The Society for Integrative and Comparative Biology
Artificial Selection on Metabolic Rates and Related Traits in Rodents1
ek1
apo2
1 Institute of Biology, University of Bia
ystok, 15-950 Biaystok,
2 Institute for Genetics and Animal Breeding, Polish Academy of Sciences, 05-552 Wólka Kosowska, Poland
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SYNOPSIS |
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Artificial selection experiments are potentially powerful, yet under-utilized tool of evolutionary and physiological ecology. Here we analyze and review three important aspects of such experiments. First, we consider the effects of instrumental measurement errors and random fluctuations of body mass on the total phenotypic variation. We illustrate this with the analysis of measurements of oxygen consumption in an open-flow respirometry set-ups. We conclude that measurement errors and fluctuations of body mass are likely to reduce the repeatability of oxygen consumption by about one third. Using published estimates of repeatability of metabolic rates we also showed that it does not tend to decline with increasing time between measurements. Second, we review data on narrow sense heritability (h2) of metabolic rates in mammals. The results are equivocal: many studies report very low (
0.1) h2, whereas some recent studies (including our own estimates of h2 in laboratory mice, obtained by means of parent-offspring regression) report significant h2 
0.4. Finally, we discuss consequences of the lack of replicated lines in artificial selection experiments. We focus on the confounding effect of genetic drift on statistical inferences related to primary (selected) and secondary (correlated) traits, in the absence of replications. We review literature data and analyze them following the guidelines formulated by Henderson (1989
, 1997). We conclude that most results obtained in unreplicated experiments are probably robust enough to ascribe them to the effect of selection, rather than genetic drift. However, Henderson's guidelines by no means should be treated as a legitimate substitute of the analysis of variance, based on replicated lines. |
INTRODUCTION |
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Physiological ecology and studies on the evolution of physiological traits have been largely dominated by comparative method (e.g., McNab, 2002
). One of the major benefits of this method is that it allows taking advantage of a large, between-species variation of analyzed traits, which greatly increases the power of statistical analyses. Although comparative studies are very informative, they have many, well recognized limitations (Harvey and Pagel, 1991). Among other, comparative studies are correlative in nature, and therefore, their results may not reflect causative relations (Garland and Adolph, 1994b). Comparative analysis is also likely to be confounded by difficult to control effects, such as phylogenetic relatedness (Garland and Díaz-Uriarte, 1999). Above all, however, because natural selection acts within- rather then between species, comparative method is usually applied at the level of biological organization, which is far removed from the action of immediate, evolutionary processes. For this reason, in recent decades there was a growing awareness of the need to study individual variation within species (Garland and Carter, 1994a; Feder et al., 2000). Such studies allow one to manipulate the traits in a manner, which is likely to reveal additive genetic associations and their effects on fitness (Hayes and Garland, 1995; Hayes and O'Connor, 1999). However, the analyses on intra-individual variation are also burdened with several pitfalls. Within species variation is small, and therefore prone to the effects of many confounding, and often unrecognizable factors. This has largely contributed to sometimes-contradictory results. They are well exemplified by equivocal conclusions of studies on within- species relations between Basal Metabolic Rate (BMR) and metabolic rates, either summit, or sustained over longer periods of time, usually measured in the filed (for review see Hayes and Garland, 1995; Koteja, 2000; Rezende et al., 2004).
One of the remedies likely to improve the efficacy of within- individual studies is to conduct them in well controlled, laboratory conditions. The major advantage of laboratory studies is that they allow for a meaningful analysis of the strength of selection and genetic architecture of the traits. Simulation of natural selection by means of artificial selection has a long tradition in evolutionary thinking. Recently, selection experiments carried on easily manageable laboratory populations of fruitflies (D. melanogaster), provided most of the experimental tests for life history theory (Rose and Mueller, 2005). In contrast, artificial selection still remains an under-utilized tool in ecology and organismal biology (Garland, 2003; Conner, 2003; Bradley and Folk, 2004). In particular, although laboratory strains of rodents were subjects of much of biomedical research, there are only few selection studies aimed to unravel mechanisms underlying the evolution of key features of mammalian behavior and physiology, which are important in ecological and evolutionary context (e.g., Ksiek et al., 2004; for review see Garland, 2003).
