Insectivore life histories: further evidence against an optimum body size for mammals

Functional Ecology 1999 ORIGINAL ARTICLE OA 000 EN Insectivore life histories: further evidence against an optimum body size for mammals M. R. E. SYMONDS University Museum of Zoology, Downing Street, Cambridge CB2 3EJ, UK Summary 1. This study tests a model of the relationship of body mass to reproductive power (the rate of conversion of energy from the environment to an organism s offspring). Specifically tested is the prediction that the regression of life-history variables on body size will change slope and sign about an optimum body mass of 100 g. 2. Life-history data from the mammalian order Insectivora have been collated and analysed using a phylogenetic comparative method to test this prediction. 3. The analyses showed little evidence for significant changes in slope or sign around 100 g body mass, or other possible optimal body masses, contradicting the predictions of the model. These findings agree with those of similar analyses on life-history variables of bats. Key-words: Body mass, comparative method, Insectivora, phylogeny, reproductive power Functional Ecology (1999) Ecological Society Introduction The study of life histories of mammals is a well-established field of evolutionary biology (Boyce 1988; Read & Harvey 1989). In particular, research has often focused on the tight link between life-history parameters and body size (Western 1979; Calder 1984). Traditionally, such studies have described the link in the form of a simple allometric equation. However, a model by Brown, Marquet & Taper (1993) has suggested that the relationship may be more complicated than this. Brown et al. (1993) defined fitness as the reproductive power of an organism. The reproductive power was in turn defined as the rate of conversion of energy into offspring in a mature organism. This process involves two steps: the acquisition of energy from the environment, and the transfer of this energy to the offspring. Brown et al. (1993) based their model (henceforth known as the BMT model) on standard allometric equations for these two processes: acquisition of energy scaling to the 0 75 power, and transfer of energy to offspring scaling to the 0 25 power. This means that as the body sizes of mammalian species increase, so do the rates of acquisition of energy. In contrast, the rates of transfer of energy to offspring decrease with increasing body size. Therefore, Brown et al. argued that there is a trade-off between these two limiting factors resulting in an optimum size at which reproductive power (and hence fitness) is maximized. In their paper they calculated this optimal body mass to be approximately 100 g for mammals. They also used this prediction to account for the right-skewed frequency distribution of mammalian body masses, a longstanding unexplained phenomenon (see Purvis & Harvey 1997). The BMT model has been criticized on several theoretical grounds (Blackburn & Gaston 1996; Kozlowski 1996; Perrin 1998). These include the assumption that transfer of energy to offspring scales as mass (M) 0 25. As both Kozlowski (1996) and Perrin (1998) have pointed out, this would mean that a mouse produces more milk per day than a cow or a whale. Obviously this is unrealistic, although it is interesting to note that the energetic content of mammalian milk does scale to birth mass raised to the power 0 28 (Payne & Wheeler 1968). Another criticism of the BMT model is that it uses assumptions about body size and metabolism of individuals to make inferences about the optimum body size of species. This point is discussed, along with other problems and suggestions for modifications to the BMT model, by Chown & Gaston (1997). Finally, the BMT model has also been criticized from empirical evidence (Jones & Purvis 1997). In terms of life-history analyses, Brown et al. (1993) make an easily testable prediction: the regressions of life-history variables (including reproductive power) on body mass will have different slopes and signs either side of the optimum body mass. Some life-history variables will be minimized at an optimal body mass (gestation length, age at weaning, age at sexual maturity), while others will be maximized (maximum life span, litter size, number of litters per year, annual fecundity, neonate mass and litter mass). