untitled

removed or added Cxx-individuals (additions are positive, removals negative) and

Cyy-individuals: C=Cx+Cy. The size of the population before the manipulation

may be estimated as:

Y 1 =(Cx−p 2 C)/(p 2 −p 1 )

As with the index-manipulation-index method, Kelker’s method assumes that the

population is closed. Hence the two surveys to estimate the class proportions must

be run close together. Additionally, all removals or additions must be recorded and

the two classes must be amenable equally to survey.

Cooper et al. (2003) have extended this approach using likelihood estimates of the

ratios. When harvesting is highly skewed towards a single sex or age class, the change

in these ratios provides information about the exploitation rate, and, when combined

with absolute numbers removed, also provides information on absolute abundance.

Mark–recapture is a special case of the change-of-ratio method. A sample of the

population is marked and released, a subsequent sample being taken to estimate the

ratio of marked to unmarked animals in the population. From data of this kind we

can estimate the size of the population, and with further elaboration (individual mark-

ings, multiple recapturing occasions) the rate of gain and loss.

The huge number of mark–recapture models available have been reviewed adequately

by Blower et al. (1981) and in detail by Seber (1982) and Krebs (1999). Bowden

and Kufeld (1995) present methods of estimating confidence limits for general

mark–resighting calculations, using the example of Colorado moose (Alces alces). Here

we outline the range of methods, provide an introduction to the most simple of these,

emphasize their pitfalls, and mention some of the recent advances which might

circumvent those pitfalls.

Petersen–Lincoln models

A sample of Manimals are marked and released. A subsequent sample of nanimals

are captured of which mare found to be marked. If Yis the unknown size of the

population then clearly:

M/Y =m/n

within the limits of sampling variation. With rearranging, that equation allows an

estimate of populations size as:

Y =Mn/m

Intuitively obvious as that is, it is not quite right because of a statistical property of

ratios that leads on average to a slight overestimation. The bias may be corrected

(Bailey 1951, 1952) by:

Y=[M(n+1)]/(m+1)

which has a standard error of approximately:

SE(Y) =√[(M^2 (n+1)(n−m))/((m+1)^2 (m+2))]

236 Chapter 13

13.6.3Mark–
recapture