Depensation phenomena and the Allee effect

One of the fundamental assumptions of the Malthusian population theory is that the ability of each individual to survive and/or reproduce is not affected by other individuals belonging to the same population. There is abundant experimental evidence to support the conclusion that in almost all populations this is not true. In most cases this mutual influence is negative, in the sense that it leads to a decrease of the ability of each organism to survive and reproduce (phenomenon of intraspecific competition). The parameter that plays a fundamental role is the density, i.e. the number of individuals in a certain area or volume: the bigger the density, the greater the mutual negative influence.

However, the presence of conspecific organisms is not always negative. In populations with a social structure, the inclusion of a further individual in a herd or flock can have a positive effect, because it can, for example, allow a better defence against predators or a more effective food research or a better offspring care. In this case there still exist density dependence effects, but they operate in the opposite direction, i.e. increasing density leads to higher birth rate and/or survival. This phenomenon is called depensation or Allee effect. Indeed, it was the American biologist Warner Allee (1931) the first to document an inverse dependence on density in the flour beetle Tribolium confusum (see Fig. 1). Subsequently, numerous examples have been well documented in natural populations outside the laboratory.

Figure 1: Per capita reproduction rate evaluated over a period of 11 days (filled circles) or 25 days (open circles) in a population of the flour beetle Tribolium confusum as a function of the initial density of individuals. Redrawn after the original figure reported in Allee (1931).

A first case of depensation in natural populations is that reported in the study of Birkhead (1977) on the common guillemot (Uria aalge) in Skomer island, South Wales. The left panel of Fig. 2 shows how the percentage of individuals that are able to reproduce, therefore the fertility, increases with density. This phenomenon is likely caused by the cooperation mechanisms against the attack of sea-gulls that prey on the eggs and juveniles of the guillemot (right panel of the same figure).

Figure 2: The left panel (modified after Birkhead, 1977) reports the positive influence of population density (assessed by a synthetic indicator) in the common guillemot Uria aalge on the percentage of individuals that manage to reproduce. The right panel shows an attack of a young guillemot by a sea-gull.

A second, very well documented example of Allee effect (Courchamp et al., 1999) is that pertaining to populations of wild dogs (Lycaon pictus, see Fig. 3) that have an important social structure. The wild dogs were once numerous and widespread in Africa, but now the wild dog is the most threatened large carnivore in this continent. Even in protected areas which have increasing abundances of once persecuted species, like the spotted hyena, wild dogs' observed decreases are of up to 30%. The reason was not clear until a few years ago. Then a group of Cambridge scientists (Courchamp et al., 1999) showed that it is exactly the Allee effect that negatively affects the populations of wild dogs. In fact they have a quite peculiar social life: when the juveniles reach the reproductive age, they leave the pack with a group of at most six other individuals of the same sex. A new pack is formed when one of these groups meets a group of the opposite sex. Then a pair becomes dominant and only these two animals reproduce, while the remaining dogs hunt and take care of the puppies. The Cambridge researchers have wondered whether there is a minimum pack size below which survival becomes difficult and found that the threshold exists and consists of three or four adults plus the dominant pair. Below this threshold, the group makes a difficult living, because a good number of “helpers” is necessary for cooperative hunting and defence against attacks by lions and hyenas, especially for the protection of puppies. Also small packs result in small cohorts of juveniles available for the colonization of new areas and so the problem is perpetuated along generations.

Figure 3: A group of wild dogs.

Even plants can display depensation effects. A documented example (Hackney and McGraw, 2001) is that of American ginseng (Panax quinquefolium L.), a perennial plant (see Fig. 4) that is grown for its root. The plant also grows in the wild and in this case the root's value is more than tripled. The survival of wild populations critically depends on pollination. It looks like for small populations the rate of pollination is reduced due to the fact that it is more difficult for pollinators to find ginseng plants. As a result the average number of fruits per flower and the average number of fruits per plant is an increasing function of plant density, as shown in Fig. 5.

Figure 4: Ginseng plants (Panax quinquefolium L.) and ginseng root.

Another possible depensation mechanism is linked to the probability of finding a partner of the opposite sex with whom to mate: for populations that are naturally low in numbers such as bears and whales, which can anyway launch signals even to great distances, the pairing probability is drastically reduced in very small populations, because the average distance between individuals is so great that signals can be received with much difficulty or are not received. It worthwhile to remark, however, that the population densities at which this effect becomes important are comparable to, if not lower than, those at which demographic stochasticity and genetic deterioration (which will be described later) start operating.

Figure 5: Reproductive success of American ginseng as a function of density (Hackney and McGraw, 2001).