No general relationship between mass and temperature in endothermic species

Kristina Riemer; Robert P Guralnick; Ethan P White

doi:10.7554/eLife.27166

. 2018 Jan 9;7:e27166. doi: 10.7554/eLife.27166

No general relationship between mass and temperature in endothermic species

Kristina Riemer ^1,^✉, Robert P Guralnick ², Ethan P White ^1,³

Editor: Christian Rutz⁴

PMCID: PMC5760208 PMID: 29313491

Abstract

Bergmann's rule is a widely-accepted biogeographic rule stating that individuals within a species are smaller in warmer environments. While there are many single-species studies and integrative reviews documenting this pattern, a data-intensive approach has not been used yet to determine the generality of this pattern. We assessed the strength and direction of the intraspecific relationship between temperature and individual mass for 952 bird and mammal species. For eighty-seven percent of species, temperature explained less than 10% of variation in mass, and for 79% of species the correlation was not statistically significant. These results suggest that Bergmann's rule is not general and temperature is not a dominant driver of biogeographic variation in mass. Further understanding of size variation will require integrating multiple processes that influence size. The lack of dominant temperature forcing weakens the justification for the hypothesis that global warming could result in widespread decreases in body size.

Research organism: Other

eLife digest

Scientists have found that individual animals of the same species tend to be smaller in hotter environments and larger in cooler ones. They named this pattern “Bergmann’s Rule” to describe how temperature can influence the size of an animal. However, most studies of Bergmann’s Rule have only looked at one or a few species at a time.

Knowing how many species follow this rule is important because globally rising temperatures could cause lots of species to become smaller. Since the size of organisms affects how much food and space they need, this could disrupt natural systems around the world.

To test if Bergmann’s rule can be extended to many species, Riemer, Guralnick, and White assessed the relationship between temperature and body mass for 952 bird and mammal species. Contrary to Bergmann’s Rule, the results showed that most of the species had similar sizes regardless of the temperature of their environment. Only about 140 species were smaller in hotter environments, and about 70 species were larger in hotter environments. This suggest that Bergmann’s Rule does not apply to most species as expected.

While most birds and mammals may not get bigger or smaller due to warming global temperatures, the few species that do change in size – and the species that interact with them – may be more likely to become endangered or extinct. If we can determine which animals are at risk, we can prioritize their conservation and design better plans for doing so. Losing even a single species disrupts our ecosystems, on which we rely for critical resources like food, building materials, and clean air.

Introduction

Bergmann's rule describes a negative relationship between body mass and temperature across space that is believed to be common in endothermic species (Bergmann, 1847; Brown and Lee, 1969; Kendeigh, 1969; Freckleton et al., 2003; Carotenuto et al., 2015). Many hypotheses have been proposed to explain this pattern (Blackburn et al., 1999; Ashton, 2002; Watt et al., 2010) including the heat loss hypothesis, which argues that the higher surface area to volume ratio of smaller individuals results in improved heat dissipation in hot environments (Bergmann, 1847). Though originally described for closely-related species (i.e., interspecific; Blackburn et al., 1999), the majority of studies have focused on the intraspecific form of Bergmann's rule (Rensch, 1938; Meiri, 2011) by assessing trends in individual size within a species (Langvatn and Albon, 1986; Yom-Tov and Geffen, 2006; Gardner et al., 2009). Bergmann's rule has been questioned both empirically and mechanistically (McNab, 1971; Geist, 1987; Huston and Wolverton, 2011; Teplitsky and Millien, 2014) but the common consensus from recent reviews is that the pattern is general (Ashton et al., 2000; Ashton, 2002; Meiri and Dayan, 2003; Watt and Salewski, 2011).

It has recently been suggested that this negative relationship between mass and temperature could result in decreasing individual size across species in response to climate change (Sheridan and Bickford, 2011) and that this may be a ‘third universal response to warming’ (Gardner et al., 2011). The resulting shifts in size distributions could significantly alter ecological communities (Brose et al., 2012), especially if the rate of size decrease varies among species (Sheridan and Bickford, 2011). While there is limited empirical research on body size responses to changes in temperature through time (but see Smith et al., 1995; Caruso et al., 2014; Teplitsky and Millien, 2014), the apparent generality of Bergmann's rule across space indicates the likelihood of a similar relationship in response to temperature change across time.

The generality of Bergmann's rule is based on many individual studies that analyze empirical data on body size across an environmental gradient (e.g., Langvatn and Albon, 1986; Barnett, 1977; Fuentes and Jaksic, 1979; Dayan et al., 1989; Sand et al., 1995) and reviews that compile and evaluate the results from these studies (Ashton, 2002; Meiri and Dayan, 2003; Watt et al., 2010). Most individual studies of Bergmann's rule are limited by: (1) analyzing only one or a few species (e.g., Langvatn and Albon, 1986); (2) using small numbers of observations (e.g., Fuentes and Jaksic, 1979); (3) only including data at the small scales typical of ecological studies (e.g., Sand et al., 1995); (4) using latitude instead of directly assessing temperature (e.g., Barnett, 1977); and (5) focusing on statistical significance instead of the strength of the relationship (e.g., Dayan et al., 1989). The reviews tabulate the results of these individual studies and assess patterns in the direction and significance of relationships across species. Such aggregation of published results allows for a more general understanding of the pattern but, in addition to limitations of the underlying studies, the conclusions may be influenced by publication bias and selective reporting due to studies or individual analyses that do not support Bergmann's rule being published less frequently (Koricheva et al., 2013).