The reasons for unpopularity of laboratory selection studies on mammals, directly related to their evolutionary and physiological ecology, seems two-fold. First, many students seem unaware of the research potential offered by the selection experiments. Second, some physiological ecologists simply consider laboratory populations and laboratory settings totally irrelevant to natural situations. Although to our knowledge, there are no hard evidences in support of such claims, there indeed exist a number difficulties inherent in the design, conductance, and the interpretation of results of selection experiments. Here we review three important aspects of selection experiments on the traits related to energy management in small mammals.
First, we shall discuss the effect of measurement errors and repeatability of selected traits on the efficacy of selection. Any selection study requires hundreds, if not thousands of measurements on individual animals (Falconer and Mackay, 1996). Massive character of measurements is likely to compromise their precision. It is therefore essential to know to what extend measurement errors may affect individual consistency (repeatability) of measured variables. High repeatability of selected traits is crucial for the success of artificial selection, because to large extend it determines their response to selection (Dohm et al., 2001; Labocha et al., 2004). Second, there is much controversy whether traits related to mammalian energetics are heritable (e.g., Nespolo et al., 2003; Sadowska et al., 2005). We shall therefore review available information on heritability of metabolic rates to learn whether selection experiments are actually feasible. Finally, a massive effort required to conduct selection experiments has repeatedly forced experimenters to restrict the experiments to a single pair of unreplicated lines (e.g., Koch and Britton, 2001; Ksiek et al., 2004). We shall therefore discuss consequences of the lack of replication for the conclusions reached in such experiments.
We would like to stress that even though we primarily focus on metabolic rates in rodents, our analysis of measurement errors, heritability and experimental design is applicable to studies on most quantitative traits in other groups of animals.
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THE EFFECT OF MEASUREMENT ERRORS ON REPEATABILITY OF METABOLIC RATES |
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Repeatability is a measure of individual's consistency over time. It is quantified either as an intraclass correlation coefficient (which is the proportion of total variance in multiple measurements, that can be attributed to the differences among individuals) or as a product-moment correlation coefficient between measurements of individual's performance (Falconer and Mackay, 1996
; for review see Hayes and Jenkins, 1997; Dohm, 2002). With some restrictions (Dohm, 2002) repeatability can be considered as the approximate estimate of the upper limit of heritability, that is, the proportion of variance that is due to genetic sources (Falconer and Mackay, 1996; Lynch and Walsh, 1998). When repeatability is low (not significantly different from 0) the measured trait is unlikely to respond to selection and most probably is also not correlated with other traits of interest.
Published estimates of repeatabilities of metabolic rates suggest that their values are often considerably lower than 1 (Fig. 1A). The question rises, however, how much of the apparent, within individual variation in metabolic rates is a consequence of unavoidable measurement errors, which result in underestimation of the true, biologically meaningful repeatability. To estimate their effects on individual variation we used the principle of propagation of errors (Bevington, 1969). According to this, the error variance of any measurement is the sum of products of variances of parameters determining the measured variable and their partial derivatives with respect to that variable, plus the respective interaction terms. Here we illustrate the application of propagation of errors principle with analysis of effects of two major instrumental determinants of oxygen consumption measured in open flow systems: the airflow rate, and fractional concentration of oxygen.
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= maximum metabolic rate elicited by exercise; 
= maximum metabolic rate elicited by cold; BMR = basal metabolic rate; RMR = resting metabolic rate; Amax = maximum energy assimilation rateConsider
calculated as
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(equation 4a of Withers, 1977), where 
and 
are the fractional concentrations of oxygen in the air entering and leaving metabolic chamber, respectively, 
is the airflow rate. The error variance of oxygen consumption (
) is the sum of products of partial derivatives of Whiter's equation (4a) with respect to and and their variances, plus the covariation term:
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For the sake of simplicity assume that the variances of and (i.e., 
and 
) are independent, and therefore the covariation term is equal to zero. Assume further that = 500 ml/min, = 0.2095, = 0.2075 (i.e., they take values yielding = 76 ml/hr, which is well within the range of oxygen consumption of a resting, small mammal). Unfortunately, to our knowledge credible estimates of and are not available. To make further progress we therefore assumed that they fall within the range of instrumental precision estimates reported by manufacturers of flow meters and oxygen analyzers. The resulting values of 
e are depicted in Figure 2. It is apparent that unless measurements of oxygen concentration and air flow rate are exceedingly inaccurate (i.e., 
> 0.005% and > 15 ml/min), e is unlikely to exceed 2.5 ml O2/hr.
