In ecological sampling, fair-sized areas should be 

 used wherever possible, but minimum-sized areas are 

 sometimes acceptable. For evaluation of this and 

 other procedures, see Goodall (1952). When the 

 number of species encountered on several randomly- 

 distributed sample plots is known, it is possible to 

 estimate statistically the actual number of species 

 present in the whole area (Evans, Clark, and Brand 

 1955). 



The size of the plot should also be adequate to in- 

 clude an accurate representation of the population 

 densities of the various species present. Much of the 

 difficulty of accurately determining population densi- 

 ties results from populations being non-randomly dis- 

 tributed in the space they could occupy (Cole 1946). 

 To be randomly distributed, populations must have 

 been scattered by chance rather than coercion, re- 

 gardless of the proximity or distance one from an- 

 other. This seldom occurs either with plants or ani- 

 mals. Plants reproduce by rhizomes, stolons, or suck- 

 ers or by seeds concentrated near the parent plants. 

 Animals usually lay eggs or drop young in local areas 

 or nests, so offspring are at least temporarily con- 

 centrated. Many animals congregate socially or 

 form colonies, concentrate on some local food supply, 

 or are grouped closely together in certain microhabi- 

 tats because of less favorable environmental condi- 

 tions elsewhere. Even the attraction of male to fe- 

 male for reproductive purposes is a variation from 

 random dispersal. Whenever the occurrence of one 

 or more organisms in an area increases the likeli- 

 hood that other organisms will occur nearby, this is 

 spoken of as contagious distribution. Species may 

 also exhibit negatively contagious distributions when 

 they are spaced more regularly than would be ex- 

 pected by chance, as for instance flocking or colonial 

 birds where each individual keeps just beyond the 

 pecking reach of its neighbor. 



When small-sized plots are used, contagious dis- 

 tribution shows itself in an excessive number of plots 

 containing no individual and of plots containing a 

 large number of individuals with a corresponding 

 deficit of plots with intermediate numbers of indi- 

 viduals. This represents a deviation from the typical 

 Poisson distribution which is expected with random 

 distribution (Snedecor 1956). In a Poisson series, 

 the mean number of individuals per quadrat should 

 equal the variance according to the formula 



S(^-J)2 _ 



x(n-l) -' 



The letter .r is the number in each quadrat, x is the 

 mean number in all quadrats, and n is the number 

 of quadrats. If the value obtained is significantly 

 greater than unity, then contagious distribution is 

 indicated, if the value is less than unity, then nega- 

 tively contagious distribution is indicated. For a 



reasonably large number of sample quadrats, say 20 

 or more, a deviation from unity would be considered 

 significant if it were greater than 2\/2n/{n — 1)^ 

 ( Andre wartha and Birch 1954). 



With contagious distribution of individuals, the 

 aggregates themselves are often randomly distrib- 

 uted, in which case quadrats may be increased in 

 size until they give a random distribution of aggre- 

 gates rather than of individuals. The total popula- 

 tion woidd then be computed by multiplying the num- 

 ber of aggregates per unit area by the average 

 number of individuals per aggregate. When aggre- 

 gation occurs but is not easily observed, then other 

 procedures must be employed (Cole 1946a, Goodall 

 1952). 



Number 



The number of sample plots needed depends 

 upon the precision desired for the statistical char- 

 acteristics to be estimated. The degree of precision 

 required will vary with the trustworthiness of the 

 data and the objectives of the study. In most sta- 

 tistical investigations, a range of 20 to 40 replications 

 is ample (Snedecor 1956: p. 104). Too few replica- 

 tions may fail to detect important differences, but too 

 many are unrewardingly wasteful of time and energy. 

 .Any differences noted between population densities 

 of different species on the same area, or of the same 

 species on different areas or at different times, should 

 be significant at least at the 5 per cent level of sta- 

 tistical probability. Where the number of samples is 

 small, the differences must be relatively large to insure 

 this level of confidence. With ecological studies in 

 the field, there are often practical difficulties involved 

 in obtaining a sufficient number of accurate measure- 

 ments to permit reliance on minor differences in pop- 

 ulation size. It is best, therefore, to be conservative 

 in evaluating the importance of differences in popula- 

 tion densities. Special care must be used in evaluat- 

 ing the densities of rare species, as such densities are 

 unlikely to be reliable if based on counts of less than 

 20 or 30 individuals (Preston 1948). 



CAPTURE-RECAPTURE METHOD 



Some general methods of calculating popu- 

 lation densities need to be considered. C. G. J. Peter- 

 sen, of the Danish Biological Station, working with 

 fish in 1896 ; F. C. Lincoln, of the US Fish and Wild- 

 life Service in 1930, trying to estimate the number 

 of ducks on the North American continent ; and 

 Jackson (1933), working with insects, all independ- 

 ently derived a formula for determining the popula- 

 tion size of various species of animals, much used in 



34 Background 