Previous analyses of publication bias in the context of Bergmann’s rule have found no evidence for selective publication, which supports the idea that it is a general rule (Ashton, 2002; Meiri et al., 2004). However, two of the most extensive studies of Bergmann’s rule, which both used museum records to assess dozens of intraspecific Bergmann’s rule relationships simultaneously, found that the majority of species did not exhibit significant positive relationships between latitude and size (McNab, 1971; Meiri et al., 2004). As a result, understanding the generality of this ecophysiological rule and its potential implications for global change requires more extensive analysis.

A data-intensive approach to analyzing Bergmann's rule, evaluating the pattern using large amounts of broad scale data, has the potential to overcome existing limitations in the literature and provide a new perspective on the generality of the intraspecific form of Bergmann's rule. Understanding the generality of the temperature-mass relationship has important implications for how size will respond to climate change. We use data from VertNet (Constable et al., 2010), a large compilation of digitized museum records that contains over 700,000 globally distributed individual-level size measures, to evaluate the intraspecific relationship between temperature and mass for 952 mammal and bird species. The usable data consist of 273,901 individuals with an average of 288 individuals per species, with individuals of each species spanning an average of 75 years and 34 latitudinal degrees. This approach reduces or removes many of the limitations to previous approaches and the results suggest that Bergmann's rule is not a strong or general pattern.

Results

Most of the species in this study showed weak non-significant relationships between temperature and mass (Figures 1 and 2). The distribution of correlation coefficients was centered near zero with a mean correlation coefficient of −0.05 across species (Figure 2A). Relationships for 79% of species were not significantly different from zero based on false discovery rate-controlled p values and associated z scores, while 14% of species' relationships were significant and negative and 7% were significant and positive (Figure 2A, Figure 2—figure supplement 1). Temperature explained less than 10% of variation in mass (i.e., −0.316 < r < 0.316) for 87% of species, indicating that temperature explained very little of the observed variation in mass for these species (Figure 2A).

Figure 1. — (A) Spatial collection locations of all individual specimens. All species shown with black points except three species, whose relationships between mean annual temperature and mass are shown at bottom (**B–D**), are marked with colored points. These species were chosen to represent the range of variability in relationship strength and direction exhibited by the 952 species from the study: *Martes pennanti* had a negative relationship with temperature explaining a substantial amount of variation in mass (B; blue points); *Tamias quadrivittatus* had no directional relationship between temperature and mass with temperature having little explanatory power (C; yellow points); *Synaptomys cooperi* had a strong positive temperature-mass relationship with a correlation coefficient (r) in the 99^th percentile of all species' values (D; red points). Intraspecific temperature-mass relationships are shown with black circles for all individuals and ordinary least squares regression trends as blue lines. Linear regression correlation coefficients and p-values in upper left hand corner of figure for each species. For remaining species relationships, see Figure 1—figure supplement 1–12.

Figure 1—figure supplement 1. — (A) Spatial collection locations of all individual specimens. All species shown with black points except three species, whose relationships between mean annual temperature and mass are shown at bottom (**B–D**), are marked with colored points. These species were chosen to represent the range of variability in relationship strength and direction exhibited by the 952 species from the study: *Martes pennanti* had a negative relationship with temperature explaining a substantial amount of variation in mass (B; blue points); *Tamias quadrivittatus* had no directional relationship between temperature and mass with temperature having little explanatory power (C; yellow points); *Synaptomys cooperi* had a strong positive temperature-mass relationship with a correlation coefficient (r) in the 99^th percentile of all species' values (D; red points). Intraspecific temperature-mass relationships are shown with black circles for all individuals and ordinary least squares regression trends as blue lines. Linear regression correlation coefficients and p-values in upper left hand corner of figure for each species. For remaining species relationships, see Figure 1—figure supplement 1–12.

Figure 2. — (A) Stacked histogram of correlation coefficients (r) for all species' intraspecific temperature-mass relationships. Colored bars show species with statistically significant relationships, both negative (purple) and positive (green), while white bars indicate species with relationship slopes that are not significantly different from zero. Percentages are of species in each group. (B) Stacked histogram of all species' correlation coefficients with bar color corresponding to taxonomic class. Dark vertical lines are correlation coefficients of zero. See Figure 2—figure supplements 1–6.

Figure 2—figure supplement 1. — (A) Stacked histogram of correlation coefficients (r) for all species' intraspecific temperature-mass relationships. Colored bars show species with statistically significant relationships, both negative (purple) and positive (green), while white bars indicate species with relationship slopes that are not significantly different from zero. Percentages are of species in each group. (B) Stacked histogram of all species' correlation coefficients with bar color corresponding to taxonomic class. Dark vertical lines are correlation coefficients of zero. See Figure 2—figure supplements 1–6.

