements in light of existing con-servation genetic theory and general knowledge ofbull trout life history.

Methods

Estimation of Ne.—In an ‘‘ideal’’ population, theexpected loss of genetic variation (represented asheterozygosity) per generation is DH 521/2N,where N is the size of the adult population (Wright1969). For example, an ideal population of 10adults would be expected to lose 1/(2 3 10), or5%, of its heterozygosity in one generation. Anideal population is one with discrete generations(all adults reproduce once and at the same age),random mating, equal sex ratio, constant popula-tion size, and an equal probability for all adults tocontribute offspring to the next generation (Ca-ballero 1994; Frankham 1995). Most populationsdo not fit the ideal.

To address this reality, effective population sizeis defined as the size of the ideal population thatwill result in the same amount of genetic drift asin the actual population being considered (Wright1969). Natural populations can deviate stronglyfrom conditions of the ideal. Family size (someadults produce more offspring than others), for ex-ample, is likely to vary substantially in salmonidfishes (e.g., Geiger et al. 1997). Strong temporalvariation in population size can have a particularlyimportant influence as well (Crow and Denniston1988; Frankham 1995; Ray 2001). As a result Ne

is expected to be smaller than the actual censusnumber for most cases.

We used a simulation approach to track the lossof genetic variation in relation to total adult num-ber for a series of hypothetical bull trout popu-lations. Our results provided an estimate of theratio of Ne to the number of adults that might ac-tually be observed or estimated in annual popu-lation monitoring. We used a range of simulationsrepresentative of the range of life history char-acteristics believed to exist in bull trout popula-tions (Pratt 1985, 1992; Fraley and Shepard 1989).We used the observed rate of loss of heterozygosityand the generation length to estimate the inbreed-

758 RIEMAN AND ALLENDORF

TABLE 1.—Spawning ages, adult survival, and resultingmean generation time used to estimate effective populationsize for bull trout in simulations with and without envi-ronmental variation. All simulations were initiated with astarting population of half the carrying capacity except forS2, which was initiated at carrying capacity. S2 was notincluded in the second set of simulations, which incorpo-rated environmental variation, reduced frequency of fe-male spawning, and reduced spawning success in males.All other parameter values used in the simulations are ex-plained in the text.

Simu-lation

Spawn-ing ages

Annualadult

survival

Meangeneration

time

S1S2S3S4S5S6S7

4–74–77–105–85–85–125

0.500.500.500.500.200.500.00

4.734.737.735.735.325.975.00

ing effective population size (Crow and Kimura1970:345) based on the following formula:

tH 5 H ·[1 2 (1/2N )]t 0 e (1)

where Ht is the heterozygosity after t generations,and H0 is the initial heterozygosity (standardizedat 1.0). In our analyses, t was the total length ofthe simulated period divided by the average gen-eration time.

The model.—VORTEX is a stochastic, age-structured, population simulation model that tracksthe genetic structure of an entire population byfollowing the history of each individual (Millerand Lacy 1999). This flexible simulation programincorporates demographic stochasticity at each in-dividual life history event and user-defined levelsof variation in age- and sex-specific mortality, mat-uration schedule, and population carrying capac-ity. The genetic composition of a population istracked at a single locus in each simulation. At theinitiation of a simulation, each individual in thepopulation is assigned two unique alleles. Matingsare random, but the relative contribution of malesand females can vary with age. Alleles are trans-mitted in random Mendelian fashion, and the fateof each allele is tracked through the pedigree ofsurviving individuals. Summary results includemean population size and growth rate (and theirstandard deviations [SDs]), mean number ofadults, expected and observed heterozygosity as aproportion of initial condition, and a variety ofstatistics related to population extinctions. Moredetail on VORTEX is available from Lindemayeret al. (1995) and Miller and Lacy (1999).

Parameter estimates and simulation approach.—We did not conduct an exhaustive study of all pos-sible population conditions or produce a precisecharacterization of any particular population.Rather we used the simulations to generate a rangeof results that would span those most likely forbull trout populations. We parameterized the mod-el to represent the range of life histories that arereasonable, given existing knowledge (Table 1).Our rationale is explained below.

