Spatial variation in the evolutionary potential and constraints of basal metabolic rate and body mass in a wild bird

An organism's energy budget is strongly related to resource consumption, performance, and fitness. Hence, understanding the evolution of key energetic traits, such as basal metabolic rate (BMR), in natural populations is central for understanding life‐history evolution and ecological processes. Here we used quantitative genetic analyses to study evolutionary potential of BMR in two insular populations of the house sparrow (Passer domesticus). We obtained measurements of BMR and body mass (Mb) from 911 house sparrows on the islands of Leka and Vega along the coast of Norway. These two populations were the source populations for translocations to create an additional third, admixed ‘common garden’ population in 2012. With the use of a novel genetic group animal model concomitant with a genetically determined pedigree, we differentiate genetic and environmental sources of variation, thereby providing insight into the effects of spatial population structure on evolutionary potential. We found that the evolutionary potential of BMR was similar in the two source populations, whereas the Vega population had a somewhat higher evolutionary potential of Mb than the Leka population. BMR was genetically correlated with Mb in both populations, and the conditional evolutionary potential of BMR (independent of body mass) was 41% (Leka) and 53% (Vega) lower than unconditional estimates. Overall, our results show that there is potential for BMR to evolve independently of Mb, but that selection on BMR and/or Mb may have different evolutionary consequences in different populations of the same species.