The weak, non-directional intraspecific relationships indicated by the distribution of correlation coefficients are consistent across taxonomic groups and temporal lags. Mean correlation coefficients for both endothermic classes are −0.006 and −0.065, for mammals and birds respectively (Figure 2B). Similarly, correlation coefficient distributions were approximately centered on zero for all of the 30 orders analyzed (−0.2 < $\bar{r}$ < 0.003 for orders with more than 10 species; Figure 3 and Figure 3—figure supplement 1), and for migrant and nonmigrant bird species (Figure 2—figure supplement 2). Correlation coefficient distributions for temperature-mass relationships using lagged temperatures were centered around zero like those using temperature from the collection year (Figure 4 and Figure 4—figure supplement 1), indicating that there was not a temporal lag effect on the response of species' masses to temperature. Correlation coefficients did not vary systematically by sample size (Figure 5A), extent of variation in temperature or mass (Figure 5B,C), species' average mass (Figure 5D), or species' average latitude (Figure 5E). While temperature is considered the actual driver, some studies use latitude as a proxy when evaluating variation in size (Bergmann, 1847; Stillwell, 2010). Using latitude, the mean correlation coefficient was −0.05 with no statistically significant latitude-mass relationship for 71% of species (Figure 2—figure supplement 3), while the respective values for temperature were −0.05 and 79% (Figure 2A). Results were robust to a variety of decisions and stringencies about how to filter the size (Figure 2—figure supplements 4 and 5) and species data (Figure 2—figure supplements 6 and 7).

Figure 3. — Histograms of correlation coefficients (r) from intraspecific temperature-mass relationships for each taxonomic order represented by more than ten species, with order shown above histogram. Height of y-axis varies depending on number of species. Bar color indicates taxonomic class. Dark vertical lines are correlation coefficients of zero. For remaining orders, see Figure 3—figure supplement 1.

Histograms of correlation coefficients (r) from intraspecific temperature-mass relationships for each taxonomic order represented by more than ten species, with order shown above histogram. Height of y-axis varies depending on number of species. Bar color indicates taxonomic class. Dark vertical lines are correlation coefficients of zero. For remaining orders, see Figure 3—figure supplement 1.

Figure 4. — Histograms of correlation coefficients (r) for all species' intraspecific temperature-mass relationships with mean annual temperature from (A) the year in which individuals were collected, (B) 25 years prior to collection year, and (C) 50 years prior to collection year. Dark vertical lines are correlation coefficients of zero. For all past year temperatures, see Figure 4—figure supplement 1.

Histograms of correlation coefficients (r) for all species' intraspecific temperature-mass relationships with mean annual temperature from (A) the year in which individuals were collected, (B) 25 years prior to collection year, and (C) 50 years prior to collection year. Dark vertical lines are correlation coefficients of zero. For all past year temperatures, see Figure 4—figure supplement 1.

Figure 5. — Variation in all species' correlation coefficients (r) across the following variables for each species: (A) number of individuals, (B) difference between hottest and coldest collection year temperatures, (C) mass range, (D) mean mass, and (E) absolute mean latitude. Horizontal lines are correlation coefficients of zero. The x-axes of some plots (**A, C, D**) are on a log scale to better show spread of values.

Discussion

In contrast to conventional wisdom and several recent review papers, our analysis of 952 species shows little to no support for a negative intraspecific temperature-mass relationship that is sufficiently strong or common to be considered a biogeographic rule. Three quarters of bird and mammal species show no significant change in mass across a temperature gradient and temperature explained less than 10% of intraspecific variation in mass for 87% of species (Figure 2A). This was true regardless of taxonomic group (Figures 2 and 3), temporal lag in temperature (Figure 4), species' size, location, or sampling intensity or extent (Figure 5). These results are consistent with two previous studies that examined museum specimen size measurements across latitude. The first study showed that 22 out of 47 North American mammal species studied had no relationship between latitude and length, and 10 of the 25 significant relationships were opposite the expected direction (McNab, 1971). The second found a similar proportion of non-significant results (42/87), but a lower proportion of significant relationships that opposed the rule (9/45) for carnivorous mammals (Meiri et al., 2004). While more species had significant negative relationships than positive in both our study and these two museum-based studies, in all cases less than half of species had significant negative correlations (14–41%). In combination with these two smaller studies, our results suggest that there is little evidence for a strong or general Bergmann's rule when analyzing raw data instead of summarizing published results.

Our results are inconsistent with recent reviews, which have reported that the majority of species conform to Bergmann's rule (Ashton, 2002; Meiri and Dayan, 2003; Watt et al., 2010). While these reviews included results that were either non-significant or opposite of Bergmann's rule, the proportion of significant results in support of Bergmann's rule was higher and therefore resulted in conclusions that supported the generality of the temperature-mass relationship. Generalizing from results in the published literature involves the common challenges of publication bias and selective reporting (Koricheva et al., 2013). In addition, because the underlying Bergmann's rule studies typically report minimal statistical information, often providing only relationship significance or direction instead of p-values or correlation coefficients (Meiri and Dayan, 2003), proper meta-analyses and associated assessments of biological significance are not possible. While several reviews found no evidence for publication bias using limited analyses (Ashton, 2002; Meiri et al., 2004), the notable differences between the conclusions of our data-intensive approach and those from reviews suggest that publication bias in literature examining Bergmann's rule warrants further investigation. These differences also demonstrate the value of data-intensive approaches in ecology for overcoming potential weaknesses and biases in the published literature. Directly analyzing large quantities of data from hundreds of species allows us to assess the generality of patterns originally reported in smaller studies while avoiding the risk of publication bias. This approach additionally makes it easier to integrate other factors that potentially influence size into future analyses. The new insight gained from this data-intensive approach demonstrates the value of investing in large compilations of ecologically-relevant data (Hampton et al., 2013) and the proper training required to work with these datasets (Hampton et al., 2017).

