Inbreeding curvature: a geometrical approach for describing the tendency of a population to inbreed or outbreed

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Vidal-Riggs, John
Mark Parker
Kelly Cline
Grant Hokit
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Inbreeding curvature: a geometrical approach for describing the tendency of a population to inbreed or outbreed
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Inbreeding is well understood, from its effects on life history and morphological traits to the genetic factors it involves (Ralls et al, 1979; Brown and Brown, 1998; Charlesworth and Hughes, 1999; DeRose and Roff, 1999; Laikre, 1999; Lynch et al, 1999; Keller and Waller, 2002). Inbreeding depression influences a number of diverse groups, examples of which include ungulates, cheetahs, jays, panthers, and adders; at least one vertebrate species is known to suffer from outbreeding depression (Ralls et al, 1979; O’Brien, 1985; Hedrick, 1995; Brown and Brown, 1998; Madsen et al, 1999; Cohen and Dearborn, 2004). Ecological and species-specific factors are important in inbreeding depression (Hedrick and Kalinowski, 2000). Different species vary in their responses to inbreeding; efficient conservation efforts require an understanding of how these species respond to different levels of inbreeding. For example, inbreeding affects species already acclimated to reduced genetic variation, like South African cheetahs (Felidae: Acinonyxjubatusjubatus) or naked mole rats (Bathyergidae: Heterocephalus glaber), less than it does species accustomed to outbreeding, like the butterfly Bicyclus anynana (Satyridae) (O’Brien, 1985; Saccheri, 1996; Ciszek, 2000). These populations become accustomed to inbreeding primarily through bottleneck events that restrict genetic variation without crippling the fitness of the population because the populations already have a certain tendency to choose more highly related mates. Levels of inbreeding in populations of any species specifically affect mate choice patterns in those populations (Ballou, 1983). While mate choice often depends on a potential mate’s fitness and the fitness of their potential offspring, several species have been shown to deliberately choose less-related mates; at least one has been shown to deliberately choose more closely-related mates (Andersson, 1994; Ciszek, 2000; Freeman-Gallant et al, 2003; Gamer and Schmidt, 2003; Cohen and Dearborn, 2004; Shutler et al, 2004). The present study uses population-specific patterns ofmate-choice to develop a geometrical measurement characterizing the tendency of a population to inbreed or outbreed. I call this measurement ‘inbreeding curvature’ of a population. I compare this measurement to the method restricted to finding the average relatedness ofmated pairs in a population (henceforth referred to as ‘average relatedness’).
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Mathematics, Engineering & Computer Science