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which is far less than 670, the arithmetic mean of 1000, 10, and 1000. (Also see Vucetich et al. 1997 and Lovatt and Hoelzel 2014 for the effect of population fluctuations.)
Example 2. Unequal numbers of females and males. If a population has an unbalanced sex ratio, the effective population size is less than the actual size and can be estimated as
where Nf is the number of breeding females and Nm is the number of breeding males (Hartl and Clark 1997). For example, if 96 females mated with four males,
This kind of imbalance, as extreme as it may seem, is fairly common. Genetic analyses that determine the mother and father of offspring frequently indicate that in many species relatively few individuals, especially among males, are responsible for a disproportionate share of a population’s reproduction (Parker and Waite 1997). Many apparently healthy adults do not leave any offspring. Such inequity is generally not a problem – it is the basis for natural and sexual selection – but it may lead to difficulties in populations that suddenly get small because of its effect on genetic diversity. Consider the endangered Española Island giant tortoise of the Galápagos (see Case Study 1.1, “Return of the Tortoises to Española”). These tortoises likely numbered in the thousands but after most were killed for food by early mariners the population plummeted to 15, consisting of 12 females and just three males, which fortunately were rescued, placed in captivity, and have produced more than 1200 offspring since 1950 that have been released back to the island where they now breed on their own (Gibbs et al. 2014). Sounds like a success? It is. But it has also been discovered that the unequal sex ratio of those 15 survivors along with the unequal reproductive activity among them had led to a genetic effective population size of just 5.7 tortoises, far smaller than the census size of 15 might suggest (Milinkovitch et al. 2004). What little genetic variation remains in this population is severely threatened by the genetic drift exerted during the very long and “tight” bottleneck this species endured for many decades. Carefully managed pairings of surviving tortoises are now being made to maximize “capture” of what little genetic diversity remains for the newer generations. The bottom line to remember is that the effective population size is often substantially less than the actual number of individuals in a population, often only 10–20% (Vucetich et al. 1997). Thus, if you want a “population” of bison with Ne = 100 (hopefully sufficient to retain 99.5% of its genetic variability through at least one generation; see Table 5.3), you actually need a census population of somewhere between 500 and 1000.
Inbreeding
Inbreeding refers to the mating between closely related individuals; such individuals are likely to share identical copies of some of their genes because they have ancestors in common. We measure inbreeding with the inbreeding coefficient, F, which is the probability that two copies of the same allele are identical by descent – in other words, derived from a common ancestor (Templeton and Read 1994). For example, in our bison example, if both MDH‐1 X alleles in the X/X homozygous buffalo calf were derived from its grandmother, those alleles would be considered identical by descent.
Among several methods to estimate F (Frankham et al. 2009), the simplest involves counting links in the pedigree chain: F = (½) n , where n is the number of individuals or links in the pedigree chain starting with one parent, going back to the common ancestor, and then going down the other branch to the other parent. Figure 5.12(a) shows the pedigree chain for the offspring (A) of a half‐sister (B) mating with her half‐brother (C) (i.e. B and C have the same mother, D, but different fathers). The inbreeding chain has three links – B, D, and C – and thus F is equal to (½)³ = 1/8 = 0.125. If B and C were full siblings (i.e. they had both the same mother D and the same father E) (Fig. 5.12b), then there would be two chains, one for each common ancestor (B, D, and C for the mother plus B, E, and C for the father). In this case the F values for each chain would be added: (½)³ + (½)³ = ¼ = 0.25.
Figure 5.12 Inbreeding pedigrees for matings between: (a) a half‐sister with her half‐brother, (b) full sister and brother, and (c) full cousins (different parents but identical grandparents). See the text for an explanation of (a) and (b).
An Important Caveat
It must be emphasized that the equations presented in this section provide only estimates of the likely effects of processes that diminish genetic diversity. Exceptions may be fairly common. For example, Indian rhinoceros appear to have retained a high level of genetic diversity despite having passed through a serious bottleneck, perhaps because of high mobility of some individuals and long generation times (Dinerstein and McCracken 1990). The same applies to Chilean blue whales (Torres‐Florez et al. 2014) likely for the same reason: both rhinos and blue whales are long‐lived animals. Similarly, an isolated population of pinyon pine (also very long generation times) retained its genetic diversity over 300 years (Betancourt et al. 1991).
Even if the predicted effects on genetic diversity occur, they may not have catastrophic consequences for a population. For example, the northern elephant seal was reduced to as few as 20 individuals in the 1890s and now seems to have extremely low genetic diversity: no allozyme polymorphism at 24 loci from a sample of 159 seals from five colonies (Bonnell and Selander 1974) or at 43 loci from a sample of 67 seals from two colonies (Hoelzel et al. 1993). Despite this lack of genetic diversity, the northern elephant seal is now thriving with a total population approaching 200,000. The Mauritius kestrel also passed through a narrow bottleneck, just one breeding pair, that sharply reduced its genetic diversity, and has now recovered to over 200 pairs (Groombridge et al. 2000). In this case, examination of genetic material in museum specimens confirms that the original population was very diverse genetically despite being confined to a small island. Under special circumstances, passing through a bottleneck might have a positive effect by eliminating all the individuals carrying deleterious recessive alleles, thus purging these alleles from a population, something hermaphroditic mollusks, including highly endangered Hawaiian tree snails with high fecundity and the ability to self‐fertilize, may be capable of.
These may be examples of just a few lucky species that survived a bottleneck; the many other species that did not survive are not around to be studied and reported upon here. Even if there might be some benefits to inbreeding, they might be short‐lived if a bottleneck left the species so genetically uniform that it was ill prepared to adapt to future environmental change. That is a big concern for elephant seals and the Española Island giant tortoise we just discussed.
Cultural Diversity
The sharing of genes between parents and offspring is not the only mechanism by which information is transmitted from one generation to the next. Among many social animals information also moves among individuals and generations through learning, a process often called cultural transmission. Because changes in behavior can occur much faster than evolution, cultural diversity
