A note on the related concepts ‘mean crowding’ and ‘mean concentration’

LLOYD's (1967) parameter m e a n c r o w d i n g is defined as the mean number of other individuals per individual per quadrat and given by . O O m = ~ x j ( x j 1 ) / ~ . x ~ = m + ( a V m 1) (1) j=l j=l where xj is the number of individuals in the j th quadrat, Q is the total number of quadrats contained in the population area, and m and o 3 are mean density and variance of the population respectively. LLOYD also proposed the related concept mean d e m a n d which is simply given by ( re+ l ) and interpreted as the mean number of individuals per individual per quadrat. Although LLOYD proposed these parameters to give appropriate measures of detecting the crowding effects (m for direct interference and m + l for indirect effect through the depletion of resources) in non-aggregated animals, either of these can be used more generally as the measure of aggregation in the population (IWAO, 1068; PmLOU, 1969). PATIL and STITELER (1074) pointed out that mean crowding can be defined more formally as the ratio of the second to the first factorial moments: ~k m = E [ X ( X 1) ] / E ( X ) = ~'(~)/~'(,). (2)