Exploring cross correlation among diversity indices

This paper analysed cross correlations among multispecies and single species bio-economic diversity measures related to a local dynamic fisheries ecosystem along the period {1986:1-2014:12}. We focused on bio-economic Simpson, Shannon and multispecies Berger Parker indexes (our proposal of multispecies pure leadership indicator) and the percentage share of income of anchovy and mackerel. These two species were chosen because they showed the highest correlation with the multispecies diversity indices, and led, respectively the “antidiversity” and “prodiversity” groups of species within the ecosystem. Time series were subjected to a double treatment to avoid the potential for spurious and biased correlations. First, the long run and seasonal cycles were removed by means of a cyclical ARFIMA modelling approach. Second, the time series were pre-whitened using conventional ARMA modelling. Correlations between the multispecies indices were remarkably high and hardly changed with the pre-whitening procedure. Conversely, the correlations of the multispecies indicators with the income shares of the two leading species decreased to almost the half after pre-withening, but still remained significant. The concentration in our particular ecosystem is high (i.e. diversity low) and it is significantly correlated with the income shares of the leading species. Accordingly, the risk of collapse for the local fishing sector is high.