Statistical modelling of aquatic size spectra: integrating data from multiple taxa and sampling methods

Size spectra are used to assess the status and functioning of marine and freshwater ecosystems worldwide. Their use is underpinned by theory linking the dynamics of trophic interactions to a power-law decline of abundance with body size in ecological communities. Recent papers on empirical size spectrum estimation have argued for Maximum Likelihood Estimation of power-law probability distributions as a more accurate alternative to traditional linear regression approaches. One major limitation of currently used size spectrum estimators from Maximum Likelihood Estimation is that they cannot account for the use of multiple sampling protocols, nor the distortions caused by gear size selectivity, and therefore they become restricted to a relatively narrow taxonomic group and size range. Further progress in the field requires new methods that are flexible enough to combine multiple trophic groups and sampling gears into a single size spectrum estimate, while taking advantage of more accurate distributional approaches. The method we propose in this paper fills this gap by deriving the distribution of observed sizes explicitly from the underlying power-law spectrum and gear selectivity functions. It specifies likelihoods as a product of two components: (i) the probability of belonging to a given group and (ii) the probability distribution within the group. Using Bayesian estimation, we applied the method to surveys of phytoplankton, zooplankton, and fishes in lakes of Quetico Provincial Park, northwestern Ontario, using Van Dorn samplers, zooplankton nets, gillnets, and hydroacoustics. The results show that the spectra estimated from subsets of trophic groups or gears are weak predictors of more complete spectra, highlighting the importance of using more inclusive community data. The two-component partitioning of likelihoods also helped demonstrate the existence of between-group spectrum slopes that were overall steeper than within-group slopes, indicating that heterogeneity of trophic transfers across the size spectrum is an important factor structuring these ecosystems.