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To gain the idea of the magnitude of effect of the measurement error, let us partition the observed variance of oxygen consumption as follows:
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where 
is the total phenotypic variance unrelated to measurement error. Let us illustrate the effect of e with data obtained in our selection experiment (Ksiek et al., 2004), in which we divergently selected laboratory mice for high and low basal metabolic rate (BMR). For the high, and low selected line SD of mass-corrected BMR was equal to 4.2 ml and 3.5 ml O2/hr, respectively (Table 1). In case of our study e = 1.52 ml/hr, which therefore accounted for about 13% and 19% of BMR variance in the high and low selected line, repectively.
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Since repeatability can be estimated as the correlation between subsequent measurements (x1 and x2), it follows from equation (3) and equation (A1) in Ricklefs et al. (1996)
that the effect of measurement error on repeatability of metabolic rates can be modeled as:
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where 
is the observed correlation between x1 and x2, whereas 
is the correlation free from the confounding effects of the measurement errors. Assuming e = 1.52 ml/h we applied equation (4) to evaluate the effect of the measurement error on the repeatability of BMR in our selection study (Ksiek et al., 2004). The resulting ratio of 
to is 0.85. Our estimates are probably close to the lower limit of true magnitude of instrumental measurement errors. So it is likely that in most other studies they account for at least 15–20% of the total variance of metabolic rates.
Another important determinant of repeatability of metabolic rates is body mass (BM). In Figure 1A we plotted published values of repeatabilities calculated for whole-BM metabolism against BM- corrected repetabilities from the same studies. Almost all values of whole-BM repeatabilities fall above diagonal line, which indicates that they tend to be higher than those, from BM-corrected estimates. This is further corroborated by statistical significance (t = 5.1, n = 11, P < 0.001) of paired t-test applied to the repeatabilities depicted in Figure 1A.
The observed systematic difference between whole-BM and BM-corrected repeatabilities is due to two effects. First, metabolic rate is a function of BM, and therefore high values of the whole-BM repeatabilities simply reflect the differences in body mass of individual animals. Second, although animals can be weighed with a great precision, it is unlikely that BM estimates are free from the effect of random fluctuations of body mass. Such fluctuations may, for example, arise from the erratic loss of mass due to urination or defecation, and are therefore totally unrelated to the relationship between BM and metabolic rates. Consider following example, illustrating that even minor fluctuations in BM (BM) may have a strong effect on the repeatability of metabolic rates. When one calculates residual with respect to BM, one adds error of the magnitude ßBM, where ß is the slope of the regression of on BM. To account for this effect, equation (4) can be rearranged as follows:
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In the case of our estimates of repeatability of BMR (Ksiek et al., 2004) ß1 = 1.16 and ß2 = 1.80. Assuming BM = 1 g, the ratio of 
to calculated with respect to the effect of BM is 0.85. Thus, the effect of random fluctuations of body mass of the magnitude of 1 g on estimates of repeatability is as strong, as the effect of instrumental uncertainties. This further suggests that the joint effect of BM and e may reduce such estimates by about one third.
Yet another concern related to the estimates of repeatability of metabolic rates is that their values may tend to decline with increasing time between measurements (e.g., Chappell et al., 1995). This is not supported by available data (Figure 1B and 1C). Both whole-BM and BM-corrected estimates of repeatabilities are surprisingly independent of the time scale of approximately 90 days (P = 0.18, n = 15; and P = 0.48, n = 16; respectively). Our analysis, though not very formal and limited in scope, suggests that repeatability of metabolic rates does not appreciably decline over a period of time comprising a considerable part of lifetime of small mammals. This is especially important for selection experiments, when measurements applied as the selection criteria are sometimes weeks, if not months apart from mating of animals.
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HERITABILITY OF METABOLIC RATES |
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Any trait can be subjected to natural or artificial selection if and only if there exits a heritable variation. Most of this variation is usually determined by the additive effect of many genes, which is quantified as additive genetic variance (VA, Falconer and Mackay, 1996
). The ratio of VA to total phenotypic variance Vp is termed narrow sense heritability (h2). Thus, h2 provides information about the magnitude of heritable variation associated with a given trait, and therefore, the potential of its response to selection (Roff, 1997).
