Abstract
As an example of applying the evidential approach to statistical inference, we address one of the longest standing controversies in ecology, the evidence for, or against, a universal metabolic scaling relationship between metabolic rate and body mass. Using fish as our study taxa, we curated 25 studies with measurements of standard metabolic rate, temperature, and mass, with 55 independent trials and across 16 fish species and confronted this data with flexible random effects models. To quantify the body mass – metabolic rate relationship, we perform model selection using the Schwarz Information Criteria (ΔSIC), an established evidence function. Further, we formulate and justify the use of ΔSIC intervals to delineate the values of the metabolic scaling relationship that should be retained for further consideration. We found strong evidence for a metabolic scaling coefficient of 0.89 with a ΔSIC interval spanning 0.82 to 0.99, implying that mechanistically derived coefficients of 0.67, 0.75, and 1, are not supported by the data. Model selection supports the use of a random intercepts and random slopes by species, consistent with the idea that other factors, such as taxonomy or ecological or lifestyle characteristics, may be critical for discerning the underlying process giving rise to the data. The evidentialist framework applied here, allows for further refinement given additional data and more complex models.
Highlights
IntroductionKleiber (1932) popularized the idea that contrary to a century of theory, a mammal’s metabolic rate (MR) scales with body mass (BM) not as a power law with an exponent of β = 0.67, but as a power law with an exponent of β = 0.75
One of most contentious controversies in ecology is the scaling relationship between an organism’s body mass and metabolic rate (Agutter and Wheatley, 2004; Isaac and Carbone, 2010; Glazier, 2018). Kleiber (1932) popularized the idea that contrary to a century of theory, a mammal’s metabolic rate (MR) scales with body mass (BM) not as a power law with an exponent of β = 0.67, but as a power law with an exponent of β = 0.75
The best model selected using Schwarz Information Criterion (SIC) came from model suite 3 with a random intercept and random slope, but with a common slope parameter of β = 0.89 (SE 0.021)
Summary
Kleiber (1932) popularized the idea that contrary to a century of theory, a mammal’s metabolic rate (MR) scales with body mass (BM) not as a power law with an exponent of β = 0.67, but as a power law with an exponent of β = 0.75. One of most contentious controversies in ecology is the scaling relationship between an organism’s body mass and metabolic rate (Agutter and Wheatley, 2004; Isaac and Carbone, 2010; Glazier, 2018). This relationship takes the form ln(MR) = β × ln(BM) + c (1). The universality of the 0.75 value is eagerly disputed, with alternative hypotheses and empirical studies putting the scaling relationship commonly between 0.5 and 1 (Bokma, 2004; Glazier, 2018)
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