The relationship between BMR and ecological conditions remains complex and unresolved, and often context-dependent (Arnold et al., 2021;Burton et al., 2011;Mathot et al., 2019). Interspecific comparisons indicate that differences in BMR are closely linked to adaptations to different environments and variation in life history (Bryant & Furness, 1995;McNab, 1994;White et al., 2006;Wiersma et al., 2007). For example, species living in cool and wet areas have higher BMR than those living in warmer and drier areas (Liknes & Swanson, 1996;Swanson & Liknes, 2006;Tieleman et al., 2003;Wiersma et al., 2007). At the intraspecific level, there is evidence for genetic differentiation in BMR between bird populations inhabiting different environments (Broggi et al., 2005;Wikelski et al., 2003). Relationships between components of individual fitness and BMR have been documented in some populations (Nilsson & Nilsson, 2016;Rønning et al., 2016), whereas (Petit et al., 2017) found that thermogenic capacity rather than BMR determined winter survival. Several recent reviews have found patterns that fit with various hypotheses, such as (i) the 'increased intake' or 'performance' hypothesis (i.e. individuals with a higher BMR also have a higher capacity to acquire energy; Arnold et al., 2021), (ii) the 'compensation' or 'allocation' hypothesis (i.e. individuals with low BMR can afford to allocate more energy to other functions such as growth and reproduction; Swanson et al., 2017), and (iii) 'the context-dependent' hypothesis (the availability of certain resources shapes the relationship between metabolic rate and fitness; Arnold et al., 2021;Burton et al., 2011).
Despite being a central trait in comparative physiology, ecology and evolutionary biology (Hayssen & Lacy, 1985;Mckechnie & Swanson, 2010), information about the evolutionary potential of BMR in free-living populations in their natural environment, potentially critical for responses to climate change, is scarce. BMR is tightly connected to body mass (M b ), a frequently measured and fitnessrelated life-history trait (Pettersen et al., 2018;White et al., 2019;White & Seymour, 2005). The allometric relationship between BMR and M b has been described as BMR = aM b b P , where a is a constant and b P is a phenotypic scaling exponent (or slope, in log-log space, such that b P = cov P (BMR,Mb) V P (Mb) ) traditionally thought to be ⅔ or ¾, but the generality of this is debated (Careau & Glazier, 2022;Glazier, 2005;White et al., 2009). Both BMR and M b are flexible and need not fluctuate in perfect synchrony (Broggi et al., 2019), thus also allowing for flexibility in phenotypic covariance, and thus in b P . Moreover, to what degree evolutionary potential in BMR is dependent on M b through allometric scaling and phenotypic and genetic integration remains an open question.
The evolutionary potential in a population, the standing level of additive genetic variance (V A ) within, and covariance (cov A ) between traits, can be described by the additive genetic covariance matrix G, with V A along the diagonal and cov A in the off-diagonal elements.
The vector of responses (R) to selection in correlated traits can then be expressed as R = Gβ (Lande, 1979;Lande & Arnold, 1983). Here β is the vector of selection gradients on each trait. For comparisons across traits, populations and species, V A is commonly standardized as narrow-sense heritability (h 2 = V A /V P , i.e. the ratio of V A to total phenotypic variance [V P ]), or as evolvability (I A = V A /μ 2 , i.e. V A divided by the squared mean of the phenotype [μ 2 ]) (Falconer, 1996;Houle, 1992), whereas cov A between traits are standardized as ge- ). Recently, estimating the additive ) has been suggested as a way to increase the understanding of the links between BMR and M b (Careau & Glazier, 2022). Interestingly, b A appears not to deviate from the traditional ⅔ or ¾ allometric scaling exponents, although studies on more taxa are needed to infer any generality (Careau & Glazier, 2022;Videlier et al., 2019). The exponent b A reflects the line of least genetic resistance and thus indicates the most likely direction of evolution of BMR and M b . The magnitude of b A relative to other components of b P , such as the residual scaling exponent ), provides insight into the contribution of environmental or genetic influence on the allometric relationship (Careau & Glazier, 2022).
The potential for evolutionary change in a trait can be constrained by genetic correlation with other traits under selection such as M b , and the effect depends on the strength of selection on each trait and their genetic correlation (Hansen & Houle, 2008;Lande & Arnold, 1983). As BMR and M b are tightly connected, phenotypic and genetic correlations between BMR and M b have the potential to influence selection on and evolution of metabolic rate, respectively (Lande & Arnold, 1983). In birds, heritability estimates of M b vary from effectively zero in tree swallows (Tachycineta bicolor) to at least h 2 = 0.73 in stonechats (Saxicola torquate maura), with most estimates being roughly around h 2 = 0.4 (e.g. Bushuev et al., 2012;Gosler & Harper, 2000;Jensen et al., 2003;Nilsson et al., 2009;Rønning et al., 2007;Teplitsky et al., 2009;Tieleman et al., 2009;Wiggins, 1989). Genetic correlations between BMR and M b in passerines range from r A = 0.08 in free-living pied flycatchers (Ficedula hypoleuca) (Bushuev et al., 2012), to r A = 0.87-0.91 in captive zebra finch (Taeniopygia guttata) (Mathot et al., 2013;Rønning et al., 2007) and effectively one in wild blue tits (Cyanistes caeruleus) . The genetic correlation between BMR and M b was also found to vary between geographically separated stonechat populations (Saxicola torquata subspp.) (Tieleman et al., 2009), indicating potential differences among populations in responses to selection on these traits. Selection on metabolic rate may be expected to change with climate change (Broggi et al., 2007;Nilsson & Nilsson, 2016;White et al., 2006), whereas a range of selective forces -most of which are independent of weather and climate, can together result in a strong stabilizing selection on M b (Blanckenhorn, 2000). For example, (Broggi et al., 2019) found BMR to be more sensitive than 2 | ME THODS

