Population Dynamics and Models of Population Regulation

One of the central questions in population ecology is – what determines the size of a natural population?

The answer is – different factors or mechanisms under different circumstances.

In a synthesis on population regulation, Krebs (1994) emphasizes the role of the following factors:

(a) Limiting factors:

A factor is defined to be a limiting factor if a change in the factor produces a change in the equilibrium or average density. For example, a disease may be a limiting factor for a fish population if fish population abundance is lower when the disease is present.

(b) Regulating factors:

A factor is defined to be a regulating factor if the percentage mortality caused by the factor increases with population density; or, alternatively a factor is defined to be a regulating factor if the reproductive rate is reduced as the population rises. For example, a disease may be a regulating factor only if it causes a higher fraction of losses as fish density goes up.

Krebs (1994) has proposed two approaches to study population regulation. These are: key factor analysis and experimental analysis. Key factor analysis, proposed by Morris (1957), is a technique of analyzing populations through the preparation of life tables (egg, larval, pupal and adult stage) and a retrospective analysis of year to year changes in reproduction and mortality.

For each drop in numbers in the life table we define:

k = log (Ns) – log (Ne)

Where, k = instantaneous mortality coefficient

N_s = number of individuals starting the stage

N_e= number of individuals ending the stage

For example, 83 larvae entered the pupal stage, and of these, 54.6 were killed by predators which reduced the population to 28.4 per square m. Hence k (instantaneous mortality coefficient for pupal predation)

= log (83.0) – log (28.4)

= 0.47

However, key factor analysis assumes that all mortality factors are additive (K = k₁ + k₂ + k₃) and it ignores compensatory mortality. Various mortality agents may cause additive compensatory losses in populations. Additive losses may limit or regulate population density, but compensatory losses may be irrelevant to both regulation and limitation.

In Experimental analysis approach, we try to identify limiting factors and study them experimentally. If we find that food is a limiting factor, we can increase the food supply and see if population size increases accordingly. But it should be noted that in many cases more than one factor may be involved (e.g., food supply and parasite levels) and often it is not possible to manipulate a suspected factor (e.g., weather).

Krebs (1994) comments that experimental analysis is forward- looking and oriented toward hypothesis testing about mechanisms of regulation; key factor analysis is backward – looking and is confined to a descriptive analysis of a population; and theoretically both method should converge to provide an understanding of population regulation.

According to Krebs (1994), population regulation in plants must be discussed as regulation of biomass rather than numbers, because most plants are modular organisms. Crawley (1990) mentioned that plant ecologists have not usually addressed the problem of population regulation in the same way as animal ecologists, but the same general principles can be applied. As a plant population increases in biomass (and numbers), their reproduction or survival is reduced by shortage of factors like space, nutrients, water or light; or damage by herbivores, parasites and diseases.

Since they have fixed location, competition for nutrients or light is considered an important factor in their population regulation. This competition has been described by the – 3/2 power rule, also called the yoda’s rule or self- thinning rule. This rule describes the relationship between individual plant size and density in even – aged populations.

Mortality or “thinning” from intra-population competition is postulated to fit a theoretical line with a slope of – 3/2, as mentioned below:

Log m = – 3/2 (log N) + K

where m = average plant weight (g)

N = plant density (individuals per square meter)

K = a constant

This line has been suggested as an ecological law (Westoby, 1984) that applies both within one plant species and between different plant species. Weller (1987) found that more shade tolerant gymnosperm trees had more shallow slopes than the predicated value. His results argue against single, quantitative thinning rule for all plant species as they differ widely in competition for nutrients, water and light.

The questions as – what stops population growth beyond a limit, and what determines average abundance have been answered by Krebs (1994) on the basis of the following theories. These general theories focus on the interactions between the population and the environmental factors o food, weather, shelter and enemies like parasites, predators and diseases.

1. Biotic School:

The biotic school suggests that density-dependent factors play a key role in preventing population increase and in determining average abundance. The two entomologists Howard and Fiske (1911)were the prototypes of biotic school of population regulation, which proposed that biotic agents like predators and parasitoids were the main agents of natural regulation.

According to Nicholson (1933), who is considered as one of the pioneers of the biotic school, the only factor that can control populations is some kind of competition (competition for food, competition for space, or the competition of predators and parasites).

Smith (1935) also favoured the main points of Nicholson and pointed out that density-dependent factors are mainly biotic in nature – competition, predation, disease; and that the density-independent factors are mainly abiotic or physical in nature, mainly die climate. But he also pointed out that climate might act as density-dependent factor under some circumstances.

For example, in the case of protective refuges, if there are only so many of these ID go around and all the unprotected individuals are killed by climate, the climate mortality would be density-dependent. The biotic school emphasizes that balance in nature is produced by density-dependent factors, which are usually biotic in nature such as predators and diseases.

2. Climatic School:

Bodenheimer (1928) was the first to suggest that the population density of insects is regulated primarily by the effects of weather. According to him, weather effects both development and survival of insects. He was also impressed by the fact that weather was responsible for the largest part of the mortality of insects, as 80 to 90 per cent of the insects in their early stages of development are killed by weather factors.

Uvarov (1931) in his paper “Insects and Climate” also pointed out the role of climatic factors on the growth, fertility and mortality of insects. Thus, climatic school emphasizes the role of weather factors and suggests that weather may act as a density-dependent control.

3. Self-Regulation School:

According to this school, a population is regulated by intrinsic factors. From a study of rodent populations Chittay (1960) proposed that all species are capable of regulating their own population densities without destroying the renewable resources of their environment or requiring enemies or bad weather to keep them from doing so. The self-regulation school thus emphasizes on events going on within a population and on individual differences in behaviour and physiology.

The general premise of this school is that abundance may change because the quality of individuals changes. Population increase may be stopped by a deterioration in the quality of individuals as density rises rather than a change in environmental factors. Average abundance may be altered by genetic changes in populations. According to this school, both quality and quantity are important aspects of natural populations and therefore the most important environmental factor for such populations is – other organisms of the same species.

Giving an example of territorial behaviour m birds, Wynne-Edwards (1962) suggested that food played an important role in the problem of self-regulation. In birds, population density is controlled by territoriality, which is a means to eliminate competition for food and further ensures that food supply will not be exhausted.

4. Comprehensive School:

Thompson (1929) was the first to adopt the comprehensive theory of natural control. He included all factors from climate to parasites and suggested that the control was due to a complex of factors. Schwerdtfeger (1941) also favored comprehensive theory and emphasized the role of joint action of many factors.

According to him, networks of interactions are involved in population control. He termed this network the “grandocoen”, which he defined as the totality of all the factors that affect the population changes of the species. This grandocoen varies from place to place and from time to time and differs for different species. Thus, he emphasized not only the connection between factors but also between species.

According to Andrewartha and Birch (1954), the numbers of animals in a natural population may be limited in three ways:

(a) By shortage of food, or places to make nests;

(b) By in accessibility of these material resources relative to the animal’s capacities for dispersal and searching; and

(c) By shortage of time when the rate of increase (r) is positive.

Of these three ways, they believe that the last is probably the most important in nature. They also pointed out that in any population an animal’s chance to survive and multiply depends on all the four components of the environment- weather, food, other animals and pathogens, and living place. Thus, there may be cases when population size is largely determined by weather, and other cases in which population size is mainly determined by other animals.

Population regulation implies that one or more factors are always involved in controlling population size whether they are constant or temporally variable in operation (Chapman and Reiss, 1995).