Testing and recommending methods for fitting size spectra to data
Summary 1. The size spectrum of an ecological community characterises how a property, such as abundance or biomass, varies with body size. Size spectra are often used as ecosystem indicators of marine systems. They have been ﬁtted to data from various sources, including groundﬁsh trawl surveys, visual surveys of ﬁsh in kelp forests and coral reefs, sediment samples of benthic invertebrates and satellite remote-sensing of chlorophyll. 2. Over the past decades several methods have been used to ﬁt size spectra to data. We document eight such methods, demonstrating their commonalities and diﬀerences. Seven methods use linear regression (of which six require binning of data), while the eighth uses maximum likelihood estimation. We test the accuracy of the methods on simulated data. 3. We demonstrate that estimated size-spectrum slopes are not always comparable between the seven regression-based methods because such methods are not estimating the same parameter. We ﬁnd that four of the eight tested methods can sometimes give reasonably accurate estimates of the exponent of the individual size distribution (which is related to the slope of the size spectrum). However, sensitivity analyses ﬁnd that maximum likelihood estimation is the only method that is consistently accurate, and the only one that yields reliable conﬁdence intervals for the exponent. 4. We therefore recommend the use of maximum likelihood estimation when ﬁtting size spectra. To facilitate this we provide documented R code for ﬁtting and plotting results. This should provide consistency in future studies and improve the quality of any resulting advice to ecosystem managers. In particular, the calculation of reliable conﬁdence intervals will allow proper consideration of uncertainty when making management decisions.