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Keywords:

  • endothermy;
  • genetic constraint;
  • genetic covariance;
  • genetic variance;
  • maximal metabolism;
  • metabolic rate;
  • resting metabolism

Abstract

  1. Top of page
  2. Abstract
  3. Introduction
  4. The model
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References

The metabolic distinction between endotherms and ectotherms is profound. Whereas the ecology of metabolic rates is well studied, how endotherms evolved from their ectothermic ancestors remains unclear. The aerobic capacity model postulates that a genetic constraint between resting and maximal metabolism was essential for the evolution of endothermy. Using the multivariate breeders’ equation, I illustrate how the (i) relative sizes of genetic variances and (ii) relative magnitudes of selection gradients for resting and maximal metabolism affect the genetic correlation needed for endothermy to have evolved via a correlated response to selection. If genetic variances in existing populations are representative of ancestral conditions, then the aerobic capacity model is viable even if the genetic correlation was modest. The analyses reveal how contemporary data on selection and genetic architecture can be used to test hypotheses about the evolution of endothermy, and they show the benefits of explicitly linking physiology and quantitative genetic theory.


Introduction

  1. Top of page
  2. Abstract
  3. Introduction
  4. The model
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References

Metabolic rates set the pace of life. They describe physiological intensity, and they correlate with a wide range of organismal, ecological and evolutionary variables (Peters, 1983; Calder, 1984; Gillooly et al., 2001; Brown et al., 2004). Perhaps the most fundamental distinction among the metabolic rates of vertebrates is endothermy vs. ectothermy. Endotherms can elevate their body temperatures above environmental temperatures by physiological heat production (i.e., thermogenesis). Ectotherms cannot. This metabolic distinction is reflected in a host of associated differences in behaviour, ecology, and life history (Pough, 1980; Cohen et al., 1993). Endotherms and ectotherms interact in very different ways with their thermal environments. As global climate changes alter the thermal environments on the planet, understanding the evolution of metabolic rates may be important in predicting how animals respond to climatic change (see Kearney & Porter, 2004; Berg et al., 2010). The evolution of endothermy is probably the most significant event in the metabolic evolution of vertebrates, but the evolution of endothermy, and indeed the evolution of metabolic rates in general, is relatively poorly understood (Block et al., 1993; Dutenhoffer & Swanson, 1996; Rezende et al., 2004; Artacho & Nespolo, 2009; Swallow et al., 2009; Swanson & Garland, 2009).

Herein, I show how the multivariate breeders’ equation can be used to put boundaries on the genetic variances, covariances, and selection gradients needed for the viability of a prominent model for the evolution of endothermy. My analysis shows how a focus on absolute genetic constraints (in this case a genetic covariance) alone can be misleading. In addition, the analysis provides new insight into how data on the relative sizes of genetic variances and selection gradients from extant populations are relevant to understanding the evolution of endothermy.

A variety of models have been proposed to explain how endotherms may have evolved from their ectothermic ancestors. These models propose possible benefits of endothermy that include expanded thermal niches, improved biochemical efficiency, enhanced parental care, increased energy assimilation capacity and greater exercise capacity (Hayes & Garland, 1995; Ruben, 1995; Koteja, 2000; Hillenius & Ruben, 2004; Boratynski & Koteja, 2009). One of the key challenges for these models is explaining what role natural selection played in the evolution of endothermy. Endothermy requires a high metabolic rate, so endotherms require more food than similarly sized ectotherms. Hence, animals on an evolutionary trajectory towards endothermy would increase both their metabolic rates and their food requirements. Increased food requirements are presumably not beneficial (i) because more food might not be available, (ii) because animals might have to compete for food, and (iii) because searching for food might increase the probability of being eaten by a predator. In addition, biophysical modelling and simple experiments suggest that initial increases in metabolic rate may not confer any increased thermoregulatory benefits (Stevenson, 1985; Bennett et al., 2000). That is, the thermoregulatory benefits of having a high metabolic rate may not result until appreciable increases in metabolic rates and heat production have evolved. According to this argument, it is difficult to account for the initial increases in metabolic rates that led to endothermy.

