# Animal Ecology

# ANIMAL ECOLOGY

Animal ecology concerns the relationships of individuals to their environments, including physical factors and other organisms, and the consequences of these relationships for evolution, population growth and regulation, interactions between species, the composition of biological communities, and energy flow and nutrient cycling through the ecosystem. From the standpoint of population, the individual organism is the fundamental unit of ecology. Factors influencing the survival and reproductive success of individuals form the basis for under-standing population processes.

Two general principles guide the study of animal ecology. One is the balance of nature, which states that ecological systems are regulated in approximately steady states. When a population becomes large, ecological pressures on population size, including food shortage, predation, and disease, tend to reduce the number of individuals. The second principle is that populations exist in dynamic relationship to their environments and that these relationships may cause ecological systems to vary dramatically over time and space. One of the challenges of animal ecology has been to reconcile these different viewpoints.

Populations depend on resources, including space, food, and opportunities to escape from predators. The amount of a resource potentially available to a population is generally thought of as being a property of the environment. As individuals consume resources they reduce the availability of these resources to others in the population. Thus, individuals are said to compete for resources. Larger populations result in a smaller share of resources per individual, which may lead to reduced survival and fecundity. Dense populations also attract predators and provide conditions for rapid transmission of contagious diseases, which generate pressure to reduce population size.

Changes in population size reflect both extrinsic variation in the environment that affects birth and death rates and intrinsic dynamics that result in oscillations or irregular fluctuations in population size. In some situations, the stable state may be a regular oscillation known as a limit cycle. Ecological systems also may switch between alternative stable states, as in the case of populations that are regulated at a high level by food limitation or at a low level by predators or other enemies. Switching between alternative stable states may be driven by changes in the environment.

## Population Increase

In the absence of the effects of crowding, all populations have an immense capacity to increase. This capacity may be expressed as an exponential growth rate, which describes the growth of a population in terms of its relative, or percentage, rate of increase, like continuously compounded interest on a bank account. The constant *r* is often referred to as the Malthusian parameter. For a population growing at an exponential rate, the number of individuals (*N*) in a population at time *t* is *N(t)* = (0)e^{rt} where *N*(0) is the number of individuals at time 0. Accordingly, the increase in a single time unit is e^{r}, which is the constant factor by which the population increases during each time period. The rate of increase in the number of individuals is then given by d*N*/d*t* = *rN*. The doubling time in years of a population growing exponentially is *t*_{2} = (*ln* 2)/*r*, or roughly 0.69/*r*.

Estimated exponential annual growth rates of unrestrained populations range from low values of 0.077 for sheep in Tasmania and 0.091 for Northern elephant seals, to perhaps 1.0 for a pheasant population, 24 for the field vole, 10^{10} for flour beetles in laboratory cultures and 10^{30} for the water flea *Daphnia.* Human populations are at the lower end of this range, but a realistic exponential growth rate of 0.03 (or slightly above 3% per year) for some human populations is equivalent to a doubling time of about 23 years and a roughly thousand-fold increase in 230 years. Clearly, no population can maintain such a growth rate for long. (Expansion at the estimated annualized rates just cited for the field vole, flour beetle, and water flea is necessarily utterly fleeting.)

The exponential growth rate of a population can be calculated from the schedule of fecundity at age *x* (*b*_{x}) and survival to age *l*) in a population. These "life table" variables are related to population growth rate by the Euler, or characteristic, equation,

whose solution requires matrix methods. When the life table is unchanging for a long period, a population assumes a stable age distribution, which is also an intrinsic property of the life table, and a constant exponential rate of growth. Thus, assuming constant birth and death rates, the growth trajectory of a population may be projected into the future. However, because populations are finite and births and deaths are random events, the expected size of a population in the future has a statistical distribution that may include a finite probability of 0 individuals, that is, extinction. As a general rule, the probability of extinction decreases with increasing population size and increasing excess of births over deaths.

## Population Regulation

Balancing the growth potential of all populations are various extrinsic environmental factors that act to slow population growth as the number of individuals increases. High population density depresses the resources of the environment, attracts predators, and, in some cases, results in stress-related reproductive failure or premature death. As population size increases, typically death rates of individuals increase, birth rates decrease, or both. The result is a slower growth rate and a changed, usually older, population. The predominant model used by animal ecologists to describe the relationship of population growth rate to population size (or density) is the logistic equation, in which the exponential growth rate of the population decreases linearly with increasing population size:

where *r*_{0} is the exponential growth rate of a population unrestrained by density (i.e., whose size is close to 0) and *K* represents the number of individuals that the environment can support at an equilibrium level, also referred to as the carrying capacity of the environment. Accordingly, the rate of growth of the population is expressed as

Notice that when *N* < *K*, the growth rate is positive and the population grows. When *N* >*K*, the density-dependent term (1 - *N*/*K*) is negative and the population declines. When *N* = *K*, the growth rate is 0 and a stable, steady-state population size is achieved. This depressing impact of density on the population growth rate is known as negative feedback.

