Ecological prophets: quantifying metapopulation portfolio effects

1. A financial portfolio metaphor is often used to describe how population diversity can increase temporal stability of a group of populations. The portfolio effect (PE) refers to the stabilizing effect from a population acting as a group or portfolio' of diverse subpopulations instead of a single homogeneous population or asset'. A widely used measure of the PE (the average-CV PE) implicitly assumes that the slope (z) of a log-log plot of mean temporal abundance and variance (Taylor's power law) equals two. 2. Existing theory suggests an additional unexplored empirical PE that accounts for z, the mean-variance PE. We use a theoretical and empirical approach to explore the strength and drivers of the PE for metapopulations when we account for Taylor's power law compared with when we do not. Our empirical comparison uses data from 51 metapopulations and 1070 subpopulations across salmon, moths and reef fishes. 3. Ignoring Taylor's power law may overestimate the stabilizing effect of population diversity for metapopulations. The disparity between the metrics is greatest at low z values where the average-CV PE indicates a strong PE. Compared with the mean-variance method, the average-CV PE estimated a stronger PE in 84% of metapopulations by up to sevenfold. The divergence between the methods was strongest for reef fishes (1.0 < z < 1.7) followed by moths (1.5 < z < 1.9). The PEs were comparable for salmon where z approximate to 2. 4. We outline practical recommendations for estimating ecological PEs based on research questions, study systems and available data. Because most PEs were stabilizing and diversity can be slow to restore, our meta-analysis of metapopulations suggests that the safest management approach is to conserve biological complexity.