Solutions to this conundrum propose that endothermy evolved as a result of correlated responses to selection on other traits. For example, the aerobic capacity model for the evolution of endothermy suggests that elevated resting metabolic rate (RMR) evolved as a correlated response to selection for high aerobic capacity during exercise (Bennett & Ruben, 1979). Aerobic capacity is also called the maximal aerobic metabolic rate (MMR) or the maximal rate of oxygen consumption (VO2max). Aerobic capacity during exercise sets the upper limit to oxygen consumption, and thereby to sustained vigorous activity. Because all aerobic metabolism ultimately results in either heat or external work (Withers, 1992), the MMR also sets the upper limit to sustained heat production or thermogenesis. If natural selection favoured higher aerobic capacity and if RMR and aerobic capacity were genetically correlated, then endothermy (or RMR high enough to elevate body temperature above the environmental temperature) could have evolved as a correlated response to selection for higher MMR.

The aerobic capacity model was originally proposed based on a phenotypic analysis which suggested that the ratio of maximal and resting metabolic rates of vertebrates was typically between 5 and 10 (Bennett & Ruben, 1979). The model posited that the physiological design of vertebrates resulted in a correlation between these variables. An implicit feature of the model is that resting metabolic rates and maximal metabolic rates (aerobic capacity) must have been genetically correlated, otherwise selection on aerobic capacity would not lead to endothermy via a correlated response to selection (Hayes & Garland, 1995).

Numerous studies have attempted to test the aerobic capacity model by examining the fundamental assumption on which it is based. That is, that resting metabolic rate and maximal aerobic metabolic rate are inescapably positively correlated. Initial efforts focused on observational studies at the phenotypic level (for reviews see Hayes & Garland, 1995; Koteja, 2004). Later studies include tests using quantitative genetic approaches to estimate the genetic correlation or to test for correlated responses to selection (Hayes & Garland, 1995; Dohm et al., 2001; Nespolo et al., 2003, 2005; Bacigalupe et al., 2004; Koteja, 2004; Sadowska et al., 2005; Gebczynski & Konarzewski, 2009a,b; Wone et al., 2009). In addition, two forms of the model have now been recognized. The ‘strong form’ proposes that the positive genetic correlation between resting and maximal metabolism was present not only in proto-endotherms but that it should continue to be present in all existing endotherms. That is, the positive genetic correlation is an essential feature of the design of all vertebrate lineages that led to endothermy (Wone et al., 2009). This model is testable because evidence for a significantly negative genetic correlation in any endotherm would falsify the fundamental assumption of the model.

One issue that arises with the strong form of the aerobic capacity model is that genetic variances and covariances would need to have persisted over long stretches of evolutionary time. Whereas the strong form does not require a constancy of the genetic architecture, it does require the persistence of a positive genetic covariance and genetic variances over time. It is clear that selection and possibly other factors can alter genetic architecture (Paulsen, 1996; Phillips & Arnold, 1999; Roff & Mousseau, 1999; Steppan et al., 2002; Arnold et al., 2008). Over long time scales, the strong form of the model would require that some mechanisms existed for maintaining genetic variances and covariances in spite of the effects of selection, drift, and so on (Lande, 1980; Turelli, 1988). Theory suggests that persistence of a genetic covariance over the long term would depend on the nature and constancy of the adaptive landscape and on the distributional and temporal variation of mutational inputs (Arnold et al., 2008). The huge diversity of metabolic rates among vertebrates suggests that abundant genetic variation for metabolic rates exists or at least that such variation existed and persisted for a considerable time. In addition, Arnold et al. (2008) wrote that ‘the correlated evolution of multiple traits is common, as reflected by consistent patterns of trait association that are apparent at all levels of divergence’. Hence, the long-term persistence of genetic covariances and variances needed for the aerobic capacity model is at least plausible.

If one wished to test this hypothesis about the ubiquity of a genetic correlation between RMR and MMR, what would be the best species in which to do so? I would argue that data for reptiles and amphibians are not germane to testing the strong form of the aerobic capacity model. The strong form of the model applies to proto-endotherms and their descendants but not to members of other clades. Hence, tests of the strong form of the model should use either birds or mammals.