Maturity and longevity.—Bull trout are thoughtto live at least 7 or 8 years and to begin maturingbetween ages 4 and 7 years (Fraley and Shepard1989; Pratt 1992; Rieman and McIntyre 1993). Inour own work on Pend Oreille Lake, Idaho, weobserved adults between ages 5 and 7 years(B.E.R. unpublished data), but anecdotal accountsfrom ongoing tagging studies suggest that somefish may live 12 years or more. Bull trout may

spawn every year or in alternate years after firstmaturity (Rieman and McIntyre 1993). In our anal-ysis we used combinations of maturity and lon-gevity that included first maturity at 4, 5, and 7years of age, with the fish spawning only once or,alternatively, for as many as five subsequent years.In simulations with only demographic stochastic-ity, we assumed that 100% of females spawnedeach year once mature. In a second series of sim-ulations used to characterize the variation possiblein family size and adult number (see section onsimulation approach), we assumed that 50% of fe-males were expected to spawn in any year, equiv-alent to every-other-year spawning cycles. Allmales were assumed to contribute to spawning inthe first series, but only 50% of males were ex-pected to be successful in the second. Althoughmales may actually return every year, it would notbe unusual to find that not all compete successfullyfor mates. We assumed a sex ratio in all simula-tions of 1:1, with males and females maturing atthe same age.

Survival.—Annual survival of bull trout popu-lations has rarely been estimated, but data fromPratt (1985) suggest that survival ranges between0.30 and 0.70 for subadult fish. We assumed thatsurvival improved from the low to high end of thisrange as fish progressed from age 1 to maturity.From our own work with population estimates ofspawning adults, immediate postspawning mor-tality appears to be about 0.50 (B.E.R. unpublisheddata). Because additional mortality may be asso-ciated with the year(s) of life between spawnings,we estimated adult survival rates at 0.50 and 0.25.

759POPULATION SIZE AND CONSERVATION OF BULL TROUT

Survival to age 1 was used to produce a stablepopulation (a mean instantaneous populationgrowth rate of 0) in all simulations. We increasedfirst-year survival with spawning age to produceequivalent numbers of adults for all scenarios be-cause the number of adults declined with stablesurvival and increasing age at maturity. Our resultsare representative of populations that are in dy-namic equilibrium (not growing or declining onaverage).

We are not aware of any estimates of the vari-ation in survival attributable to the influence ofenvironmental variation on these populations. Toconsider a range of possibilities, we included oneseries of simulations with only demographic sto-chasticity in mortality based on the binomial sam-pling error incorporated in the model. In a secondseries we included variation in mortality after age1 equivalent to a standard error of about 0.10. Weincluded greater variation in first-year survival.Because we have no empirical estimates, we chosea SD in first-year survival that produced a SD inpopulation growth rates between about 0.30 and0.50, values characteristic of those observed fromlong-term monitoring of bull trout populations inIdaho and Montana (Rieman and McIntyre 1993).

Fecundity.—Two attributes of VORTEX limitits utility for fish populations. One is the limitedrange of fecundities that can be assigned to adultfemales. Another is an inability to specify an age–size relationship in fecundity that correlates withgrowth in iteroparous fish like bull trout. To com-pensate for the reduced fecundities in VORTEX,we collapsed two life stages (e.g., between egg tofry and fry to age-1) as suggested in the users’manual. We varied fecundity expected for any fe-male in direct proportion to the distribution of fe-cundity predicted from the bull trout growth, sur-vival, and fecundity models reported by Riemanand McIntyre (1993) to simulate the variation infecundity expected with females of different agesand sizes.

Density dependence.—Although VORTEX al-lows density dependence in some life history pro-cesses, we did not include it in the model. Themodel imposes a reflecting boundary as a carryingcapacity that we did use. In essence, our popula-tions grew or declined in size only as a functionof random variation in mortality and reproduction.If a population reached carrying capacity, furtherreproduction was preempted, thereby representingan ‘‘all or nothing’’ form of density dependence.To consider the effect that a reflecting boundarymight have on estimated loss of genetic variation,

we included a single simulation in which the pop-ulation was initiated at carrying capacity (S2) (i.e.,carrying capacity equaled the initial populationsize, regardless of what that size was). All othersimulations used carrying capacities that weretwice the initial population size, regardless of whatthat was.

Simulation approach.—As noted above, we usedtwo series of simulations to capture the potentialrange of conditions possible for bull trout. In thefirst, we included only the demographic variationin life history processes inherent in VORTEX. Weused a range of values in age at maturity, longevity,survival, and initial population size in relation tocarrying capacity, to explore the influence of var-iation in general life history and generation timeon Ne and the loss of genetic variation (S1–S7;Table 1). Being based on a stable age structure andno variation in fecundity, these simulations rep-resent the most optimistic scenarios possible forthe retention of genetic variation.