The earliest studies found non-significantly different from zero estimates of h2 of BMR and related traits (Lacy and Lynch, 1979; Lynch and Sulzbach, 1984; Lynch, 1986). These very low estimates of h2 were generally explained in terms the "fundamental theorem of natural selection," which predicts that the traits closely and directionally related to fitness will exhibit low heritabilities (Fisher, 1958). Lynch (1986) attributed the apparent lack of additive, genetic variance to strong directional selection for high metabolic rates, which resulted in exhaustion of genetic variance in the evolutionary history of mammals. This has led her to conclusion that "in the house mice, physiological traits are not sufficiently heritable to respond to selection" (Lynch, 1986). However, this is only in partial agreement with the results of a number of more recent studies summarized in Table 1.
We estimated heritability of BMR in two subsequent, randomly bred generations of outbred Swiss-Webster in the base population, from which we derived our selected lines. We measured BMR as described in Ksiek et al. (2004) and analyzed h2 by means of parent-offspring regression (Fig. 3A). We then doubled the obtained coefficient of regression of male offspring on father's metabolic rates (Falconer and Mackay, 1996). We obtained quite high estimate of h2 = 0.38, albeit barely statistically significant (P < 0.02), due to a large SE.
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By means of the same approach we have also recently estimated h2 of
elicited by 5 mins swimming in 23°C water in another population of Swiss-Webster mice, giving rise to the replicated lines, selected for high (Konarzewski, unpublished data). The obtained h2 = 0.40 was statistically significant (P = 0.02, Fig. 3B).
Our estimates of h2 of both BMR and are in good agreement with the part of results summarized in Table 1. Estimates of heritabilities may vary between populations, environments, and applied statistical methods (Lynch and Walsh, 1998). Labocha et al. (2004) reported low correlation between BMR of full sib families of the bank vole (Clethrionomys glareolus), which implied its low heritability. In contrast, subsequent studies carried out by the same research group (Sadowska et al., 2005) yielded highly significant h2 of BMR for the same population (Table 1). Likewise, h2 of metabolic traits in leaf-eared mouse (Phyllotis darwini) were low and non-significant (Bacigalupe et al., 2004), whereas most recent study (Nespolo, personal communication) detected highly significant h2 of maximum metabolic rate in this species. Also, Lacy and Lynch (1979) reported non-significant h2 of BMR in genetically heterogeneous stock of laboratory mice, whereas Lynch and Sulzbach (1984) obtained significant h2 of BMR in females of the crosses of inbred mouse strains (Table 1). A comparison of results reported by Labocha et al. (2004) and Sadowska et al. (2005) shows that the power of such estimates, especially those, based on animal models of partitioning of genetic variance, are very much dependent on the number of included animals (Lynch and Walsh, 1998). It is also important to note that our demonstration of potentially significant effects of measurement errors on repeatability is applicable to estimates of h2. In our view such effects are likely to contribute to large standard errors commonly found in estimates of h2 (Table 1).
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ON THE SIGNIFICANCE OF REPLICATION |
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The aim of every selection experiment is to change the frequency of allels affecting selected trait. However, in small populations, such as those subjected to selection experiments, values of traits may vary stochastically even without directional selection. This phenomenon, called genetic drift is due to random fixation of allels. The major process determining the rate of their fixation is inbreeding, that is, mating of individuals related to each other by common ancestry. Inbreeding is quantified as so-called coefficient of inbreeding (F), taking values between 0 and 1 (Falconer and Mackay, 1996
). F reflects the probability of mating of close relatives, which in turn affects changes in mean phenotypic values of traits.