The strong form of the aerobic capacity model may not be true, perhaps because the necessary genetic architecture does not persist over long evolutionary time scales (see Turelli, 1988; Shaw et al., 1995; Arnold et al., 2008), but even if it is not true, the weak form of the aerobic capacity model might be. The weak form of the aerobic capacity model proposes that a positive genetic correlation was present in proto-endotherms but it was lost in some or all lineages subsequently. Existing methodologies do not provide a means to reliably estimate the genetic correlation of extinct populations. In addition, fossils generally do not provide reliable indicators of physiology, although some of the physiological inferences that can be drawn from fossils are fascinating (Hillenius, 1992, 1994; Ruben et al., 1996, 1998). For example, it has been argued that animals with high metabolic rates, and consequently with high respiration rates, use maxilloturbinal bones to limit evaporative water loss. Further, the presence of ridges indicating the attachment site for the maxilloturbinals is considered to be an indicator of endothermic physiology. Bone histology, isotope ratios, and other fossilizable indicators have also been used to hypothesize the physiological status of fossil groups (for reviews see Bakker, 1971; Ruben, 1995; Hillenius & Ruben, 2004). Nonetheless, fossils cannot be used to reconstruct genetic correlations. Perhaps with sufficient data and improved methodologies it will be possible to infer the ancestral genetic architecture of proto-endotherms, but uncertainties about the construction of ancestral character states may preclude the success of this approach (Cunningham et al., 1998; Steppan et al., 2002; Ekman et al., 2008). Hence, in the absence of a reliable method for estimating the genetic correlation of populations that have been long extinct, the weak form of the aerobic capacity model does not appear to be testable.

Reconstructing how natural selection shaped metabolic rates deep in evolutionary history is a formidable task. Even one of the architects of the aerobic capacity model has written that such efforts may shed heat but not a lot of light (Bennett, 1991). Nonetheless, progress is possible if we can think of tests that can potentially falsify models. One thing that could promote progress is an increasing formalization and specificity of the assumptions and predictions consistent with the existing models. Herein, I show the benefits of doing so using the multivariate breeders’ equation (Lande & Arnold, 1983). With this equation it is possible to put more specific bounds on the relative genetic variances, covariances, and selection gradients that are consistent with the aerobic capacity model. Thereby, it becomes possible to assess the plausibility of the aerobic capacity model and other models for the evolution of endothermy in new ways.

The model

  1. Top of page
  2. Abstract
  3. Introduction
  4. The model
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References

The aerobic capacity model looks at the joint evolution of resting metabolic rate (RMR) and maximal aerobic metabolic rate (MMR). Following Lande & Arnold (1983), the response to selection for multiple traits can be calculated using the multivariate form of the breeders’ equation.

  • image(1)

where inline image is a vector (n × 1) of changes in the phenotypic mean across generations, G is an additive genetic variance-covariance matrix (n × n), and β is a vector (n × 1) of direct selection gradients. Following this equation, the responses to selection inline image are the sum of the direct effects of selection on each trait plus the correlated effects because of selection on genetically correlated traits. In the case of the aerobic capacity model, where we have only two traits, RMR and MMR, the equation equals

  • image(2)

where V is a variance, C is a covariance, and the subscripts r and m refer to resting and maximal metabolic rates, respectively.

Accordingly the change in the phenotypic mean of RMR across a generation is

  • image(3)

where the direct effect of selection caused by Vr · βr acts to reduce RMR and the effect of selection on MMR (βm) acts to increase RMR via the genetic covariance Crm.

Model constraints

The variables in the model are constrained as follows: (i) inline image because Vr and Vm are variances, and variances are by definition positive, (ii) βm > 0 because the aerobic capacity model postulates that increases in MMR are beneficial, (iii) Crm > 0 because a positive correlated response to selection for higher MMR requires that the covariance be positive, (iv) βr < 0 because the aerobic capacity model is developed with the assumption that higher RMR is costly, so selection should oppose increases in RMR, and (v) inline image, because the maximum covariance of two variables is less than or equal to the positive square root of the product of the variances of those variables. Note that these constraints (e.g., that there must be additive genetic variance for a response to selection or that the covariance of two traits must be equal to or less than the square root of the product of their variances) are not necessarily specific to the aerobic capacity model. However, they are listed here to make clear the conditions that apply to the subsequent analyses.