The differential form of the logistic equation may be integrated to provide a function for the trajectory of population size over time,

The curve is sigmoid (S-shaped), with the rate of growth, d*N*/d*t* reaching a maximum (the inflection point) at *N* = *K*/2. Because this is the density at which individuals are added to the population most rapidly, the inflection point also represents the size of the population from which human consumers can remove individuals at the highest rate without causing the population to decline. Thus, the inflection point is also known as the point of maximum sustainable yield.

Density dependence can take on a variety of forms. One of these is a saturation model where the exponential growth rate remains constant and positive until a population completely utilizes a nonrenewable resource such as space, and population growth stops abruptly. The approach of a population to an equilibrium level determined by density-dependent processes can be altered by environmentally induced changes in the intrinsic rate of population growth or in the carrying capacity of the environment.

Difficulties in finding mates and maintaining other social interactions at low densities, including group defense against predators, may also cause the population growth rate to decrease as density declines (the Allee effect), and, below a certain density threshold, may even result in population decline to extinction. This type of response is a *positive* feed-back, one that promotes population instability. For example, after commercial hunting had reduced populations of the passenger pigeon to low levels, the decline in social interactions in this communally nesting species is thought to have doomed it to extinction.

Populations have inherent oscillatory properties that can be triggered by time lags in the response to changing density and which cause populations to fluctuate in a perpetual limit cycle, with alternating population highs and lows. In these cases higher values of *r* can send a population into unpredictable chaotic behavior, increasing the risk of extinction. In a population with continuous reproduction, regular population cycles occur when there is a lag, often equal to the period of development, in the response of a population to its own density effects on the environment. When the time lag is of period τ, limit cycles develop when rτ exceeds π/2, and the period of the cycle is 4 to 5 times τ.

## Metapopulations

Most natural populations consist of many subpopulations occupying patches of suitable habitat surrounded by unsuitable environments. Oceanic islands and freshwater ponds are obvious examples. But fragmentation of forest and other natural habitats resulting from clearing land for agriculture or urban development is increasingly creating fragmented populations in many other kinds of habitats. These subpopulations are connected by movement of individuals, and the set of subpopulations is referred to as a metapopulation. Metapopulations have their own dynamics determined by the probabilities of colonization and extinction of individual patches. A set of simple metapopulation models describes changes in the proportion of patches occupied (). When the extinction probability (*e*) of an individual patch is independent of *p*, the rate of loss of subpopulations is simply *pe*. The rate of colonization is proportional to the number of patches that can provide potential colonists and the proportion of empty patches that are available to receive them. Hence, colonization is equal to *cp*(1-*p*), where *c* is the rate of colonization.

The metapopulation achieves a steady state of number of patches occupied when colonization balances extinction, that is *pe* = *cp*(1-*p*), or *p̂* = 1-*e/c*. In this model, as long as the rate of colonization exceeds that of extinction, the metapopulation will persist. In more complex models, particularly when the probability of population extinction is reduced by continuing migration of individuals between patches (which keeps the sizes of subpopulations from dropping perilously low), the extinction rate and colonization rate both depend on patch occupancy. In this case, the solution to the metapopulation model has a critical ratio of colonization to extinction, below which patch occupancy declines until the metapopulation disappears. Thus, changes in patch size or migration between patches can cause an abrupt shift in the probability of metapopulation persistence.

## Predator-Prey Interactions

The dynamics of populations are influenced by interactions with predator and consumer populations. Because these interactions have built-in lag times in population responses, they often result in complex dynamics. Among the most spectacular fluctuations in size are those in populations of snowshoe hares and the lynx that prey on them. Population highs and lows may differ by a factor of 1,000 over an oscillation period of about ten years. Oscillation periods in other population cycles of mammals and birds in boreal forest and tundra habitats may be either approximately four years or nine to ten years.