Since values of traits may vary due to genetic drift alone, it is essential to estimate to what extend its effect can confound the results of a given selection experiment. Consider a set of lines of organisms originating from a large, outbred, base population. Let as assume that these lines are not subjected to any intentional selection on the trait if interest x. The difference between any pair of lines is therefore solely due to random effects. For simplicity we also assume that this difference can be ascribed to additive genes with no sampling error. Under slow inbreeding (that is, when F does not change appreciably between generations) within- (
) and between-lines variance (
) of the trait x can be approximated as
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where 
is the additive, genetic variance of the trait x in the base population (Table 15.1 in Falconer and Mackay, 1996). Now consider two sets of lines, as in a typical selection experiment, but again, not subjected to any intentional selection. It is reasonable to assume, that the variance between the lines within each set is equal . Because are independent, the expected variance of differences in a trait x between the two sets of lines can be expressed as
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with a mean equal to zero (Henderson, 1997). Since
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where 
is the phenotypic variance of the trait x, is equal to 
. Thus, the expected standard deviation of the mean difference between two lines, each belonging to a different set is
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where h is the square root of narrow sense heritability. On the other hand, standard error of the difference between means of the trait x in the particular pair of lines under comparison is
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(Sokal and Rohlf, 1995). For simplicity, let us assume that n1 = n2 = n, where n is the number of families within each line. Since both lines originate from the same base population it is also reasonable to assume that they share F value. Thus, from equations (7), (9) and (11), 
can be expressed as:
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Let us express the between line difference 
1 – 2 due to genetic drift as k multiples of the expected standard deviation given by equation (10), that is
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Statistical significance of 1 – 2 due to genetic drift can therefore be tested by examining the value of following ratio with t distribution:
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In Figure 4 we illustrate possible, spurious effect of genetic drift on the statistical comparison of the difference between two hypothetical, selected lines. Here we assumed that 1 – 2 equals one standard deviation (i.e., k = 1). The difference of such magnitude can be expected in one out of six comparisons. From the inspection of Figure 4 it is clear that even when F is as low as 0.1, genetic drift alone can result in values of t statistics significant at P = 0.05. As inbreeding increases in the course of selection, genetic drift is likely to produce between-line differences, which are significant at much higher probability levels.
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For this reason, the most appropriate way to control for the confounding effect of genetic drift is to replicate the artificial selection experiments. The efficacy of replication can be best illustrated by somewhat simplified analysis of the partitioning of variance in replicated experiments. Modifying slightly Henderson's (1989)
notation, the total variance related to selection (
) can be partitioned as follows:
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where 
is the variance related to directional, artificial selection on the trait x; 
is the variance related to genetic drift; and 
is the sum of remaining components of the variance, primarily related to the variance within families. On the other hand, the variance associated with replicated lines (nested within the effect of selection) can be partitioned as 
. Thus, the most powerful way to statistically control for the spurious effect of random drift in the selection experiment is to apply the F test with the mean square (MS) computed from as the numerator (with df = 1) and MS computed from 
as denominator (with df = 2(k – 1), where k is the number of replicated lines, Henderson, 1989).
Despite undeniable efficacy of replication as the means for controlling random effects, many selection experiments aimed to select physiological traits have not been replicated (e.g., Koch and Britton, 2001; Ksiek et al., 2004). The major reason for the lack of replication in such studies is time and resource limitation. For example, in our unreplicated, divergent selection on BMR in mice we are able to obtain satisfactory measurements of BMR in 8–9 animals a day. It takes us 4–6 weeks to collect the measurements on the sufficient number of animals to carry out the selection in just one pair of selected lines. The maintenance of another 3–4 replicates is unfeasible, at least with the use of selection criteria adopted in our study. It is therefore important to learn whether the results of unreplicated experiments are trustworthy. In Table 2 and 3 we analyzed the results of 5 unreplicated experiments on traits related to metabolic rates in laboratory rodents. Following Henderson's (1989) suggestion, we expressed the magnitude of separation of the high and low or control lines with respect to the selected trait, as the multiples of the standard phenotypic deviation:
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where SDh and SDl are standard deviations of the trait x, for the high and low selected line, respectively. The magnitude of separation of the primary selected traits ranged from d = 0.80 to d = 6.20. Except for the least successful selection study by Nagai et al. (1995) the remaining, between-line differences were greater than 2 SDs and fell outside 95% confidence limits of the normal distribution. It is therefore probably safe to conclude that they are due to the applied selection protocols, rather than genetic drift.