Conditions for RMR to increase

The aerobic capacity model seeks to explain an increase in RMR. For RMR to increase, it is necessary that

  • image(4)

Subtracting the second term from both sides of the inequality yields

  • image(5)

As described in the model constraints Cr−m is positive and βr is negative. Accordingly, −βr must be positive. Consequently dividing by Cr−m and then by −βr which are both positive does not change the direction of the inequality, so we obtain the result

  • image(6)

In addition, hereafter we define f as minus 1 times the ratio of the selection gradient for MMR divided by the selection gradient for RMR, i.e.

  • image(7)

Note that f must be positive because βm is positive and βr is negative. RMR will increase if f is greater than Vr/Crm. This inequality (6) provides a more explicit description of the necessary conditions for the aerobic capacity model than merely saying that the genetic covariance/correlation must be positive or that it must be absolute (i.e., equal to 1).

Another useful idea for approaching the model is looking at how genetic variances constrain the genetic covariance. The genetic covariance equals

  • image(8)

where ρrm is the genetic correlation. The largest possible genetic correlation is 1 so the genetic covariance cannot be greater than the square root of the product of the genetic variances. If

  • image(9)

then

  • image(10)

and

  • image(11)

describes the conditions needed for RMR to increase. It does so in terms of minus 1 times the ratio of the selection gradients (f), the genetic correlation (ρrm), and the square root of the ratio of the genetic variance of MMR divided by the genetic variance of RMR (inline image). Note that ρrm must be greater than zero (the covariance must be positive) for the aerobic capacity model to work, and because it is a correlation it must also be less than or equal to one.

Conditions for MMR to increase

In addition to the requirement that RMR increase, the aerobic capacity model also requires that MMR increase, i.e., that

  • image(12)

The response to selection for MMR is

  • image(13)

and for the model to hold

  • image(14)

must be true. Consequently, the second condition for the aerobic capacity model to work is that

  • image(15)

In other words, MMR will increase if f is greater than the genetic covariance for RMR and MMR divided by the genetic variance for MMR. Again, this inequality, like the one that applies to RMR, provides a more explicit description of the necessary conditions for the aerobic capacity model than merely saying that the genetic covariance/correlation must be positive. And finally

  • image(16)

So MMR will increase when

  • image(17)

This inequality will always be true whenever

  • image(18)

is true, because whenever 0 < ρrm ≤ 1 then

  • image(19)

Now with the model cast in terms f and g, the genetic covariance (and correlation) needed for the inequalities to be true (i.e., how strong the genetic correlation needs to be for the model to work) can be calculated. That is, instead of arguing that the model only works if there is a perfect correlation between the traits, one can calculate how strong the correlation needs to be for the aerobic capacity model to be potentially viable.

I calculated the minimum correlation needed for RMR to increase for varying f and g. RMR and MMR can be measured in the same units and MMR is typically roughly 5–10 times RMR. Hence, it is reasonable to expect that the genetic variance of MMR is likely to be as large or larger than the genetic variance of RMR. Accordingly, I performed calculations for = 1, 2, 5, 10, 50, and 100. The strength of selection on metabolic rate is not well characterized. Given this dearth of baseline information, I performed calculations for = 1, 2, 5, 10, 20, 50, and 100 (indicating stronger selection on MMR than on RMR) and for the reciprocals of those values (indicating stronger selection on RMR than on MMR).

The minimum genetic covariance needed for the aerobic capacity model to work is not the only way to characterize the magnitude of the genetic constraint, and as a measure of constraint it is not easily comparable to other studies of multivariate constraint. Walsh & Blows (2009) review several other metrics for assessing multivariate constraint, and they note that θ, the angle between the actual response to selection and the vector of selection gradients is a readily comparable measure of constraint (Hansen & Houle, 2008). The angle θ falls between zero (no constraint) and 90° (absolute constraint) with smaller angles indicating lesser constraint and larger angles indicating greater constraint. In addition to calculating the minimum necessary covariance, I also calculated θ as a measure of multivariate constraint.