Our analyses and conclusions are limited to the intraspecific form of Bergmann’s rule. This is the most commonly studied and well-defined form of the relationship, and the one most amenable to analyses using large compilations of museum data. Difficulty in interpreting Bergmann’s original formulation has resulted in an array of different ideas and implementations of interspecific analyses (Blackburn et al., 1999; Meiri and Thomas, 2007; Watt et al., 2010; Meiri, 2011). The most common forms of these interspecific analyses involve correlations between various species-level size metrics and environmental measures and are conducted at various taxonomic levels from genus to class (e.g., Blackburn and Gaston, 1996; Diniz-Filho et al., 2007; Boyer et al., 2009; Clauss et al., 2013). Efforts to apply data-intensive approaches to the interspecific form of this relationship will need to address the fact that occurrence records are not evenly distributed across the geographic range of species, and determine how the many interpretations of interspecific Bergmann’s rule are related to one another and the biological expectations for interspecific responses to temperature.

The original formulation of Bergmann's rule, and the scope of our conclusions, apply only to endotherms. However, negative temperature-mass relationships have also been documented in ectotherms, with the pattern referred to as the size-temperature rule (Ray, 1960; Angilletta and Dunham, 2003). In contrast to the hypotheses for Bergmann's rule, which are based primarily on homeostasis (Gardner et al., 2011), the size-temperature rule in ectotherms is thought to result from differences between growth and development rates (Forster et al., 2011). The current version of VertNet contained ectotherm size data for only seven species, which is not sufficient to complete a comprehensive analysis of the ectotherm size-temperature rule. Future work exploring the ectotherm size-temperature rule in natural systems using data-intensive approaches is necessary for understanding the generality of this rule in ectotherms, and data may be sought for this effort in the literature or via a coordinated effort by museums to continue digitizing size measurements for specimens.

A number of mechanisms have been suggested to explain why higher temperatures should result in lower body sizes, including heat loss, starvation, resource availability, migratory ability, and phylogenetic constraints (Blackburn et al., 1999). Most of the proposed hypotheses have not been tested sufficiently to allow for strong conclusions to be drawn about their potential to produce Bergmann's rule (Blackburn et al., 1999; Watt et al., 2010; Teplitsky and Millien, 2014) and the widely studied heat loss hypothesis has been questioned for a variety of reasons (James, 1970; McNab, 1971; Blackburn et al., 1999; Watt et al., 2010; McNamara et al., 2016). While no existing hypotheses have been confirmed, it is possible that some processes are producing negative relationships between size and temperature. The lack of a strong relationship does not preclude processes that result in a negative temperature-mass relationship, but it does suggest that these processes have less influence relative to other factors that affect intraspecific size.

The relative importance of the many factors besides temperature that can influence size within a species is as yet unknown. Size is affected by abiotic factors such as humidity and resource availability (Teplitsky and Millien, 2014), characteristics of individuals like clutch size (Boyer et al., 2009), and community context, including possible gaps in size-related niches (Smith et al., 2010) and the trophic effects of primary productivity on consumer size (Sheridan and Bickford, 2011). Temperature itself can have indirect effects on size, such as via habitat changes in water flow or food availability, that result in size responses opposite of Bergmann's rule (Gardner et al., 2011). Anthropogenic influences have been shown to influence the effect of temperature on size (Faurby and Araújo, 2016), and similar impacts of dispersal, extinctions, and the varying scales of climate change have been proposed (Clauss et al., 2013). Because our data primarily came from North America, further analyses focused on species native to other continents could reveal differing temperature-mass relationships due to varying temperature regimes. While our work shows that more species have negative significant relationships between temperature and mass than positive, only 21% of species have statistically significant relationships and it consequently appears that some combination of other factors more strongly drives intraspecific size variation for most endothermic taxa.

The lack of evidence for temperature as a primary determinant of size variation in endothermic species calls into question the hypothesis that decreases in organism size may represent a third universal response to global warming. The potentially general decline in size with warming was addressed by assessments that evaluated dynamic body size responses to temperature using similar approaches to the Bergmann's rule reviews discussed above (Sheridan and Bickford, 2011; Gardner et al., 2011; Teplitsky and Millien, 2014). The results of these temporal reviews were similar to those for spatial relationships, but the conclusions of these studies clearly noted the variability in body size responses and the need for future data-intensive work (Sheridan and Bickford, 2011; Gardner et al., 2011) using broader temperature ranges (Teplitsky and Millien, 2014) to fully assess the temperature-size relationship.

