Estimating the variables from life tables and fecundity schedules

In populations with overlapping generations (or continuous breeding), r is the intrinsic rate of natural increase that the population has the potential to achieve; but it will only actually achieve this rate of increase if the survivorship and fecundity schedules remain steady over a long period of time. If they do, r will be approached gradually (and thereafter maintained), and over the same period the population will gradually approach a stable age structure (i.e. one in which the proportion of the population in each age class remains constant over time; see below). If, on the other hand, the fecundity and survivorship schedules alter over time - as they almost always do - then the rate of increase will continually change, and it will be impossible to characterize in a single figure. Nevertheless, it can often be useful to characterize a population in terms of its potential, especially when the aim is to make a comparison, for instance comparing various populations of the same species in different environments, to see which environment appears to be the most favorable for the species.

This is only approximately equal to the true generation time T, because it takes no account of the fact that some offspring may themselves develop and give birth during the reproductive life of the parent.

Thus Equations 4.15 and 4.16 allow us to calculate Tc, and thus an approximate value for r, from a cohort life table of a population with either overlapping generations or continuous breeding. In short, they give us the summary terms we require. A worked example is set out in Table 4.5, using data for the barnacle Balanus glandula. Note that the precise value of r, from Equation 4.14, is 0.085, compared to the approximation 0.080; whilst T, calculated from Equation 4.13, is 2.9 years compared to Tc = 3.1 years. The simpler and biologically transparent approximations are clearly satisfactory in this case. They show that since r was somewhat greater than zero, the population would have increased in size, albeit rather slowly, if the schedules had remained steady. Alternatively, we may say that, as judged by this cohort life table, the barnacle population had a good chance of continued existence.

Table 4.5 A cohort life table and a fecundity schedule for the barnacle Balanus glandula at Pile Point, San Juan Island, Washington (Connell, 1970). The computations for R0, Tc and the approximate value of r are explained in the text. Numbers marked with an asterisk were interpolated from the survivorship curve.

Age (years)

Table 4.5 A cohort life table and a fecundity schedule for the barnacle Balanus glandula at Pile Point, San Juan Island, Washington (Connell, 1970). The computations for R0, Tc and the approximate value of r are explained in the text. Numbers marked with an asterisk were interpolated from the survivorship curve.

Age (years)

x

ax

lx

m

lx^x

xlx^x

0

1,000,000

1.000

0

0

1

62

0.0000620

4,600

0.285

0.285

2

34

0.0000340

8,700

0.296

0.592

3

20

0.0000200

11,600

0.232

0.696

4

15.5*

0.0000155

12,700

0.197

0.788

5

11

0.000110

12,700

0.140

0.700

6

6.5*

0.0000065

12,700

0.082

0.492

7

2

0.0000020

12,700

0.025

0.175

8

2

0.0000020

12,700

0.025

0.200

1.282

3.928

R0 = 1.282;

7 = 3.928 = 3.1; ' 1.282

r _ ln R 7C

= 0.08014.

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