Using standard methods for calculating the angle between two vectors, I calculated the angle θ as follows. Each vector, one vector for the response to selection and one vector for the selection gradients, has an RMR component and an MMR component. First, I calculated the magnitudes of each vector by squaring each of the two components in the vector and then taking the square root of the sum of those squared terms. Second, I multiplied the RMR components of the two vectors and the MMR components of the two vectors and added these products together to obtain the scalar product. Third, I divided the scalar product by the product of the magnitudes of the vectors to obtain the cosine of θ. Fourth, I calculated the arccosine of cos(θ) to obtain θ.

Results

  1. Top of page
  2. Abstract
  3. Introduction
  4. The model
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References

An absolute genetic constraint (i.e., genetic correlation of + 1) is not required for RMR to increase by the mechanism proposed by the aerobic capacity model. Even excluding the more extreme values for f and g, higher RMR can evolve even when the genetic correlation is modest or even low (Table 1). For example, if selection on MMR is twice as strong as selection on RMR (i.e., = 2) and if the genetic variance of MMR is twice as big as the genetic variance of RMR (i.e., = 2), then a genetic correlation greater than 0.36 will lead to increased RMR (Figs 1 and 2). If f is 5 and g is 5, then the minimum genetic correlation needed to evolve an increased r would be < 0.1.

Table 1.   Minimum genetic correlation between resting and maximal metabolic rate needed for the aerobic capacity model to be viable as a function of f (minus one times the ratio of the selection gradient for maximal aerobic metabolic rate divided by the selection gradient for resting metabolic rate) and g (the ratio of the genetic variance for maximal metabolic rate divided by the genetic variance for resting metabolic rate). Dashes indicate that the aerobic capacity model is not viable under those conditions. When f is ≤ 0.1 the aerobic capacity model is not viable for any of the values of g (1, 2, 5, 10, 50, 100) that were examined. When f is ≥ 20, the minimum correlation needed is ≤ 0.05 for all the values of g that were examined. A geometric indicator that is comparable with other studies of multivariate constraint is θ, the angle between the actual response to selection and the vector of selection gradients (Hansen & Houle, 2008; Walsh & Blows, 2009)
fgMinimum ρr−mθ (°)fgMinimum ρr−mθ (°)
0.21210.50071.6
0.22220.35461.8
0.25250.22450.7
0.2102100.15844.1
0.2500.70786.72500.07134.6
0.21000.50084.421000.05032.3
0.51510.20056.3
0.52520.14146.6
0.550.89487.5550.08935.4
0.5100.63281.05100.06328.9
0.5500.28371.55500.02819.4
0.51000.20069.151000.02017.0
111010.10050.7
120.70780.31020.07141.0
150.44769.11050.04529.8
1100.31662.510100.03223.3
1500.14153.010500.01413.8
11000.10050.7101000.01011.4
image

Figure 1.  Minimum genetic correlation required for resting metabolic rate to increase. Plotted as a function of f (minus one times the ratio of the selection gradient for maximum metabolic rate divided by the selection gradient for resting metabolic rate) on the abscissa for four values of g (the ratio of the genetic variance for maximal metabolic rate divided by the genetic variance for resting metabolic rate).

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image

Figure 2.  Minimum genetic correlation required for resting metabolic rate to increase. Plotted as a function of g (the ratio of the genetic variance for maximal metabolic rate divided by the genetic variance for resting metabolic rate) on the abscissa for four values of f (minus one times the ratio of the selection gradient for maximum metabolic rate divided by the selection gradient for resting metabolic rate).

Download figure to PowerPoint

Discussion

  1. Top of page
  2. Abstract
  3. Introduction
  4. The model
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References

Genetic constraints on adaptation are one of the central interests of evolutionary biologists. One source of insight into constraints on multivariate evolution is quantitative genetics. Another source of insight into functional and design constraints is physiology. Much might be gained by combining the perspectives of functional biologists (e.g., physiologists and comparative physiologists) with those of quantitative geneticists, but the mathematical complexity of quantitative genetic theory can be a barrier to functional biologists. This barrier can hold back the progress that can come from interdisciplinary study. In a recent review, Walsh & Blows (2009) emphasized Barton’s (1990) inference that there ‘cannot be a large number of genetically independent traits.’ They suggest that the ‘number of pleiotropically independent traits is likely to be on the order of 10s rather than … 100s or 1000s’. They conclude that ‘substantial multivariate genetic constraints are likely to be present in natural populations.’ This perspective is one that deserves serious scrutiny by functional biologists and by anyone interested in the evolution of physiological traits, such as metabolic rates.

