J. Spatial dynamics within populations

1. Scales of space utilization

All organisms occur somewhere in space, but there are large differences in the way they use space, in the area used, and in the time-scale of its use. Plants and sessile animals (benthos, aphids) are fixed at their substrate in a particular site (or microsite). As the individual grows, its site changes in size. Territorial animals also have individual sites, at least part of their lives.

Many non-sessile animals are more or less sedentary, and have a home range where they forage, usually with a nest site, den or burrow. Home ranges often overlap among individuals of a population, and their use varies in time scale from short periods of minutes to seasons, to the individual's lifespan. Many animals do not have home ranges as they are constantly on the move alone or in groups.

At small scales of time and space, animals (both with and without home ranges) choose particular places or parts of the landscape to search for food. These foraging patches are utilized for short periods of time, in contrast to life-long sites or long-term home ranges. The way animals behave in and among foraging patches has important consequences for population dynamics of both consumer and food organisms (MacArthur and Pianka 1966).

At the larger spatial scale, populations of animals, plants and microorganisms may exist in particular patches, separated by areas where density is much lower or where the organisms cannot live. Such configurations have been studied using different approaches, from island biogeography (MacArthur and Wilson 1965) to relationships in structured populations (Pulliam 1988, Fretwell and Lucas 1970) and metapopulation dynamics (Levins 1969). Especially the latter subject receives much attention, in particular because it addresses "modern" problems of habitat fragmetation and biodiversity conservation.

2. Foraging in patches

The way animals utilize food patches depends on the relationship between consumption rate or efficiency and food density or supply rate. There are three main types of functional responses of consumers to food density (Fig. 1A), based on the changes in a) searching and b) handling efficiency at different food densities (Begon et al. 1990, Chapter 9.5).

Type I depicts a situation where there is negligeable handling time, and the consumer is limited in its intake by food availability alone. Food availability affects searching efficiency, the amount of food ingested per time unit. At a particular density, food is handled at maximum searching efficiency, and more food does not increase it. This happens in Daphnia, which eats by moving a constant volume of water through its digestive system. Some grazing herbivores may also operate this way.

Type II is probably the most common functional response to food density, especially in invertebrate predators. At low food density, handling time is long, and decreases at higher density until the consumer handles the prey at maximum efficiency. This has been studied a lot for parasitoid wasps as they lay eggs in other insects.


Fig. 1. (A) Functional responses of consumers at various food densities, (B) consumer aggregation in patches with varying food density.

Type III functional responses are the same as the previous ones, but at low food density intake rate starts to increase disproportionately. This comes about by an increase of both searching rate and handling time as food becomes more common. Learning (in vertebrates) may lead to this kind of response.

Because animals tend to maximize food intake rate, they aggregate in patches with high food density (Fig. 1B). While in predators high intake rate is sufficient to explain aggregation, in herbivores the cause of aggregation is often protection against predation. Because consumption rate is highest at high food density, and because animals aggregate there, food is rapidly depleted. As a result, consumption rate decreases, even if the animals do not interfere with each other, which usually happens, and they tend to leave the food patch. However, this is only profitable if other patches are at least as rich in food as the one they are about to leave. The Ideal Free Distribution (Fretwell and Lucas 1970) describes situations where it can be assumed that a) the animals have perfect knowledge about the distribution of food density among all the patches in the landscape, and b) the costs of moving between the patches are negligeable. Thus, the animals will move into the richest food patches, and soon begin to leave them for poorer but less-utilized patches. This will lead to a distribution of consumers where food intake rate is constant throughout the landscape, but where consumer densities vary according to food density (Fig. 2).

Fig. 2. The ideal free distribution of consumers in three food patches (with high, medium and low quality); arrows indicate changes in consumer density as they aggregate, and switching to lower quality patches until profitability is equalized over all patches.

3. Structured populations

The phenomena of consumer aggregation and the IFD are often refered to as habitat selection, and occur at the level of individuals within populations, during foraging. It is logical that similar dynamics as the IFD may be found for sets of sub-populations living in distinct patches throughout most of their life cycle, not just for groups of animals in food patches. This is an important distinction, since the similarity is essentially an analogy involving demographic processes rather than short-term behavior. In the case of sub-populations inhabiting patches, population growth rate (or individual fitness) will be equalized over the landscape, in stead of food intake rate. The sub-populations differ in density according to the overall quality of the patches. The population dynamics in the patches are only partly determined individually, but depend on all others. Therefore, the entire network consists of one population, subdivided into sub-populations.

Structured populations with ideal free distribution of population densities over a large network of habitat patches may occur in more or less sedentary animals, and possibly sessile animals and plants. Because updating of information and switching among patches is unlikely, early assessment of both patch quality and density are required, which may often be impossible. Cohen (1967) and Shachak and Brand (1988) describe situations that may lead to the IFD at the population level, for (some) desert plants and for desert isopods, respectively. Since their success in growing, surviving and reproducing depend on the amount of water available in the patch where they settle or germinate, these organisms can assess ultimate patch quality early on in their growing season. Such precise selectivity is not likely to occur in environments where quality depends more strongly on more abiotic factors or on what other organisms do.

Even when they have no information on quality and population density in other patches, animals often migrate when they are young, in search of other patches in which to establish. In many animals this happens if local density is high and asymmetric competition for food or sites leads to very low or zero fitness of smaller or weaker individuals. In many other animals, juveniles emigrate irrespective of local density, either actively or passively. This is also the case in many plants, in the form of dispersal of seeds (or other propagules). Passive dispersal usually requires larger numbers of propagules than active dispersal, as many will not arrive in sites suitable for establishment and perish.

For local population growth and dynamics of the "source population", emigration is not different from mortality or lower fertility, since it does not matter whether individuals leave or die. Therefore, simple transition matrix models are applicable. For the "target" population, however, immigration of individuals produced elsewhere increases population density, which can increase population growth rate and/or lead to density-dependent effects. The effects of immigration can be modelled with transition matrices used as simulation models, but these provide less information on population growth than simple projection models. Immigration not only adds individuals to existing populations, but is also the mechanism for colonization of new populations in unoccupied patches, and can rescue doomed populations from extinction.

A special case of migration among patches containing sub-populations of structured populations is described by Pulliam (1988), where immigrants establish "sink" populations, which would not persist without immigration (population growth rate <1). The immigrants come from "source" populations that export "surplus" individuals. According to this model, sink populations can persist as long as there is a source population nearby, producing immigrants.

References

Cohen, D. 1967. Optimizing reproduction in a randomly varying environment when a correlation may exist between the conditions at the time a choice has to be made and the subsequent outcome. Journal of Theoretical Biology 16.

Fretwell, S. D. and Lucas, H. L. 1970. On territorial behavior and other factors influencing habitat distribution in birds. Acta Biotheoretica 19: 16-36.

Gilpin, M. 1992. Demographic stochasticity: A Markovian approach. Journal of Theoretical Biology 154: 1-8.

MacArthur, R. H. and Pianka, E. R. 1966. On optimal use of a patchy environment. American Naturalist 100: 603-609

MacArthur, R. H. and Wilson, E. O. 1967. The theory of island biogeography. Princeton, New Jersey, Princeton University Press.

* Pulliam, H. R. 1988. Sources, sinks, and population regulation. American Naturalist 132: 652-661.

* Shachak, M. and Brand, S. 1988. Relationship among settling, demography and habitat selection: An approach and a case study. Oecologia 76: 620-626.