To generate a more realistic view of the potentialloss of genetic variation, we included a second setof simulations that incorporated variations in pa-rameters that might result from environmental var-iation and breeding structure. All of these simu-lations were reiterations of those in the first set(except for S2), but with additional variation infecundity and survival, spawning frequency in fe-males, and spawning success in males (S1v–S7v).We refer to the additional variation as ‘‘environ-mental variation’’ in the remainder of the paper.In all, we simulated 13 life history scenarios. Eachscenario included five different average populationsizes that ranged from about 50 to 550 adults. Theinitial population size was varied to produce av-erage adult numbers distributed at five levelsacross this range (i.e., 50–75, 100–150, 200–250,300–375, 450–550). The actual averages variedslightly because of the stochastic process inherentin the model. We chose the upper bound becausewe anticipated that loss of genetic variation wouldaccelerate as numbers decreased to somewhere be-low about 500 adults. We restricted the lowerbound because simulated populations much small-er than this frequently went extinct within the pe-riod of simulation as a result of demographic pro-cesses alone. Each simulation was for 200 years.Simulations for each scenario and population sizewere replicated 500 times.

We summarized the proportion of expected het-erozygosity retained at the completion of each sim-ulation. We estimated a mean for the replicated

760 RIEMAN AND ALLENDORF

FIGURE 1.—Mean expected heterozygosity, as a pro-portion of the original, retained over 200 years in 500simulations of bull trout populations with varied lifehistory patterns and mean number of adults. Panel Aincludes simulations with demographic variation only,panel B simulations with both demographic and envi-ronmental variation. Simulations are as defined in thetext and Table 1.

FIGURE 2.—Mean expected heterozygosity retainedover 200 years in 500 simulations of bull trout popu-lations with a single life history pattern (S5v) and variedmean number of adults. The vertical lines indicate 61SD.

scenario–population size combinations with effec-tive population size calculated as follows:

log H /te tN 5 (1/2)·(1 2 e )e (2)

where all terms are as defined in equation (1). Tocontrast Ne and the N that might actually resultfrom population inventory and monitoring, wesummarized adult populations in several ways. Thefirst measure of population was mean number ofadults (Nadult), defined as the mean number of in-dividuals of spawning age in the population wheth-er they spawn or not. The second measure wasmean number of spawners (Nspawn), defined as themean number of fish that return to spawn in a givenyear. This number is identical to Nadult in simula-tions where spawning frequency is 1 (i.e., S1–S7;Table 1) but is approximately 0.75 Nadult when fe-males are expected to spawn only half of the time

(i.e., S1v–S7v). Nspawn was used as an approxi-mation of population size that would be consistentwith typical escapement monitoring. The thirdmeasure was ideal population (Nideal), defined asthe population size estimated by assuming thecharacteristics of an ideal population as Nnew 3 g(Hill 1972), where Nnew is the mean number ofindividuals entering the adult population each yearand the g is mean generation time in years; weused this estimate to compare our results with es-timates of Ne/N ratios in the literature (e.g., Frank-ham 1995; Allendorf et al. 1997).

Results

In simulations that did not include environmen-tal variation (S1–S7), the loss of heterozygositydiffered among life histories and increased sharplywith fewer numbers of adults (Figure 1A). Dif-ferences in heterozygosity were greatest betweensimulations with delayed (S3) and early (S1) mat-uration, but the differences were relatively minoramong other life histories.

In simulations that included environmental var-iation (S1v–S7v), the losses of heterozygosity anddifferences among the extremes in life historieswere more pronounced (Figure 1B). The rate ofloss of genetic variation increased noticeably withsimulations involving fewer than about 250–400adults.

Although loss of heterozygosity differed amonglife histories, the variation within any scenario thatincluded environmental variation was also sub-stantial (Figure 2). The SD in the loss of geneticvariation in the series of simulations for a singlelife history (Figure 2) was similar to or greater

761POPULATION SIZE AND CONSERVATION OF BULL TROUT

FIGURE 3.—Ratios of estimated effective populationsize (Ne) to (A) the mean number of adults, (B) spawners,and (C) the ideal population in 500 simulations of bulltrout populations with varied life history patterns andmean number of adults. The different bars associatedwith each life history scenario represent the simulationswith means for the number of adults ranging from ap-proximately 500 (leftmost bar) to 50 (rightmost bar).

than the range in the average loss of variationamong all life histories (Figure 1). The SD alsoincreased with fewer numbers of adults. Thus, notall populations will experience a loss of geneticvariation, but some may lose far more than ex-pected. The potential for substantial loss of het-erozygosity also increased dramatically as popu-lation size fell.

