Detecting inbreeding depression is difficult in captive endangered species

During the past two decades, pedigree analysis has documented inbreeding depression in many captive populations. This and subsequent research has led to a recognition that inbreeding depression is a potentially important determinate of small population fitness, in both captivity and the wild. Modern captive-breeding programmes now universally avoid inbreeding. We use simulation to investigate how much traditional pedigree analysis will reveal about the effect of inbreeding in such populations. We find that pedigrees typical of breeding programmes designed to avoid inbreeding have low statistical power to detect inbreeding depression. All correspondence to: Steven Kalinowski. Present address: National Marine Fisheries Service, Conservation Biology Division, Seattle, WA 98112, U.S.A. Tel: 602-965-4556; Fax: 602-965-2519; E-mail: [email protected]. pedigree and the many-founders pedigree, are shown in Fig. 1 and listed in the Appendix. The few-founders pedigree was modelled after the captive-breeding programme of the Mexican wolf (Canis lupus baileyi), which was founded by three wild-caught individuals (Siminski, 1998). In our model pedigree, there are 200 individuals, with eight non-inbred births and 192 inbred births distributed in three levels of inbreeding. The average inbreeding coefficient overall is 0.18, and 0.1875 for inbred births only. Like the Mexican wolf pedigree, 50% of the inbred individuals have an inbreeding coefficient of 0.1875. The many-founders pedigree was modelled after the captive breeding programme of the red wolf (Canis rufus), which was founded from 14 individuals (Waddell, 1997). In our model pedigree, there are 600 individuals, with 300 non-inbred births and 300 inbred births distributed among 15 levels of inbreeding. In the red wolf pedigree, most of the first inbred births had f = 0.0625 (mostly first-cousin matings) and we incorporated this feature in to our many-founders pedigree. Similar to that of the red wolf pedigree, the average inbreeding coefficient is 0.0313 overall, and 0.0625 among inbred births. Estimating the effect of inbreeding In order to estimate the effect of inbreeding upon viability, inbreeding coefficients and viability data (survival to a specified age) are needed for each individual in the analysis. In practice, this usually requires data from a studbook. The impact of inbreeding upon viability can be estimated by fitting the model: (1) to the data, where Si is the expected viability of an individual with an inbreeding coefficient fi surviving to a specified age, S0 is the expected viability of non-inbred individuals, and B is a measure of how fast viability decreases with inbreeding (Morton, Crow & Muller, 1956). In addition, 2B is approximately equal to the number of lethal equivalents in a diploid genome. A lethal equivalent is a unit of genetic variation and the number of lethal equivalents in an individual is equal to the sum of the selective disadvantage when that individual is homozygous for all detrimental or lethal alleles (Cavalli-Sforza & Bodmer, 1971). Deciding whether there is significant inbreeding depression in a pedigree is equivalent to deciding if 2B is significantly greater than zero. This can be done by calculating a confidence interval for 2B and observing whether the interval includes zero. A confidence interval of 1– α will provide a test of significance of inbreeding depression at the α/2 level. Demonstrating that viability in a pedigree has not been affected by inbreeding is equivalent to showing that 2B = 0 and not any other value. This is impossible, but we can test whether 2B is less than a critical value for which the impact of inbreeding is considered minimal. Figure 2 shows the cost of inbreeding, 1 – Si /S0, expected from the model of Morton et al. (1956) as a function of 2B and f. As can be interpreted from the figure, 2B = 1 is the highest number of lethal equivalents that can be considered to have minimal effect upon viability in moderately inbred individuals. For example if 2B = 1, then matings between half siblings (f = 0.125) should have an expected viability of 6% less than non-inbred births and matings between full siblings would have an expected viability of 12% less than non-inbred births. For heuristic purposes, we will consider a pedigree with 132 S. T. KALINOWSKI & P. W. HEDRICK Fig. 1. The distribution of inbreeding coefficients, f, in hypothetical pedigrees with few founders (black) and many founders (white). S S i Bfi = − 0e Fig. 2. The expected cost of inbreeding as a function of the inbreeding coefficient, f, and the number of lethal equivalents,