Herein, I explicitly identify the relationships among selection gradients, genetic architecture and response to selection needed for the aerobic capacity model for the evolution of endothermy to be viable. The aerobic capacity model is a good example of a hypothesis (derived from considerations of functional biology) that critically depends upon a particular genetic constraint. A two-trait form of the multivariate breeders’ equation makes clear that the relative genetic variances, strengths of selection and genetic covariance are all important to understanding the requirements of the aerobic capacity model. Genetic constraints may be important even if they are not absolute (i.e., it is not just a question of whether the genetic correlation between RMR and MMR is +1 or nearly so). Hence, it would now seem appropriate to turn attention to obtaining data on (i) the relative strength of selection on RMR vs. the strength of selection on MMR, (ii) the size and relative size of the genetic variances for those traits, and (iii) the genetic covariance between the traits. Currently, such data are sparse.

At present, there are insufficient data on the strength of selection on metabolic rates to inform the relative likelihood of various models for the evolution of endothermy. Only a few studies have tested whether phenotypic selection acts on metabolic rates in nature. All of these studies on metabolic rates used recaptures of marked animals to indicate survival and failures to recapture to indicate mortality. Because none of these studies used formal mark-recapture models, they potentially conflate mortality with capture probability and emigration (Kingsolver & Smith, 1995; see Sears et al., 2006). Nonetheless, one of the studies was conducted on bank voles (Myodes glareolus) introduced to an island where there was limited potential for successful emigration (Boratynski & Koteja, 2009). In that study if a marked animal was not captured during a trapping session (t), it was never recaptured during a subsequent (later) trapping session (i.e., t + Δt). Hence, the low probability of successful emigration and the temporal pattern of recaptures suggest that recapture data alone were an adequate measure of survival. Based on logistic regression analyses of all their data, there was not significant directional selection on either basal metabolic rate (BMR) or MMR, but there was stabilizing selection on MMR for both males and females. For BMR, there was stabilizing selection on females and disruptive selection on males.

One other study has measured selection on maximal metabolic rate in mammals. In that study, the directional selection gradient for increased maximal metabolic rate of deer mice (Peromyscus maniculatus) was significant 1 year but not the subsequent year, possibly because of changes in spring snow load and localized flooding (Hayes & O’Connor, 1999). Lastly, another study measured selection on resting metabolic rate of mammals. Mass-independent RMR and over winter survival were positively correlated in short-tailed voles (Microtus agrestis), but whole animal RMR or peak metabolic rate were not (Jackson et al., 2001). These studies appear to be the only published studies of phenotypic selection on metabolic rates of mammals. Hence, it is not surprising that we know little about the evolution of endothermy, given that we know almost nothing about the microevolution of metabolic rates in extant mammals.

It is possible that field studies of phenotypic selection on physiology are rare because they are logistically demanding (Kingsolver et al., 2001). Quantitative genetic studies are also logistically demanding, and they generally require large sample sizes if they are to have reasonable power to detect biologically significant levels of variation (Klein et al., 1973; Barton & Turelli, 1989). Hence, when a study fails to find a significant genetic variance or covariance, it is important to consider whether this results from a true lack of genetic variation or whether the result might be because of insufficient sample size. Obtaining large sample sizes is particularly challenging for studies of metabolic rates (and other physiological measures) because physiology is typically time-consuming to measure.

Nonetheless, there are more data on the genetic architecture of metabolic rates in mammals than there are for the strength of selection. Significant genetic variation for resting metabolic rates has been reported for humans and bank voles (Bouchard et al., 1998; Sadowska et al., 2005), but not for leaf-eared mice (Phyllotis darwini) (Nespolo et al., 2003, 2005; Bacigalupe et al., 2004). For lab mice (Mus spp.), some studies report significant additive genetic variance and others do not (Lacy & Lynch, 1979; Dohm et al., 2001; Wone et al., 2009). Relatedly, three species of birds possess heritable variation for BMR, although it is less clear whether mass-independent BMR is heritable (Ronning et al., 2007; Nilsson et al., 2009; Tieleman et al., 2009).