The biologists Alfred Lotka and Vito Volterra independently developed models for the cyclic behavior of predator-prey systems in the 1920s. The most basic model expresses the rate of increase in the prey population in terms of the intrinsic growth capacity of the prey population and removal of prey individuals by predators, which is proportional to the product of the predator and prey population sizes. The growth of the predator population is equal to its birth rate, which depends on how many prey are captured, minus a density-independent term for the death of predator individuals. The joint equilibrium of the prey and predator populations is determined by the predation efficiency and the relative rates of birth and death of the prey and predator, respectively. However, the equilibrium is neutral, which means that any perturbation will set the system into a persisting cycle. More complex models of predator-prey interactions include a balance between various stabilizing factors, such as density-dependent control of either population, alternative food resources for predators, and refuges from predators at low prey densities, and destabilizing factors, such as time lags in the response of the predator and prey to each other. For the most part, these models predict stable predator and prey populations under constant conditions.

Both empirical and experimental studies have shown that the rate of predation is nonlinear, violating one of the assumptions of the Lotka-Volterra model. When predation is inefficient at low prey densities and predator populations are limited by density-dependence at high predator densities, there may be two stable points. One of these is at a high prey population level limited by the prey population's own food supply, the other at a low prey population level limited by predators. When a prey population, such as a crop pest, is released from predator control following depression of the predator population by extrinsic factors such as climate, disease, pesticides, and so on, the prey may increase to outbreak levels and become a severe problem. Thus, agricultural practices that incidentally depress the populations of natural control organisms can have unwanted consequences.

A special kind of predator-prey model is required to describe the interactions between parasites, including disease-causing organisms, and their hosts. These models need to take into account the fact that parasites generally do not kill their hosts, that the spread of parasites among hosts may depend on population density and the presence of suitable vectors, and that hosts may raise defensive immune reactions. Immune reactions create a time lag in the responses of parasite and host populations to each other and may result in strong fluctuations in the prevalence of parasitic diseases.

## Conclusion

The study of animal populations tells us that for any given set of conditions the size of a population is limited by the resources available to it. The human population is no exception. At high densities, the stresses of poor nutrition and social strife all too often signal a reduced quality of life.

The study of animal populations has provided guidelines for the management of nonhuman populations, including those of domesticated animals, game birds and mammals, fish stocks, species of conservation concern, pests, and disease organisms. In general, fragmentation and simplification of systems lead to exaggerated population fluctuations and the development of alternative stable states, and they may thus increase the probability of epidemics, pest outbreaks, and extinction. Hunting, overfishing, and overgrazing have led to severe reduction in some food sources and deterioration of habitat quality. Controls on populations are so complex that manipulation of environmental factors in complex systems often results in unforeseen consequences. In a classic case, nineteenth-century hunting of sea otters on the Pacific coast of North America resulted in the explosion of populations of their sea urchin prey, which in turn seriously harmed the kelp beds that serve as important nurseries for fish stocks. Many such examples show how difficult it is to replace natural controls with human management, although the need to maintain a high quality of life for the human population in an increasingly stressed environment makes it imperative that we learn to do this wisely.

**See also:** *Biogeography; Biology, Population.*

## bibliography

Anderson, Roy M., and Robert M. May. 1991. *Infectious Diseases of Humans. Dynamics and Control.* Oxford: Oxford University Press.

Ballou, Jonathan D., Michael E. Gilpin, and Thomas J. Foose, eds. 1995. *Population Management for Survival and Recovery. Analytical Methods and Strategies in Small Population Conservation.* New York: Columbia University Press.

Begon, Michael, Martin Mortimer, and David J. Thompson. 1996. *Population Ecology: A Unified Study of Animals and Plants,* 3rd edition. Oxford: Blackwell Science.

Caswell, Hal. 2001. *Matrix Population Models: Construction, Analysis, and Interpretation,* 2nd edition. Sunderland, MA: Sinauer Associates.

Gotelli, Nicolas J. 2001. *A Primer of Ecology,* 3rd edition. Sunderland, MA: Sinauer Associates.

Hanski, Ilkka A., and Michael E. Gilpin, eds. 1997. *Metapopulation Biology, Ecology Genetics, and Evolution.* San Diego, CA: Academic Press.

Nisbet, Roger M., and William S. C. Gurney. 1982. *Modelling Fluctuating Populations.* New York: Wiley.

Pielou, Elizabeth C. 1997. *Mathematical Ecology.* New York: John Wiley.

Pimm, Stuart L. 1991. *The Balance of Nature?* Chicago: University of Chicago Press.

Tilman, David. 1982. *Resource Competition and Community Structure.* Princeton, NJ: Princeton University Press.

Robert E. Ricklefs

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**Animal Ecology**