Simulations without environmental variationproduced estimates of Ne that ranged betweenabout 1.50 Nadult and 2.40 times Nadult comparedwith estimates between 0.5 and 1.2 when environ-mental variation was included (Figure 3A). Esti-mates of Ne relative to Nspawn were identical tothose for total adults with no environmental var-iation but were slightly higher with variation in-cluded (0.6–1.5; Figure 3B). The increase resultedbecause the number of ‘‘spawners’’ was less than

the total number of adults under the assumptionsassociated with environmental variation. Estimatesof Ne relative to the Nideal ranged between about0.38 and 0.68 without environmental variation andbetween about 0.15 and 0.27 with variation (Figure3C). The ratio of Ne to the different estimates ofN varied with life history scenario (e.g., S1 versusS3 or S1v versus S3v; Figure 3), but the largestdifferences were clearly between those simulationswith and without environmental variation (e.g., S1versus S1v). There was no apparent pattern in theratios of Ne to the different N values associatedwith varied mean number of adults within eachscenario; that is, the smallest or largest means werenot associated consistently with the smallest orlargest ratios (Figure 3).

Discussion

Genetic variation will be lost through time inisolated populations and this loss will occur morequickly in small populations than in large ones(Allendorf and Ryman in press). Our simulationsshow that even populations averaging approxi-mately 500 adults annually can lose more than 10%of original heterozygosity in 200 years; this lossis expected to accelerate dramatically as popula-tion sizes fall. A population of fewer than 100 maylose five or more times that much in the sameperiod.

Our results also show that the variation in lifehistory and demographic characteristics amongbull trout populations will almost certainly influ-ence the loss of genetic variation that can be ex-pected in those populations. Some populations willface greater risks than others. In our simulationsthe most extreme differences in life history pro-duced a two- to threefold range in the relative dif-ference between Ne and the number of adults orspawners in simulations including environmentalvariation. The difference was between four- andfivefold if we contrast simulations with and with-out environmental variation. Clearly, populationcharacteristics that we know relatively little aboutin many populations can strongly influence the lossof genetic variation and the relationship betweenNe and the numbers we might observe in thosepopulations.

The interaction of life history and environmen-tal variation and their influence on Ne can be com-plex but, in some cases, predictable (e.g., Gaggiottiand Vetter 1999). A detailed analysis based on abetter understanding of the characteristics of anyreal populations (e.g., Waples and Teel 1990) couldproduce a better understanding of the immediate

762 RIEMAN AND ALLENDORF

threats to a population. Without that information,managers must simply be more conservative andacknowledge a range of possible results.

Our range of estimates of Ne/Nideal (0.15–0.27)for the hypothetical bull trout populations are com-parable with other work. Frankham (1995) sum-marized estimates that averaged about 0.10 for awide variety of wildlife species. Existing estimatesfor salmonids range widely (0.04–0.83) (Simon etal. 1986; Bartley et al. 1992) and may be partic-ularly variable for hatchery populations (Bartleyet al. 1992), where mating structures are highlyartificial. Allendorf et al. (1997) concluded thatNe/Nideal 5 0.2 is a reasonable approximation forwild populations of Pacific salmon. McElhaney etal. (2000) suggested 0.3 as an appropriate startingpoint. Our results suggest that natural bull troutpopulations will fall in about this range.

In applying these models, it is useful to considerthe ratio of Ne to the actual observations of pop-ulation numbers likely to be made in the field.Based on the range of conditions we included inour analysis, estimates of Ne ranged between about0.5 and 1.5 times the number of adults that wouldbe observed in an annual spawning run of bulltrout. Thus, a population with an average of 100spawners per year would have an effective pop-ulation size between 50 and 150. Although we didnot use an exhaustive combination of parameterestimates, most of our simulations with environ-mental variation produced ratios close to or lessthan 1. In addition, our values may be overesti-mates because we did not account for all possiblesources of variability in reproductive success (e.g.,sexual selection). Therefore, in the absence ofmore detailed local population and demographicinformation, we believe the best estimate of Ne isbetween 0.5 and 1.0 times the mean number ofadults observed annually.

Management Recommendations

In the process of developing recovery plans,managers of threatened or endangered speciesmust establish recovery criteria and goals for man-agement of critical populations (W. Fredenberg,U.S. Fish and Wildlife Service, personal com-munication). Managers may also prioritize limitedresources for habitat conservation and restoration,based on some measure of risk (e.g., Allendorf etal. 1997). If we accept the general guidance of the50/500 criteria (Allendorf and Ryman in press), acautious interpretation of our results would be thatapproximately 100 (i.e., 100 3 0.5 5 50) adultsspawning each year would be required to minimize

the risks of inbreeding in any population. An av-erage of 1,000 (i.e., 1000 3 0.5 5 500) adultsspawning annually would be necessary to maintaingenetic variation indefinitely. Those criteria mightbe relaxed if there were clear evidence that theadult population is larger than the number of fishspawning in any year (because all females do notspawn in all years), or if more precise estimatesof other life history parameters and variation wereavailable.