Procedures to measure RMR are relatively standardized. There is a broader diversity of ways to measure MMR. MMR can be measured by exercising (e.g., running, swimming, or bicycling) animals to their aerobic limit or by exposing animals to cold sufficient to elicit their maximal thermogenic response. Significant genetic variance for MMR has been reported for leaf-eared mice, bank voles, humans, and Mus (Bouchard et al., 1998; Dohm et al., 2001; Nespolo et al., 2005; Sadowska et al., 2005; Wone et al., 2009). There are too few data and too many analytical caveats to reach definite conclusions (Wilson, 2008), but the available evidence intriguingly suggests that the genetic variances for mass-independent metabolic rate may be 100 or more times larger than the genetic variances for mass-independent RMR (Dohm et al., 2001; Konarzewski et al., 2005; Nespolo et al., 2005; Sadowska et al., 2005; Wone et al., 2009). If similar variances existed in the animals that took the first step along the pathway from ectothermy to endothermy, then the implications are large for the aerobic capacity model. They indicate that the genetic correlation between RMR and MMR could have been appreciably < 1 and the aerobic capacity model would still be viable. For example if g (the ratio of the genetic variance for MMR/RMR was 100) and if selection acted equally strongly on RMR and MMR (f = 1), then RMR and MMR would both increase (at least initially) as long as their genetic correlation was at least 0.1. Hence, the available data suggest that the aerobic capacity model might be viable even if the genetic correlation between RMR and MMR was much less than one.

Besides genetic covariances/correlations, quantitative genetics provides another more integrated way to categorize the degree of constraint with the angle θ (i.e., the angle between the vector of selection gradients and the vector of selection responses). Along with each calculation of the minimum genetic correlation, I calculated the corresponding value for θ (Table 1). Although there is a strong correlation between the minimum necessary genetic correlation and θ, the correlation is far from perfect. In the context of the aerobic capacity model, it is easy as a functional biologist to view the ramifications of the genetic correlation, but for the purposes of comparison with multivariate constraints, θ is a more useful measure (Walsh & Blows, 2009).

Genetic variances and covariances may change over time as may the strength of selection (Kingsolver et al., 2001; Steppan et al., 2002). For example, in the current context one could imagine that selection for low RMR might become stronger as RMR evolved farther away from a local optimum consistent with ectothermy. In turn this might alter the relative strength of selection on RMR and MMR and hence the evolutionary trajectory (i.e., response to selection). But endothermy and ectothermy are both viable physiological strategies as demonstrated by the fact that there are more than 10 000 species of endotherms and an even larger number of ectotherms. The viability of both ectothermic and endothermic physiologies suggests that there must be at least two, if not many, local optima for resting metabolic rates, and likely for maximal metabolic rates as well. At some point during the evolution of endothermy, resting metabolic rate would cross a valley in the adaptive landscape to enter a region where selection for increased RMR would be beneficial (for a graphical illustration of this idea see Steppan et al., 2002). Biophysical models and studies of selection in extant populations could do much to clarify why and at what point populations might cross the threshold where selection for RMR shifted from negative to positive. Yet, another possibility is that despite plausible arguments that high RMR is costly, selection on RMR might actually be weak or weak most of the time (Boratynski & Koteja, 2009). This might be the case, for example, if animals spent little of their time at metabolic levels approximating RMR, such that RMR had little effect on daily energy expenditure (DEE). But data for mammals suggest that RMR and DEE are strongly correlated (Ricklefs et al., 1996). This correlation suggests that increased RMR is costly in terms of daily energy expenditure and consequently in terms of food requirements.