| Study populations, design, and data collection
We examined house sparrows in three insular house sparrow populations on the islands Leka, Vega, and Lauvøya, separated by 60-220 km along coastal mid-Norway and northern Norway ( Figure S1.1 in Appendix S1). The house sparrow is a sedentary bird in Norway, breeding in buildings and nest boxes and in the study islands they live near dairy farms that provide shelter and food. Yet, evolution in house sparrows is still shaped largely by environmental variation (Geue et al., 2016). Adult sparrows feed on seeds, whereas nestlings rely on insects for food, whose abundance and availability varies locally with for example, vegetation and weather conditions (Anderson, 2006). Local population densities and age, structure may vary both temporally and spatially (Baalsrud et al., 2014;Holand et al., 2016). The house sparrows within the study area are exposed to predation with cats and sparrow hawks as the main predators.
For a more comprehensive overview of the ecology of house sparrows, see (Anderson, 2006;Husby et al., 2006;Jensen et al., 2013;Pärn et al., 2009). The study populations were included in a long- Vega populations were the sources for a translocation to create one admixed population on a third island Lauvøya, where native birds had been removed (further details below). Consequently, the pedigree is naturally structured into two distinct genetic groups from the two source populations. Natural dispersal between these populations has not been recorded and would thus be unexpected (Jensen et al., 2013;Pärn et al., 2012;Ranke et al., 2021;Tufto et al., 2005).
The three study islands have a coastal climate and weather, characterized by mild winters and moist, cool summers (monthly total precipitation and monthly mean temperature during 1990-2022: 20-300 mm and −4-+5°C during January, February and March; 20-210 mm and +8-+16°C for June, July, and August), largely regulated by the oceanic water masses and the North Atlantic Gulf Stream (Ringsby et al., 2002;(MET), Norwegian Meteorological Institute, 2022). Leka tends to have more precipitation; otherwise, these islands largely experience similar climatic conditions (Table   S1.1 in Appendix S1). Other environmental differences may exist between (and within) populations, such as social environment (sex ratio or relatedness clustering within or between farms), microclimate (due to differences in location, construction, and practices of farms), or population density (natural density fluctuations as well as density consequences of the selection experiment). Environmental differences between populations were pooled in the higher-order environmental effect of population. Most sparrows in each population (>90%) were captured using mist nets during late winter (February-March, to avoid interfering with the breeding season) 2012-2015 (Vega until 2014). At first capture, each bird was given a numbered metal ID-ring and a unique combination of three plastic colour rings.
A small blood sample (25 μL) was collected by brachial venipuncture and stored on 96% ethanol for later genetic analyses. After the blood sample was taken, all birds were released into a sealed aviary (a former cowshed) on each island of approx. 150 m 2 and 2.5 m room height heated to 10-15°C, which is the normal temperature range in cowsheds in this part of Norway during winter. In the aviary, they were then provided water and food (a range of bird seeds and bread) ad libitum, and branches were put up to allow birds to perch and hide.
As soon as possible (mostly within 0-1 day, range 0-7 days) the birds were recaptured, and their metabolic rates measured (see below).
To investigate spatial patterns in genetic and environmental sources of variation and any phenotypic differences between populations, we made use of a selection experiment conducted on BMR at Leka and Vega during -2015. In that selection experiment, the populations at Leka and Vega were selected for low and high whole-body BMR, respectively. In the present study, we could take advantage of this selection experiment by translocating a subset of the birds that were removed from Leka and Materials S2 in Appendix S1 for details). M b was measured to the nearest 0.01 g using a digital balance at the beginning and the end of each metabolic rate measurement, and the mass at time of reaching BMR was estimated assuming constant mass loss between measurements. After metabolic measurements, all individuals were kept in the aviaries until artificial selection was conducted (see above).
The study was carried out in accordance with permits from the Norwegian Food Safety Authority (permits 4011 and 5978) and the Bird Ringing Centre at Stavanger Museum, Norway.

| Determination of the genetic pedigree
SNP data were obtained from the blood samples following (Lundregan et al., 2018). A genetic pedigree was constructed using the sequoia R-package (Huisman, 2017) based on 603 SNPS that were shown to be highly informative for parentship in the study populations (Lundregan et al., 2018;Niskanen et al., 2020). Additionally, a microsatellite pedigree was available for ancestors in Leka and Vega providing additional relatedness information (Rønning et al., 2016).
Of the 911 individuals phenotyped in our study, both parents were known for 53.4%, and one parent only was known for 22.0%. Mean number of ancestral generations across all populations was 3.83, whereas the highest number of ancestral generations for one individual was 12 ( Figure S3.1 and Table S3.1 in Appendix S1).