Our results in combination with those from other studies suggest that much of the observed variation in size is not explained simply by temperature. While there is still potential for the size of endotherms, and other aspects of organismal physiology and morphology, to respond to both geographic gradients in temperature and climate change, these responses may not be as easily explained solely by temperature as has been suggested (Sheridan and Bickford, 2011; Gardner et al., 2011). Future attempts to explain variation in the size of individuals across space or time should use integrative approaches to include the influence of multiple factors, and their potential interactions, on organism size. This will be facilitated by analyzing spatiotemporal data similar to that used in this study, which has broad ranges of time, space, and environmental conditions for large numbers of species and individuals. This data-intensive approach provides a unique perspective on the general responses of bird and mammal species to temperature, and has potential to assist in further investigation of the complex combinations of factors that determine biogeographic patterns of endotherm size and how species respond to changes in climate.

Materials and methods

Data

Organismal data were obtained from VertNet, a publicly available data platform for digitized specimen records from museum collections primarily in North America, but also includes global data (Constable et al., 2010). Body mass is routinely measured when organisms are collected, with relatively high precision and consistent methods, by most field biologists, whose intent is to use those organisms for research and preservation in natural history collections (Winker, 2000; Hoffmann et al., 2010). These measurements are included on written labels and ledgers associated with specimens, which are digitized and provided in standard formats, e.g., Darwin Core (Wieczorek et al., 2012). In addition to other trait information, mass has recently been extracted and converted to a more usable form from Darwin Core formatted records published in VertNet (Guralnick et al., 2016). This crucial step reduces variation in how these measurements are reported by standardizing the naming conventions and harmonizing all measurement values to the same units (Guralnick et al., 2016). We downloaded the entire datasets for Mammalia, Aves, Amphibia, and Reptilia available in September 2016 (Bloom et al., 2016a, Bloom et al., 2016b, Bloom et al., 2016c, Bloom et al., 2016d) using the Data Retriever (Kironde et al., 2017; Morris and White, 2013) and filtered for those records that had mass measurements available. Fossil specimen records with mass measurements were removed.

We only analyzed species with at least 30 georeferenced individuals whose collection dates spanned at least 20 years and collection locations at least five degrees latitude, in order to ensure sufficient sample size and spatiotemporal extent to accurately represent each species' temperature-mass relationship. We conducted sensitivity analyses to determine if these thresholds were appropriate (Figure 2—figure supplements 6 and 7). We selected individual records with geographic coordinates for collection location, collection dates between 1900 and 2010, and species-level taxonomic identification, which were evaluated to ensure no issues with synonymy or clear taxon concept issues. To minimize inclusion of records of non-adult specimens, we identified the smallest mass associated with an identified adult life stage category for each species and removed all records with mass values below this minimum adult size. Results were not qualitatively different due to either additional filtering based on specimen lifestage (Figure 2—figure supplement 4) or removal of outliers (Figure 2—figure supplement 5). Temperatures were obtained from the Udel_AirT_Precip global terrestrial raster provided by NOAA from their website at http://www.esrl.noaa.gov/psd/, a 0.5 by 0.5 decimal degree grid of monthly mean temperatures from 1900 to 2010 (Willmott and Matsuura, 2001). For each specimen, the mean annual temperature at its collection location was extracted for the year of collection.

Analysis

We fit the intraspecific relationship between mean annual temperature and mass for each species with ordinary least squares linear regression (e.g., Figure 1B,C,D and Figure 1—figure supplements 1–12) using the statsmodels.formula.api module in Python (Seabold and Perktold, 2010). The strength of each species’ relationship was characterized by the correlation coefficient, its significance at alpha of 0.05, and the associated z score. When assessing statistical significance with large numbers of correlations it is important to consider the expected distribution of these correlations under the null model that no correlation exists for any species.

We addressed this issue by using false discovery rate control (Benajmini and Hochberg, 1995) implemented with the stats package in R (R Core Team, 2016). This method determines the expected distribution of values for p (or Z) in the case where no relationship exists for individual correlation and adjusts observed values to control for excessive false positives. Specifically, it maintains the Type I error rate (proportion of false positives) across all tests at the chosen value of alpha and therefore gives an accurate estimate of the number of significant relationships (Benajmini and Hochberg, 1995). This allows us to estimate the number of species with true positive and negative correlations (i.e., those that have values that exceed those expected from the null distribution). We then compared the number of species with positive and negative correlation coefficients, and the proportion of those with statistically significant adjusted p-values.

We investigated various potential correlates of the strength of Bergmann's rule. Because it has been argued that Bergmann's rule is exhibited more strongly by some groups than others (McNab, 1971), we examined correlation coefficient distributions within each class and order. Additionally, distributions for migrant and nonmigrant bird species were compared due to conflicting evidence about the impact of migration on temperature-mass relationships (Ashton, 2002). As a temporal lag in size response to temperature is likely due to individuals of a species responding to temperatures prior to their collection year (e.g., Stacey and Fellowes, 2002), we assessed species' temperature-mass relationships using temperatures from 1 to 110 years prior to collection year. We also examined the relationship between species' correlation coefficients and five variables to understand potential statistical and biological influences on the results. We did so with the number of individuals, temperature range, and mass range to determine if the relationship was stronger when more data points or more widely varying values were available. Because it has been argued that Bergmann's rule is stronger in larger species (Steudel et al., 1994) and at higher latitudes (Freckleton et al., 2003; Faurby and Araújo, 2016), we examined variability with both mean mass and mean latitude for each species. We also conducted all analyses using latitude instead of mean annual temperature. The reproducible code for these analyses is available (https://github.com/KristinaRiemer/MassResponseToTemp; Riemer and White, 2017) and archived (https://zenodo.org/badge/latestdoi/17957630).

