Testing and recommending methods for fitting size spectra to data

Abstract

Summary1. The size spectrum of an ecological community characterizes 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 regressionbased 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.

Fishing degrades size structure of coral reef fish communities

“…(Edwards et al ., ) and was numerically optimized to estimate b , adapting code from Edwards et al . ().…”

“…The size spectrum is usually fitted to frequencies of body sizes and predicted to approximate a power law distribution (Vidondo et al, 1997;Andersen & Beyer, 2006). Here, we used maximum likelihood estimation to estimate the size spectrum exponent, b (Vidondo et al, 1997;Edwards, 2008;White et al, 2008;Edwards et al, 2016). We fitted body size data for individual fishes from each island, for each year, to a bounded power law distribution with probability density function…”

“…where x is body mass, b is the scaling exponent, and the distribution is bounded by the minimum and maximum possible body sizes (x min , x max ) (White et al, 2008;Edwards et al, 2016). An alternative formulation is required for b = À1, but this value does not occur for our data.…”

“…Standing stock biomass is widely used as a metric of fishery health and of exploitation impacts at regional scales (Cinner et al, 2009(Cinner et al, , 2012aMacNeil et al, 2015) and, although declines in the abundance of large fishes on coral reefs are well documented (Sandin et al, 2008;Williams et al, 2015), analyses of associated impacts on coral reef fish community size structure have been infrequent (Nash & Graham, 2016). Steepening of size spectra slopes due to overfishing of large fishes has thus far been detected only in Fijian small-scale reef fisheries, and across only moderate gradients in exploitation pressure (Dulvy et al, 2004;Graham et al, 2005;Wilson et al, 2010; though see Edwards et al, 2016). Other direct comparisons between fished and protected areas have found that community size structure is highly variable and unrelated to exploitation (McClanahan & Graham, 2005;Graham et al, 2007), which may reflect unmeasured environmental influences.…”

Size‐based interactions across trophic levels in food webs of shallow Mediterranean lakes

“…However, negative values of size diversity (extremely low size diversity) are feasible in that the method uses a continuous probability density function for the probability estimation, and probability densities over 1 are possible.The use of size diversity for analysis of the shape of size distributions has several advantages: (1) its meaning is easy to interpret since the concept of diversity is well established-high size diversity means a wide size range and/or similar proportions of the different sizes along the size distribution (e.g Emmrich et al, 2011); . (2) after data standardisation, samples measured with different units, such as length, weight or volume, are comparable; (3) in contrast to the traditional biomass size spectrum, size diversity and size evenness indices do not require creation of arbitrary size classes and statistical fitting and their estimates are therefore insensitive to the strength of model fit (but seeEdwards, Robinson, Plank, Baum, & Blanchard, 2017); and…”