A number of models have been proposed to explain the evolution of endothermy (McNab, 1978; Bennett & Ruben, 1979; Ruben, 1995; Farmer, 2000, 2003; Koteja, 2000; Angilletta & Sears, 2003; Hillenius & Ruben, 2004). Many of these models are not mutually exclusive, and indeed it may be better to start thinking about what each of these models might potentially contribute to understanding the evolution of endothermy, rather than thinking of them as competing models (Koteja, 2004; Kemp, 2006). Once higher RMR has evolved, there are many possible benefits and costs for high RMR, and the specific environmental circumstances may determine whether selection is positive or negative at any given time. However, if one accepts that initial increases in RMR did not have immediate thermal benefits, then the crux of the problem in accounting for the evolution of endothermy is what led to increased RMR before RMR reached the point where higher RMR was directly beneficial in and of itself. The benefits of increased assimilation efficiency of food, increased aerobic capacity, and other physiological correlates of RMR may all have acted together to drive the early increase in RMR that eventually led to endothermy. If indeed there are a relatively small number of pleiotropically independent traits then one group of traits might be those pleiotropically linked to RMR. More extensive study of genetic architectures associated with aerobic metabolic rates could illuminate this issue.

To elaborate, consider that RMR may be correlated with many aspects of physiology besides maximal aerobic metabolic rate. For example, RMR might be correlated with rate of energy assimilation by the gut. In this case, the response to selection for RMR would be

  • image(20)

where Cr−assim is the genetic covariance between RMR and energy assimilation by the digestive tract and where βassim is the directional selection gradient for energy assimilation. Physiologically it seems reasonable that a high daily energy expenditure might also correlate with RMR because RMR reflects the costs of maintaining the visceral organs and biochemical machinery needed for digestion (Ricklefs et al., 1996; Koteja et al., 2000). High daily energy use and assimilation rates might also be expected in animals that operate near the upper capacity for aerobic activity (Hayes, 1989a,b). Hence, it is easy to envision how the aerobic physiology of animals would form suites of traits that might evolve in concert (perhaps because of pleiotropic gene action). This perspective potentially connects the functional biological perspective with the notion from quantitative genetic theory that there are relatively few pleiotropically independent traits.

Covariances with body mass are another genetic constraint deserving investigation. Most physiological traits are strongly phenotypically correlated with body mass, and pleiotropic effects of body mass are potentially widespread. That is, the evolution of physiology at the whole animal level may be strongly influenced by interdependencies with body mass. The analyses in this paper ignore the effects of body mass. The negative allometric scaling of whole-animal metabolic rates with body mass is firmly established (Glazier, 2005 and references therein). Whole animal metabolic rates increase with size, but with a scaling exponent less than one (i.e., larger animals generally have higher metabolic rates). The model proposed herein is one that would apply if endothermy evolved without changes in body mass. That is, where metabolic intensity increases to the point where an animal becomes endothermic but without a concomitant change in size. As such, the model applies to selection on mass-independent metabolic rates, not whole-animal metabolic rates. It is not clear whether changes in mass played a role in the evolution of endothermy (McNab, 1978), but this issue merits further study.

In summary, absolute genetic correlations are not required for the aerobic capacity model for the evolution of endothermy to be viable. A better understanding of evolutionary constraints and trajectories results from considering all of the parameters in the breeders’ equation (i.e., selection gradients and genetic variances and covariances) simultaneously than from considering only the genetic covariance/correlation in isolation. Indeed, this is likely to be true for all studies of the evolution of complex adaptations, not just for the evolution of endothermy. This article clarifies how the relative sizes of selection gradients and genetic variances in extant populations are potentially useful for informing models of endothermy. Lastly, the evolution of metabolism more broadly (not just endothermy) offers a potentially fruitful area in which to explore possible links between physiological and genetic constraints.

Acknowledgments

  1. Top of page
  2. Abstract
  3. Introduction
  4. The model
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References

I thank Cynthia Downs, E. Robert Donovan, Marta Labocha, Mike Sears, and Bernie Wone for their hard work on an artificial selection experiment that prompted me to explore the issues in this manuscript. I thank Leo Baciagalupe, Pawel Koteja, Bruce Walsh and an anonymous reviewer for their helpful suggestions for improving the manuscript. Supported by NSF IOS 0344994.

References

  1. Top of page
  2. Abstract
  3. Introduction
  4. The model
  5. Results
  6. Discussion
  7. Acknowledgments
  8. References