Acknowledgements

Thanks to all of the VertNet data providers, Dan McGlinn for assistance with developing this research, Rafael LaFrance for his trait extraction work, and Dave Harris for helping us divide by two.

Funding Statement

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Contributor Information

Kristina Riemer, Email: kristina.riemer@weecology.org.

Christian Rutz, University of St Andrews, United Kingdom.

Funding Information

This paper was supported by the following grants:

Gordon and Betty Moore Foundation GBMF4563 to Ethan P White.
National Science Foundation DEB 0953694 to Ethan P White.
National Science Foundation DBI 1062148 to Robert P Guralnick.

Additional information

Competing interests

No competing interests declared.

Author contributions

Conceptualization, Formal analysis, Visualization, Methodology, Writing—original draft, Writing—review and editing.

Data curation, Validation, Writing—review and editing.

Conceptualization, Formal analysis, Funding acquisition, Visualization, Methodology, Writing—original draft, Writing—review and editing.

Additional files

Transparent reporting form

elife-27166-transrepform.pdf^{(282.7KB, pdf)}

DOI: 10.7554/eLife.27166.029

Major datasets

The following previously published datasets were used:

Willmott CJ, author; Matsuura K, author. Terrestrial Air Temperature and Precipitation: Monthly and Annual Time Series (1950 - 1999) [Air Temperature Monthly Mean V3.01] 2001 https://www.esrl.noaa.gov/psd/data/gridded/data.UDel_AirT_Precip.html Publicly available at the NOAA Earth System Research Laboratory website (https://www.esrl.noaa.gov/)

Bloom D, author. VertNet Amphibia. 2016 https://dx.doi.org/10.7946/P2F59W Publicly available at Data Commons (http://datacommons.cyverse.org/)

Bloom D, author. VertNet Aves. 2016 https://dx.doi.org/10.7946/P2K01C Publicly available at Data Commons (http://datacommons.cyverse.org/)

Bloom D, author. VertNet Mammalia. 2016 https://dx.doi.org/10.7946/P2TG68 Publicly available at Data Commons (http://datacommons.cyverse.org/)

Bloom D, author. VertNet Reptilia. 2016 https://dx.doi.org/10.7946/P2Z59J Publicly available at Data Commons (http://datacommons.cyverse.org/)

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eLife. doi: 10.7554/eLife.27166.041

Decision letter

Editor: Christian Rutz¹

In the interests of transparency, eLife includes the editorial decision letter and accompanying author responses. A lightly edited version of the letter sent to the authors after peer review is shown, indicating the most substantive concerns; minor comments are not usually included.

Thank you for submitting your article "No general relationship between mass and temperature in endotherm species" for consideration by eLife. Your article has been favorably evaluated by Diethard Tautz (Senior Editor) and three reviewers, one of whom, Christian Rutz (Reviewer #1), is a member of our Board of Reviewing Editors. The following individual involved in review of your submission has agreed to reveal their identity: Alison Boyer (Reviewer #2).

The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission.

Summary:

Your study uses an unprecedented dataset of animal measurements to assess the generality of one of the best-known biogeographic 'rules', and as such holds great potential for stimulating future research. The reviewers agreed that this is a noteworthy advance, but have identified a few issues that need to be addressed in a revision (essential revisions).

Essential revisions:

- Scope. You rightly note in the Introduction (first paragraph) that Bergmann's rule was originally formulated for closely-related species (i.e., interspecific patters), but you then proceed – like most earlier studies – to explore intraspecific relationships only. A comprehensive assessment of this long-standing hypothesis would cover both intra- and interspecific perspectives, and the reviewers wondered whether you could add results for the latter? These additional analyses shouldn't be too onerous, yet they would add substantial value to the manuscript. Otherwise, it should be made clear throughout that the intraspecific facet of Bergmann's rule is being examined.

- Statistical analyses. While the reviewers enjoyed the intuitive graphical illustration of results, and found that the overall patterns look compelling, they think it is essential that formal statistical analyses are conducted to support the study's conclusions. What is the null hypothesis for Figure 2A (and accompanying supporting figures)? Given the distribution of latitudes, sample sizes etc., what is the expected distribution of r values? Can Fisher's r-to-z transformation be used to calculate a null distribution, and to estimate the excess of positive and negative values?

- Migratory birds. The results for birds are complicated because many of them are migratory (e.g., in the USA, birds migrate between North and South America). This is an important confounding factor, as for almost all species, it is impossible to satisfactorily define the latitude at which they exist (in fact, this problem may even apply at smaller scales, if species move in response to extrinsic factors, such as harsh weather conditions). This alone argues against the generality of Bergmann's rule, and suggests that it has little applicability to birds. Please formally explore the effect of this confound on the overall patterns observed, for example, by re-running analyses with (migratory) birds excluded.

[Editors' note: further revisions were requested prior to acceptance, as described below.]

Thank you for sending your article entitled "No general relationship between mass and temperature in endothermic species" for peer review at eLife. Your article is being evaluated by one peer reviewer, and the evaluation is being overseen by a Reviewing Editor and Diethard Tautz as the Senior Editor.

