Detection of interspecific competition in parasite communities

Matrices of correlation coefficients between the abundances or intensities of all pairs of helminth species, across all individual hosts in a sample, are regularly used to detect possible cases of interspecific competition in parasite communities. In these matrices, however, the range of possible values that any correlation coefficient can take is not -1 to 1, contrary to what is generally assumed. The number and magnitude of other correlation coefficients in a matrix will constrain the values that any given correlation can achieve. This property of matrices, and of inter-related natural variables, is explained and illustrated with 2 examples from real helminth communities. As a rule, the presence of many negative correlations in a matrix raises the lower value that any of them can possibly achieve. This has important but previously overlooked implications for the interpretation of correlation coefficients, and the detection of competition in natural parasite communities.