Nonlinear density dependence of birth and death rates and the Allee effect

As mentioned above, density-dependent birth and death rates are assumed to vary linearly with density (Fig. 2.9). Although it is known from both laboratory (Smith and Cooper 1982) and field studies (Arcese and Smith 1988) that birth and death rates are often nonlinear (Fig. 2.10), such differences seem to have a minimal impact on natural populations. One major exception, however, is known as the Allee effect (Allee 1931). Allee proposed that many species have a minimum viable population (MVP) size. As described in Chapter 1, although Allee may have had a specific number in mind, below which death rates rise and/or birth rates collapse, a more modern view is that the probability of extinction has become unacceptably high when a population becomes small (Shaffer 1981, Miller and Lacy 2003), but there is no one specific number described as a MVP.

Why should there be higher death rates in very small populations? Proposals include: (i) group cooperation reduces losses from predators; (ii) group foraging for food is more efficient (foraging facilitation); and (iii) small populations are more subject to density-independent or stochastic extinctions as well as genetic effects such as inbreeding depression. Low birth rates in small populations could result from pollination failure in plants, male and female animals unable to locate each other, or the chance of a very unequal sex ratio (large number of males, few females).

Population size

Figure 2.9 Linear response of birth and death rates to population density. b, birth rate; d, death rate; r, intrinsic rate of increase; K, carrying capacity.

1 50 100

Population size

Figure 2.10 Nonlinear response of birth and death rates to population density.

For example, the common guillemot or murre (Uria aalge) nests in colonies. Breeding success in south Wales was found to be only 25% in the least dense populations as compared to an average of 75% in the densest populations (Birkhead 1977). The reason for this appears to be that predation on eggs and chicks by gulls is reduced in dense guillemot populations. A similar result was obtained in a study on lapwings (Vanellus vanellus) in which egg clutches lost to avian predators declined with an increase in the number of close neighbors (Berg et al. 1992). Nest parasitism also appears to increase in low populations. For example, small dickcissel (Spiza americana) populations are particularly hard hit by brown-headed cowbirds (Molothrus ater) (Fretwell 1986).

Other studies have found that cooperative hunters such as lions, hyenas, wolves and various fish species have much higher success rates when hunting in large groups and do poorly when population sizes fall (Caraco and Wolf 1975, Major 1978). This translates into a higher mortality rate in the smaller groups. From the perspective of the prey, a dense population is harder to surprise, and mortality from predation is lower in larger prey populations (Kenward 1978, Jarman and Wright 1993). Colonial nesting sunfishes have even been found to suffer lower rates of fungal infections on their eggs as compared to solitary sunfish (Cote and Gross 1993). Therefore higher density leads to higher, not lower, survivorship.

Although this is an oversimplification, we can illustrate the Allee effects graphically by identifying a minimum viable population size, MVP (Fig. 2.11). Below point MVP, the population declines to extinction. Above point MVP the population increases rapidly before slowing down as it approaches K. The value of r is positive above MVP and below K, but is otherwise negative (Figure 2.11).

The extinction of the heath hen (Tympanuchus cupido) is a likely example of the Allee effect. By 1870, hunting and habitat loss had restricted it to Martha's Vineyard off the coast of Massachusetts. In 1908 a 650 ha refuge was established and the population grew to about 2000 birds. In 1916, however, a fire swept across the island, destroying nests, eggs, and females on the nests. The following winter was severe and an unusually heavy concentration r < 0

Population size

Figure 2.11 Birth and death rate versus population density, showing the AUee effect. MVP, minimum viable population.

of goshawks (Accipiter gentilis) arrived. The population was reduced to less than 150, of which most were probably males. By 1928 the population had declined to a single male that died in 1932. In this case, abiotic effects contributed significantly to the extinction of the heath hen. Although we can never be sure, it appears likely that something of a similar nature happened to the passenger pigeon (Ectopistes migratoris) described in the introduction to Part I. They were mercilessly hunted and no one imagined the possibility of extinction. But once their flocks were drastically reduced, they appeared unable to recover (Souder 2004).

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