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However, the aim of virtually all selection studies is not only to achieve a high degree of between-line separation in the selected trait, but also to demonstrate correlated responses in other traits, not subjected to a direct selection. Indeed, the results of all selection studies listed in Table 2 and 3 were subsequently used to infer the associations between primary, selected traits and secondary (unselected) traits. Unfortunately, in the case of such traits, the reasoning behind equation (10) still holds. Therefore, the unknown part of between-line difference in any unselected trait y must be ascribed to genetic drift. Fortunately, the magnitude of the effect of genetic drift on the association between x and y can be estimated with the fair amount of precision (Henderson, 1989
, 1997). Although such estimates by no means substitute the analysis of variance based on replicated lines, the guidelines offered by Henderson greatly aid the interpretation of unreplicated, between-line differences in non-selected characters. Henderson (1997) proposed to evaluate the effect of drift, based on the following, generalized form of equation 6:
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where 
is genetic correlation between x and y. He formulated a set of equations for the estimation of the 95% confidence intervals (CI) of the between-line differences in new characters, resulting from genetic drift and sampling error. To estimate the 95% CI of between-line differences in the secondary traits analyzed in studies listed in Table 2 we used equation 16 from Henderson (1997):
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The magnitude of separation of the majority of secondary traits listed in Table 3 places their values outside 95% CIs computed with Henderson's equation. However, our analysis also exposes the danger of committing type II statistical errors in the correlation analysis and ANOVA models of unreplicated studies. For example, between-line differences in lifespan were reported by Nagai et al. (1995) as statistically significant, which prompted them to ascribe these differences to genetic correlation. However, small magnitude of the separation expressed as dy makes this conclusion questionable. Also, even though between-line difference in maximum metabolic rate elicited by swimming is highly statistically significant in our selection experiment (P = 0.006), we refrain from concluding that it is genetically correlated with BMR, because dy for this trait is only 0.59 (Table 3).
It is also important to note that the magnitude of 95% CIs strongly depend on h2 (equation 17), which is especially important in the light of controversy over the heritability of metabolic traits. For this reason, in Table 3 we report their 95% CIs assuming low (h2 = 0.1) and fairly high (h2 = 0.4) heritability. In our earlier study (Konarzewski et al., 1997), we have assumed that h2 of elicited by cold exposure in Heliox atmosphere is close to 0.1, which permitted us to suggest the existence of a strong, genetic correlation between and swim-stress induced analgesia (SSIA). However, if h2 of elicited by cold exposure is close to 0.4, then between-line divergence in reported in Konarzewski et al. (1997) can no longer be considered as the indication of strong genetic correlation (Table 3).
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FINAL REMARKS |
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Artificial selection experiments have already proven to be extremely informative and useful tool in studies on energetics of mammals (e.g., Swallow et al., 1998a
, b; for review see Garland, 2003). In the near future they will most probably contribute to resolving some long-standing controversies in evolutionary and physiological ecology. For example, they will most likely serve as decisive test of the existence of genetic correlations between the measures of energy expenditures (Hayes and Garland, 1995; Sadowska et al., 2005).
We close with two pieces of advice for planning and conducting artificial experiments on metabolic traits. First, it is advisable to estimate the effect of measurement errors on the repeatability of selected trait(s) along the lines outlined in our review. This will help to optimize measurement procedures with respect to unavoidable trade-off between precision and numbers of the measurements. Second, whenever feasible, replicated experiment should be carried out. Although the use of guidelines formulated Henderson (1989, 1997) greatly reduce the risk of committing type II error, the power of such inference is unlikely to match the power of analysis of variance, based on the replicated lines.
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ACKNOWLEDGMENTS |
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M.K. is thankful to John Swallow and Ted Garland for their invitation to participate in Annual SICB Meeting held in New Orleans. The authors thank P. Koteja and two anonymous reviewers for criticism and comments. We are also greatly indebted to B. Lewo
czuk, M. Lewoc, and our numerous students for technical assistance and patience in carrying out the selection experiment. This study was supported by Polish Committee for Scientific Research (KBN) grants PB 0197/P04/05/09 and 3P04C 002 22 to M. K.
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FOOTNOTES |
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1 From the Symposium Selection Experiments as a Tool in Evolutionary and Comparative Physiology: Insights into Complex Traits presented at the Annual Meeting of the Society for Integrative and Comparative Biology, 5–9 January 2004, at New Orleans, Louisiana.
2 E-mail: marekk{at}uwb.edu.pl
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References |
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