| Statistical analyses
Analyses were performed by fitting GGAM with heterogeneous additive genetic variances (Aase et al., 2022;Muff et al., 2019). In our case, the base population was partitioned into three genetic groups (1) Leka; (2) Vega and (3) (Sorensen et al., 2001). To avoid potential model selection bias, no model selection was performed (Freedman & Freedman, 1983). BMR is expected to generally have a relatively large measurement error (ME) (Bouwhuis & Sheldon., 2011;Broggi et al., 2009;Rønning et al., 2005). Unpublished data from our own studies suggest that ME (instrumental and biological) may constitute up to 40% of V P of BMR and 15% in M b . Thus, to qualitatively explore if and how ME may influence estimation of parameters, we specified a point-prior for the ME variance (V ME ) using the mevargument in MCMCglmm, assuming ME is normally distributed with mean 0 (Hadfield, 2010). In the absence of prior knowledge, but to illustrate potential effects of ME, models were fitted with V ME corresponding to roughly 0, 20 and 40% of total variance of BMR and 0%, 8% and 15% of total variance in M b (Bouwhuis & Sheldon, 2011;Broggi et al., 2009;Rønning et al., 2005).
The group-specific narrow sense heritability was estimated as (Falconer, 1996), and group-specific evolvability as I A(z) = V A(z) /μ 2 (z) (Houle, 1992). V A(z) , V P(z) and μ 2 (z) are the groupspecific additive genetic variance, phenotypic variance, and mean phenotype squared of each trait in group z in 2012, respectively.
The base population in the respective genetic groups were used for calculation of V P(z) , cov P(z) and μ 2 (z) . Consequently, no admixed individuals contribute to V P(z) , cov P(z) or μ 2 (z) for either trait. Note that due to inability to estimate ME the calculated V P includes V ME , thus downward bias h 2 . The group-specific genetic correlation between BMR and M b for each group z (r A(z) ) was calculated as Following (Hansen et al., 2003;Hansen & Houle, 2008), conditional genetic variance in one trait x independent of another trait y is given by (2) where V C(z) (x| y) is the group-specific additive genetic variance in trait x that is independent of trait y. The effect of conditioning 1 − r 2

A(z)
thus represents the proportion of V A that is independent of the other trait within the genetic group. Conditional heritability and evolvability can then be calculated as above, substituting V C for V A . In addition, allometric scaling exponents were estimated by fitting the GGAM with log e -transformed BMR and M b , yielding group-specific, amongindividual, and residual (co)variances allowing to estimate groupspecific additive genetic (b A(z) ), among-individual (b ID ) and residual (b R ) allometric scaling exponent, respectively (Careau & Glazier, 2022).
Below we report the results from the GGAM fitted with the highest prior level of V ME (40% of BMR and 15% of M b ), presented as posterior means for fixed effects and modes for variance components, and 95% highest posterior density (HPD) credible interval in square brackets. Instead of relying on statistical significance testing with a set p-value threshold, we present our results in the gradual language of evidence, evaluated by the respective 95% HPD credible intervals (Muff et al., 2021). Results from models fitted with lower V ME can be found in Supplementary Materials S5 in Appendix S1.

| Phenotypic variation
There was little or no evidence for any phenotypic differ- year-specific phenotypic mean BMR ranged from 75.5 to 81.5 mL O 2 h −1 and variance from 56.8 to 119.9 (mL O 2 h −1 ) 2 , and M b from mean 28.6 to 29.8 g and variance from 2.17 to 3.62 g 2 ( Table 1).

ences between Leka and Vega in BMR or
During the selection experiment, there was very strong evidence   Figure S5.1 in Appendix S1).

| Genetic group compositions
The proportion of the unknown group increased in all populations for each year (from 0% in 2012 to a maximum of 73% in Lauvøya in 2015), but the increase appeared to differ somewhat between populations and years ( Figure 2). This variation was presumably due to demographic processes such as differences in immigration between populations and

| Mean breeding value
There was no evidence for a difference between the groups in mean breeding values in either trait. There was a very weak tendency that the mean breeding values of BMR in the base population of the unknown genetic group was somewhat higher than in the Leka and Vega genetic groups, with estimated differences of 1.  (Table S5.3 in Appendix S1).

