Number, length, area or biomass: Can there be intermidiates?

Abstract

The abundance of a given species is usually expressed in terms of either the number of individuals per unit area or volume (i.e., density), or biomass. These two abundance metrics generate different results at both the statistical analysis level (e.g., comparison of means) and the ecological level (e.g., diversity comparisons). We seek here to unify different abundance metrics using the formula A = N(BIN)kl3 where A is the abundance of a given species, k represents a fractional dimension, N is the number of individuals per unit of area and B is the biomass of the sampled species. When k = O, A is density and when k = 3, A is the biomass. A value of k = 1 would give abundance approximately proportional to the sum of the length of individuals and k = 2 would give abundance approximately proportional to the sum of their surface areas. Metrics intermediate between density, length, area and biomass are possible using non-integer values of k. Applying this methodology to ichthyological data characterized by highly variable intraspecies biomass, we examined the effect of the abundance metric on the results of a three-factor analysis of variance (depth, season and site). In some cases, differences which could not be seen with either density or biomass could be seen with intermediate metrics. We suggest that many ecological results could be usefully evaluated in terms of the effect of the fractional dimension of sampling. In some cases, such an approach could identify the optimal metric.