One of the original reviewers has kindly provided further comments on your statistical analyses, and we would appreciate if you could briefly respond to these, as there may have been a misunderstanding:

They clarified that their point was that you could have more simply converted the r -> z and overlain a z distribution rather than highlighting statistically significant values. They noted that overlaying a z-distribution on z-transformed r values would show the extent of disagreement or not in the tails more clearly. They also commented that r is just bounded at -1 and 1, so the information is quite limited, and that overall, r is not a particularly informative comparative measure of effect size for heterogeneous data varying in sample size etc.

eLife. 2018 Jan 9;7:e27166. doi: 10.7554/eLife.27166.042

Author response

Essential revisions:

- Scope. You rightly note in the Introduction (first paragraph) that Bergmann's rule was originally formulated for closely-related species (i.e., interspecific patters), but you then proceed – like most earlier studies – to explore intraspecific relationships only. A comprehensive assessment of this long-standing hypothesis would cover both intra- and interspecific perspectives, and the reviewers wondered whether you could add results for the latter? These additional analyses shouldn't be too onerous, yet they would add substantial value to the manuscript. Otherwise, it should be made clear throughout that the intraspecific facet of Bergmann's rule is being examined.

We have decided, after extensive discussion, that adding interspecific analyses of Bergmann’s rule would make the current manuscript too complex and difficult to follow and therefore these analyses warrant their own manuscript. The reason for this is that the interspecific analyses in the literature have been conducted in a number of different ways, none of which immediately aligns with large scale individual-level data. The most common older form of this analysis involves assessing changes in the average size of a species as a function of the latitudinal centroid of its geographic distribution, where each point is a species within a genus. Two examples from the literature illustrate the variety in this type of analysis: correlations between body length and mean breeding range latitude for species within genus, family, and order (Boyer et al., 2010) and correlation between geometric mean mass and six environmental variables, including a phylogenetic component, for species within an order (Diniz-Filho et al., 2007). Newer analyses do something similar using range maps for entire assemblages and look at how the average size of all species in the assemblage varies across grid cells in response to environmental factors, as in Blackburn and Gaston (1996). Neither of these approaches are well suited to analysis using VertNet data because these data are not necessarily collected broadly or evenly across each species’ geographic range.

This diversity of approaches comes from the range of conclusions that have been reached about the contents of Bergmann (1847). Bergmann states that the pattern should apply across “races”. This is difficult to interpret, especially given how taxonomic classification has changed. It is generally agreed upon that “closely related species” is analogous, though this is only somewhat less vague in terms of selecting useful and appropriate analyses. Many of the interspecific approaches taken also have statistical and inference limits that need to be explored. Consequently, addressing the pattern more broadly is quite a bit more complicated than, e.g., using genus instead of species to group individual-level sizes. As a result of these complexities, a sufficient exploration of interspecific Bergmann’s rule would require additional data, new analyses, and the space of a full manuscript to explain and explore this approach.

That said, we certainly agree that this is an important topic to explore, including in new ways using the kinds of data used in this paper. Therefore, we have added a paragraph to the Discussion summarizing the importance and challenges of pursuing this question as in future research. We have also added language throughout the manuscript to emphasize that the analyses pertain to the intraspecific version of Bergmann’s rule.

- Statistical analyses. While the reviewers enjoyed the intuitive graphical illustration of results, and found that the overall patterns look compelling, they think it is essential that formal statistical analyses are conducted to support the study's conclusions. What is the null hypothesis for Figure 2A (and accompanying supporting figures)? Given the distribution of latitudes, sample sizes etc., what is the expected distribution of r values? Can Fisher's r-to-z transformation be used to calculate a null distribution, and to estimate the excess of positive and negative values?

If we understand correctly, we believe that this question reflects a failure on our part to clearly communicate the analyses that we have already conducted. The null hypothesis for Figure 2A is that no species has an intraspecific relationship between temperature and mass. Given the distribution of temperatures/latitudes and sample sizes, this null hypothesis would lead to a distribution of correlation coefficients roughly centered on zero with some species showing larger positive and negative values of r by chance and some of these relationships (roughly 5%) appearing to be statistically significant at p < 0.05 based on their Z scores. The standard approach to assessing the expected (null) form of this distribution and to estimate the number of excess positive and negative values is by controlling the false discovery rate (Verhoeven et al., 2005; Garcia, 2004; Pike, 2010; Waite and Campbell, 2006; Nakagawa, 2004). This analysis has already been conducted and presented in Figure 2. In that figure, r values falling within the null distribution are presented in white and the “excess” negative and positive values are shown in purple and green, respectively. As is standard when controlling the false discovery rate, we did the calculations on the p-values which are calculated from Z scores. Therefore it is our understanding that we have already performed the requested analysis. If we have misunderstood, we would be happy to conduct additional analyses.

We clearly failed to discuss this analysis in sufficient detail to communicate effectively. Consequently we expanded our description of how we assess r and p-values in the Materials and methods, including their expected distributions under both the null and alternative hypotheses. Additionally, we better explained the role of false discovery rate control and what it accomplishes in identifying those species with excess positive and negative relationships beyond the null, and the proportion of species that have no relationship between temperature and mass.