| Evolutionary potential
There was strong evidence that both BMR and M b have considerable additive genetic variation and thus the potential to evolve if under selection ( Table 2). Among the two genetic groups, Leka tended to have the higher estimates of heritability and evolvability of BMR, although with little evidence, and this tendency was stronger in the conditioned (h 2 (BMR|Mb) and I A(BMR|Mb) ) than unconditioned (h 2 and I A ) estimates ( Table 2). In M b , Vega tended to have the higher estimates, but only in the unconditioned estimates and with little evidence (Table 2). Furthermore, BMR was estimated to have lower heritability, but higher evolvability than M b in both populations.

| Genetic correlations and additive genetic scaling exponent
There was a positive additive genetic covariance and genetic correlation between BMR and M b in both genetic groups, suggesting that the two traits generally have partially the same genetic basis ( Table 2). There was no evidence that cov A (BMR, M b ) or r A differed between the groups, although Vega tended to have higher estimates ( Table 2). Conditional heritability and evolvability indicate that BMR and M b can evolve independently of each other and suggest that genetic constraints on independent evolution were slightly stronger in Vega ( Table 2). Conditioning the traits on each other following equation (2) reduced estimates of V A , h 2 and I A by 42% [13.5, 69.4] in Leka,and 57% [19.5,82.2] in Vega (detailed results in Table S5. [3][4] in Appendix S1). The additive genetic scaling exponents were similar F I G U R E 2 Genetic group structure in the three insular house sparrow populations (Lauvøya, Leka and Vega) measured as proportion of the total gene pool within the winter populations each year that belonged to each of the three genetic groups Leka (red), Vega (green) or unknown (grey). Individual genetic group affiliation was estimated from the pedigree assuming Mendelian inheritance. The population in Lauvøya in 2012 consisted exclusively of the released individuals from Leka and Vega. between the two groups and there was no evidence for any differ-

| DISCUSS ION
We quantified the heritable genetic variation and covariation of A particular strength of our study was that we applied bivariate GGAMs jointly with a common garden experimental design (de Villemereuil et al., 2016;Muff et al., 2019). This allowed us to estimate additive genetic (co-)variance parameters separately in different genetic groups that were genetically connected within an admixed population, while controlling for potential biases in estimates caused by prior environmental differences and potential immigration from adjacent populations. ME did not appear to influence estimates of V A or cov A in the focal traits.
The ability for evolution of BMR independent of M b may be particularly important for population persistence under environmental change. Previous studies have suggested that the genetic correlation between BMR and M b can be close to 0 or 1 in passerines (Bushuev et al., 2012;Nilsson et al., 2009). Consequently, the corresponding reductions in evolutionary potential when conditioning BMR and M b were effectively 0% or close to 100% (Bushuev et al., 2012;Nilsson et al., 2009;Tieleman et al., 2009), whereas three studies have reported r A ranging from 0.4-0.9, corresponding to 16-84% reduction due to conditioning (Mathot et al., 2013;Rønning et al., 2007;Tieleman et al., 2009). In the present study, we found 42% and 57% reduction in evolutionary potentials in Leka and Vega, respectively.
Hence, after accounting for their common additive genetic basis, there was still additive genetic variance in both traits in both populations. That indicates that there is potential for their independent evolution, for example under directional selection on BMR and stabilizing selection on M b or selection in opposing directions, although the rate of the independent evolution may be somewhat limited.
Estimated b A 's were relatively high (b A(Leka) = 0.96 and b A(Vega) = 1.08), although highly uncertain. Thus, there was no evidence for any difference in b A from the b = ⅔ or ¾ 'laws' that have been the common view (Careau & Glazier, 2022;Glazier, 2005). While (Careau & Glazier, 2022) found b P and b R to be lower than b A , and ascribe the low estimates partly to ME, we found b R to be higher than b A in both groups, and b A > b P in Leka whereas b A < b P in Vega. This may suggest that some environmental conditions are important for the allometric relationship between BMR and M b , and these conditions may differ between the two populations. But again, the uncertainty in estimates makes those conclusions highly speculative.
There was a tendency for differences between the populations in genetic covariance and correlation between the traits, but the uncertainties in estimates were too large for a clear assessment. Note  Phillips et al., 2001). The sizes of our study populations were both relatively small and variable prior to our study (annual census population sizes during 2002: N Leka > 89 and N Vega > 102 [Kvalnes et al., 2017), thus genetic drift may have influenced population Gmatrices (Phillips et al., 2001). Furthermore, Vega had a higher increase of unknown individuals than Leka, which may indicate higher immigration from a somewhat genetically divergent gene pool, and also contribute to increased genetic diversity and changes in the Gmatrix (Guillaume & Whitlock, 2007). However, both drift and gene flow should have similar effects across all loci; hence, the population differences in evolutionary potentials should be similar across traits.
Our results indicate, however, that evolutionary potentials of BMR and M b potentially may have been differently affected by evolutionary forces in these two populations. One obvious difference in evolutionary histories of the Leka and Vega populations is the artificial selection experiment on body size (for large size on Leka and small size on Vega) that was conducted over 4 years and ended 7 years prior to the start of the current study (Boratyński et al., 2013). Although we have previously shown that body size rapidly returned to pre-experimental means phenotypically, we know that body size and body mass are genetically correlated (Araya-Ajoy et al., 2019;Jensen et al., 2003) and can therefore hypothesize that the strong selection on body size in the recent past may have influenced Gmatrices for BMR and M b differently in the two populations. Direct and indirect selection target loci (and loci in linkage disequilibrium with those) that are causal to the trait under selection and is thus expected to reduce V A , although selection alone will probably not substantially change genetic variation in traits that are determined by a large number of loci (Bulmer, 1971).
Consequently, while we compared components of the group-specific Gmatrices for BMR and M b and found only weak tendencies for any differences ( Table 2), several processes may have occurred in different strengths in these populations and caused the group-specific Gmatrices to diverge, potentially resulting in different future evolutionary trajectories even under similar selection pressures.

