Migration and inbreeding: the importance of recipient population size for genetic management

Sewall Wright demonstrated 70 years ago thatthe number of migrants required to maintainspecified levels of gene flow (i.e. avoidexcessive inbreeding) is virtually independentof the size of the recipient population. According to conventional wisdom, this idea isvalid provided population size exceeds 20. Itis well known that this independence implicitlyassumes that a population's effective size(N_e) is equal to its census size(N). However, it is not obvious whetherindependence between the required number ofmigrants (to avoid excessive inbreeding) andpopulation size constitutes a reasonableassumption for real populations of conservationconcern. Relying on empirical data, wedemonstrate that for real populations, theassumption (i.e. N_e = N) isroutinely violated to a degree such that therequired number of migrants is stronglydependent on the size of the recipientpopulation. Because a population's effectivesize (N_e) is typically much smallerthan its census size (N), the number ofmigrants required to avoid inbreeding isactually dependent on N even when it isconsiderably greater than 20. For example,when N_e/N = 0.1, the number ofmigrants required to maintain the inbreedingcoefficient (F) at 0.2 doubles (from 4 to8) as N increases from 9 to 60. Similarly, when N_e/N = 0.05, thenumber of migrants required increases by 50%as N increases from 18 to 45, andincreases again by 50% as N increasesfrom 45 to 260. Thus, for populations muchlarger than 20, the required number of migrantsincreases asymptotically with N, anddramatically so when N_e/N1. Simple conventions regarding the requisitenumber of migrants may not apply to manypopulations of conservation concern. Geneticmanagement should routinely rely on models thatexplicitly account for this and other recentconsiderations. Failure to do so mayjeopardize the viability of populations thatare sensitive to altered levels of inbreeding.