Few local bull trout populations are likely tosupport spawner numbers averaging 1,000 or moreper year. The largest local spawning aggregationswe are aware of contain between several hundredand several thousand adults (Rieman and McIntyre1993; Dunham et al. 2001). Many populations maybe isolated and much smaller (Rieman et al. 1997).That does not mean the latter populations shouldbe written off as lost causes; rather, managersshould recognize that those populations face great-er threats associated with small population size andmay require more aggressive management andmore immediate attention to mitigate those threats.Improved habitat capacity and mitigation of de-mographic threats (e.g., excessive mortality orcompetition) that may compound the effects of re-duced genetic variation could be important objec-tives.

Perhaps a more important point is that main-taining the natural connections and potential forgene flow among populations can be critical (Rie-man and Dunham 2000). Dispersal and the fullexpression of life histories in salmonid populationsrequire free movement of migratory fish. Meta-population theory has been a focus of growingattention in work with fishes (Rieman and Dunham2000) and in our own work with bull trout (Dun-ham and Rieman 1999; Spruell et al. 1999). Atpresent, no simple rules guide consideration of theeffective population size of a metapopulation(Hedrick and Gilpin 1997), and simulating meta-population processes to generate estimates for bulltrout would be highly speculative. Clearly, how-ever, the natural substructuring of populations as-sociated with metapopulations can actually en-hance the maintenance of genetic diversity beyondthat expected in the sum of the local populations(Ray 2001). Disruption of the natural structurecould also accelerate the loss well beyond thatexpected from the composite of local populations(Ray 2001). At present, where local populationscannot support the minimum size necessary tomaintain genetic variation, managers should seekto conserve a natural collection of populations that

763POPULATION SIZE AND CONSERVATION OF BULL TROUT

is at least large enough in total to meet the min-imum. For example, 10 or more interconnectedpopulations that each support an average of at least100 spawners would be an appropriate objective.Managers should also seek to conserve the fullexpression of life history and processes influenc-ing natural dispersal and gene flow among thosepopulations. Removal of barriers to migration, res-toration of habitat conditions in migratory corri-dors, and the maintenance of at least some pop-ulations large enough to act as sources for dis-persal could be important (Rieman and McIntyre1993; Rieman and Dunham 2000).

Managers must often make decisions with lim-ited information. Although population biologyprovides theory and sophisticated models relevantto many issues, management must often default toapparently simple rules-of-thumb, such as the 50/500 criteria for maintenance of genetic diversity.Unfortunately, that guidance is not so simple toapply; indeed, our analysis grew out of our owndifficulties in interpreting Ne for species like bulltrout that have overlapping generations. Our re-sults clarify that problem and allow a more directapplication of the existing guidance. We empha-size, however, that our analysis is simply an ap-proximation, built on other approximations. With-out detailed information, managers should ac-knowledge this uncertainty and recognize that theguidelines we have provided are conservative min-imums and not goals that will assure the viabilityof any population.

Maintenance of genetic variation is only oneissue in the challenge that faces managers chargedwith the conservation of species like bull trout.Mitigation of extinction threats associated with de-mographic processes may require larger popula-tion sizes regardless of the genetic issues (Lande1988; Rieman and McIntyre 1993). Our work andother work with demographic and empirical mod-els, for example, indicate that many smaller pop-ulations (e.g., less than 100 spawning adults) maybe prone to extinction if they are isolated (Riemanand McIntyre 1993; Dunham and Rieman 1999).Maintenance of the full expression of life history,dispersal, and the phenotypic diversity that can bedistributed among diverse habitats may be as im-portant as maintenance of genetic variation if pop-ulations are to remain resilient and productive inthe face of natural disturbances (Healey 1994;Healey and Prince 1995; Rieman and Dunham2000). Maintenance of genetic diversity is essen-tial, but not necessarily sufficient, for effectiveconservation.

AcknowledgmentsWe thank R. Lacy for his advice on the use of

VORTEX, D. Horan for help in preparation of themanuscript, and P. Spruell for constructive review,food, and hours of entertainment. R. Remmick andtwo anonymous reviewers provided helpful com-ments on an earlier draft.

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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 Ne = (1/2) (1-elogeHt/t ) The correct equation 2 should be Ne = 1 _ 2(1-e(logeHt)/t )