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17 Conservation in theory

In this chapter we deal with theory that has been developed to account for why and

how populations become extinct. Most of that theory deals with extinction as a

consequence of low numbers, the various difficulties that a population can get into

when it is too small. A second class of extinction processes – those caused by a per-

manent and deleterious change in the population’s environment – is less well served

by theory, but promising new approaches are under development.

Demography deals with the probability of individuals living or dying and, if they live,

the probability that they will reproduce. Those individual probabilities, accumulated

over all individuals in the population, determine what the population as a whole will

do next, whether it will increase, decrease, or remain at the same size. Three effects

can influence the population outcome underlain by those individual probabilities: indi-

vidual variation, short-term environmental variation, and environmental change.

These will be examined in turn, particularly in the context of the likelihood of the

population going extinct.

A population’s rate of increase is determined by the age-specific fecundity rates

interacting with the age-specific mortality rates, but its value is predictable only when

the population has a stable age distribution. If it does not have a stable age distri-

bution, or if numbers are low, the actual rate of increase may vary markedly in either

direction from that predicted by the life table and fecundity table (see Chapter 6).

This effect is called demographic stochasticity.

Take the hypothetical case of a population of 1000 large mammals whose in-

trinsic rate of increase is rm=0.28. A female can produce no more than one offspring

per year. The population is at a low density ofD=0.01/ km^2 so there will be little

competition for resources and consequently rate of increase will be close to rm. On

average the probability of an individual surviving 1 year isp=0.9, and the prob-

ability that a female will produce an offspring over a year is b = 0.95. The

beginning of the year is defined as immediately after the birth pulse, at which

time the population contains 500 males and 500 females. By the end of the year

the population will have been reduced by natural mortality to about 900 (i.e.

1000 ×0.9) and these animals produce about 428 offspring (450 ×0.95) at the next

birth pulse. The population therefore starts the next year with about 1328 indi-

viduals (900 +428), having registered a net increase over the year at about the rate

r=loge(1328/1000) =0.28, or 32%. The actual outcome will be very close to those

figures because the differences in demographic behavior between individuals tend to

cancel out.

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17.1 Introduction

17.2 Demographic problems contributing to risk of extinction

17.2.1Effect of
individual variation