Enumeration of Fish or Other Aquatic Animals

Abstract

There are various ways of estimating the size of a natural population of large, mobile animals in a freshwater habitat. Obviously, the most accurate method would involve catching or, in some way, counting the entire population. However, this approach is usually either impossible to do in practice or, at least, destructive to the natural populations. Instead, a mark-and-recapture procedure frequently is used to obtain a statistical estimate of the size of the natural population.

The mark-and-recapture technique is based on the premise that recognizable (marked) organisms released to the population will be recaught in numbers proportional to their abundance in that population. The size of the natural population can be estimated from the proportion of marked to unmarked organisms in random samples obtained from the entire population.

The basis for this technique apparently was first published in 1662 by John Graunt in an article on human demography in London (Ricker, 1975). Later, Petersen (1896) applied the method to fish populations, and others have used it in various ways since, e.g., the Lincoln (1930) index for birds. According to this procedure:

$$\hat N = \frac{{SM}}{R}$$

where N̂ = estimate of total number in the population; S = total number of organisms in a sample from the population; M = total number of marked organisms in the population; and R = number of marked organisms in the sample. However, certain basic assumptions must be made for the mark-and-recapture technique to be valid:

• 1. There can be no difference in mortality or emigration between marked and unmarked organisms.

• 2. Tags or other marks must remain recognizable and must not be lost. All marks on recaptures must be reported.

• 3. There must not be a difference in catch-ability between marked and unmarked organisms.

• 4. Marked organisms must be mixed randomly within the entire population.

• 5. There can be no unknown recruitment or immigration to the population.

There are many modifications of the basic Petersen relationship [cf., Ricker (1975)], but only the two commonly used for fish or other aquatic vertebrates will be presented here.