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Body size scaling relationships, such as the positive association between body mass and metabolic rate, are well-known at the individual organism level and are now being studied at higher levels of organization1,2,3. These allometric relationships are most often power-law functions of the form Y = aMb, where Y is the variable of interest (e.g., metabolism, abundance, or home range size), M is the body mass of a single or average individual, b is a scaling coefficient, and a is a constant. For statistical convenience, Y and M data are often log-transformed prior to analysis then modeled with linear equations of the form log (Y) = log (a) + b log (M), where b and log (a) become the linear model slope and intercept, respectively.
The size spectrum is a type of allometric relationship that predicts density (D, the number of individuals per unit area) or biomass (B, the summed mass of individuals per unit area) as a function of M (See Section 4 for additional information on the use of ‘normalized’ D or B estimates.) Like other scaling relationships between M and D or between M and B, the size spectrum plays a central role in basic and applied ecology. At the population-level, biologists often interpret negative D
M relationships as evidence of density-dependent survival or as models of ecosystem carrying capacity (i.e., the ‘self-thinning rule’)4,5. At the community-level, B
M relationships can be used to study system-level effects of anthropogenic perturbations, such as size-selective fishing6,7. Allometric scaling of D and B with M are also central to recent efforts to unite population, community, and ecosystem ecology2,8,9.
One particularly important characteristic of the size spectrum is the fact that it is entirely ataxic9,10. This point is easy to miss when comparing scatterplots of D
M or B
M data but the distinction between taxic and ataxic models is a critical one. In taxic models, a single M value is used to represent the average body mass of every individual of a given species or taxa11. In ataxic models, all individuals within a data set are partitioned among a series of body size intervals or M bins, regardless of their taxonomic identity12. The latter, ataxic approach is advantageous in aquatic ecosystems where many taxa exhibit indeterminate growth and experience one or more ontogenetic shifts in feeding behavior; in these instances, a single species-level M average will obscure the fact that a species can fill different functional roles throughout its life history9,13,14.
Here, we present a complete protocol to quantify the size spectrum within wadable streams and rivers. The protocol begins with field sampling methods to collect the necessary fish and benthic macroinvertebrate data. Fish will be collected through a ‘three-pass depletion’ sampling process. Abundance will then be estimated from the depletion data with the Zippin method15. In depletion sampling, individual fishes within a closed study reach (i.e., individuals can neither enter nor leave the enclosed reach) are removed from the reach through three successive samples. Thus, the number of remaining fishes will be progressively depleted. From this depletion trend, total abundance within the study reach can be estimated then converted to D (in fish per m2), using the known surface area of the study reach. Benthic macroinvertebrates will be collected with standard fixed-area samplers, then identified and measured in the laboratory.
Next, the combined fish and macroinvertebrate data will be partitioned among size bins. Traditionally, the octave or log2 scale (i.e., doubling intervals) has been used to set size bin boundaries16. Once a list of size bins has been established, partitioning of individual benthic macroinvertebrates among their respective size bins is straightforward because invertebrates are directly enumerated as numbers of individuals per unit area. However, estimating fish abundances within size bins is more abstract because these estimates are inferred from the depletion data. Detailed instructions are therefore provided to estimate fish abundance within size bins, irrespective of taxonomic identity, from depletion sample data.
Finally, linear regression will be used to model the size spectrum. This protocol is fully compatible with the original, general method of Kerr and Dickie16 and identical to the methods used by McGarvey and Kirk, 201817 in a study of fish and invertebrate size spectra in West Virginia streams. By using this protocol, investigators can insure that their results are directly comparable with other studies that build upon Kerr and Dickie16, thereby accelerating a broad and robust understanding of body size scaling relationships in freshwater ecosystems and the mechanisms that drive them.