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This section outlines some of the methods available for calculating the size of a

population by techniques that do not necessarily depend on accurate counts of

animals. The line-transect method could well come under this head but it is placed

in “sampled counts” because it requires accurate counting of animals on the line.

If we obtain two indices of population size, I 1 and I 2 , the first before and the second

after a known number of animals Cwas removed, the population’s size can be

estimated for the time of the first index by:

Y 1 =I 1 C/(I 1 −I 2 )

The proportion removed is estimated as p* =(I 1 −I 2 )/I 1 and the proportion of those

remaining as q* = 1 −p*. Following Eberhardt (1982), the variance of the estimate

of Ycan be approximated by:

Var(Y 1 ) ≈Y 12 (q*/p*)^2 (1/I 1 +1/I 2 )

from which SE(Y 1 ) =√Var(Y 1 ). Eberhardt (1982) gives three examples from popu-

lations of feral horses. The data from his Cold Springs population were:

I 1 = 301

I 2 = 76

C = 357

p* =0.748

Thus, the population at the time of the first index is estimated as:

Y 1 =(301 ×357)/(301 −76) = 478

with a variance of that estimate of:

Var(Y 1 ) ≈ 4782 (0.252 /0.748)^2 (1 / 301 +1 / 76) = 428

from which SE(Y 1 ) =√ 428 =21.

The index-manipulation-index method assumes that the population is closed (no

births, deaths, immigration, or emigration) between the estimation of the first and

second indices. That assumption is approximated when the entire experiment is run

over a short period.

If a population can be divided into two classes, say males and females or juveniles

and adults, and one class is significantly reduced or increased by a known number

of animals, the size of the population can be estimated from the change in ratio. Kelker

(1940, 1944) introduced this method to estimate the size of deer populations man-

ipulated by bucks-only hunting.

The two classes are designatedxand y. Before the manipulation there was a pro-

portion p 1 of x-individuals in the population, and p 2 after the manipulation which

COUNTING ANIMALS 235

13.6 Indirect estimates of population size

13.6.1Index-
manipulation-index
method

13.6.2Change-of-
ratio method