| Measurement error considerations
We did not have statistical power to estimate ME directly, due to lack of within-session repeated measures, but prior specification of its contribution to the variance using the mev-argument in MCMCglmm show that our estimates of fixed effects as well as additive genetic (co)variances were little affected by ME variances up to 40% in BMR and 15% in M b . Reassuringly, when increasing V ME , the error largely appeared to be absorbed in the residual variance and affected the identifiability of the ID variance. Hence, the estimates of interest therefore remained little affected (Table S5.3 and Figure   S5.2 in Appendix S1). This finding suggests that our estimates of V A in both BMR and M b as well as their cov A and quantitative genetic parameters based on these estimates are robust and approximately unbiased by ME for both traits. Moreover, the discrepancy between conclusions regarding evolutionary potential based on heritability and evolvability (h 2 lower, whereas I A higher, of BMR than of M b ) highlights the importance of evaluating their specific suitability, for example by evaluating how the two measures may be biased by ME.
Our inability to estimate the true ME means any potential contribution of ME to the phenotypic variance produces a downward bias in our h 2 estimates, whereas I A is presumably unbiased by ME (Ponzi et al., 2018). Thus, I A is likely to better reflect evolutionary potentials of our focal traits in the presence of ME.

| CON CLUDING REMARK S
Application of GGAM, concomitant with a common garden approach, allowed us to disentangle genetic from environmental effects on BMR and M b in two natural populations of house sparrows.
Differences in mean breeding values and local environmental effects between the two populations were negligible, whereas there were weak tendencies for differences in evolutionary potential of BMR and M b . However, conditioning the traits on each other removed these differences. In general, our results indicate substantial evolutionary potential of BMR in natural populations, indicating that there is potential for responding to changing selection on BMR, induced by, for example, environmental change, but that the evolutionary responses may be population-specific. While studies on a larger number of populations and species are needed to assess generality, these findings suggest potential for intraspecific variation to influence species-level responses to climate change.

ACK N O WLE D G E M ENTS
We thank two anonymous reviewers for their very constructive comments on the manuscript. We also thank the farmers of Lauvøya, Leka and Vega, whose hospitality made this study possible. Finally, we thank fieldworkers for their contribution in the field work, and

CO N FLI C T O F I NTER E S T S TATEM ENT
The authors have no conflict of interest to declare.