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Nakagawa, Shinichi. “A Farewell to Bonferroni: The Problems of Low Statistical Power and Publication Bias.” Behavioral Ecology 15, no. 6 (2004): 1044–45. doi:10.1093/beheco/arh107.

Pike, Nathan. “Using False Discovery Rates for Multiple Comparisons in Ecology and Evolution.” Methods in Ecology and Evolution 2, no. 3 (2011): 278–82. doi:10.1111/j.2041-210X.2010.00061.x.

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Waite, Thomas A., and Lesley G. Campbell. “Controlling the False Discovery Rate and Increasing Statistical Power in Ecological Studies 1.” Ecoscience 13, no. 4 (2006): 439–42.

- Migratory birds. The results for birds are complicated because many of them are migratory (e.g., in the USA, birds migrate between North and South America). This is an important confounding factor, as for almost all species, it is impossible to satisfactorily define the latitude at which they exist (in fact, this problem may even apply at smaller scales, if species move in response to extrinsic factors, such as harsh weather conditions). This alone argues against the generality of Bergmann's rule, and suggests that it has little applicability to birds. Please formally explore the effect of this confound on the overall patterns observed, for example, by re-running analyses with (migratory) birds excluded.

This is a really important point, and we thank the reviewers for catching it. We have added separate analyses on bird species in our dataset known as migrants or nonmigrants, see new Figure 2—figure supplement 1. The proportion of species with negative statistically significant, positive statistically significant, and no relationships were similar (i.e., varying by no more than one percentage point) between the migrant species and nonmigrant species. The mean correlation coefficients for migrant species and nonmigrant species were -0.06 and -0.07, respectively. There is a somewhat more apparent shoulder of small r values below zero, but these are all within the null distribution. Therefore our assessment of the new results is that migration had minimal impact on the conclusions of this manuscript. We have added the appropriate text for this figure to the Materials and methods and Results sections.

[Editors' note: further revisions were requested prior to acceptance, as described below.]

One of the original reviewers has kindly provided further comments on your statistical analyses, and we would appreciate if you could briefly respond to these, as there may have been a misunderstanding:

They clarified that their point was that you could have more simply converted the r -> z and overlain a z distribution rather than highlighting statistically significant values. They noted that overlaying a z-distribution on z-transformed r values would show the extent of disagreement or not in the tails more clearly. They also commented that r is just bounded at -1 and 1, so the information is quite limited, and that overall, r is not a particularly informative comparative measure of effect size for heterogeneous data varying in sample size etc.

We received a very thoughtful comment from one reviewer about the benefits of the inclusion of the z scores for each species in our dataset. Consequently, we have included a figure of these z scores in the supplemental material for this manuscript, with corresponding edits to the manuscript text.

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Supplementary Materials

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elife-27166-transrepform.pdf^{(282.7KB, pdf)}

DOI: 10.7554/eLife.27166.029

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PERMALINK

No general relationship between mass and temperature in endothermic species

Kristina Riemer

Robert P Guralnick

Ethan P White

Roles

Abstract

eLife digest

Introduction

Results

Figure 1. Species spatial distributions and selected temperature-mass relationships.

Figure 1—figure supplement 1. Species’ temperature-mass relationships.

Figure 1—figure supplement 2. Species’ temperature-mass relationships.

Figure 1—figure supplement 3. Species’ temperature-mass relationships.

Figure 1—figure supplement 4. Species’ temperature-mass relationships.

Figure 1—figure supplement 5. Species’ temperature-mass relationships.

Figure 1—figure supplement 6. Species’ temperature-mass relationships.

Figure 1—figure supplement 7. Species’ temperature-mass relationships.

Figure 1—figure supplement 8. Species’ temperature-mass relationships.

Figure 1—figure supplement 9. Species’ temperature-mass relationships.

Figure 1—figure supplement 10. Species’ temperature-mass relationships.

Figure 1—figure supplement 11. Species’ temperature-mass relationships.

Figure 1—figure supplement 12. Species’ temperature-mass relationships.

Figure 2. Species correlation coefficients by statistical significance and taxonomic class.

Figure 2—figure supplement 1. Species z scores and z distribution.

Figure 2—figure supplement 2. Species correlation coefficients by bird migratory status.

Figure 2—figure supplement 3. Species correlation coefficients for latitude-mass relationships.

Figure 2—figure supplement 4. Species correlation coefficients for temperature-mass relationships with lifestage sensitivity analysis.

Figure 2—figure supplement 5. Species correlation coefficients for temperature-mass relationships with outlier sensitivity analysis.

Figure 2—figure supplement 6. Species correlation coefficients for temperature-mass relationships with species thresholds increased.

Figure 2—figure supplement 7. Species correlation coefficients for temperature-mass relationships with species thresholds decreased.

Figure 3. Species correlation coefficients for selected taxonomic orders.

Figure 3—figure supplement 1. Species correlation coefficients for remaining taxonomic orders.

Figure 4. Species correlation coefficients with selected past year temperatures.

Figure 4—figure supplement 1. Species correlation coefficients for all past year temperatures.

Figure 5. Variability of species correlation coefficients across several variables.

Discussion

Materials and methods

Data

Analysis

Acknowledgements

Funding Statement

Contributor Information

Funding Information

Additional information

Competing interests

Author contributions

Additional files

Major datasets

References

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Author response

Associated Data

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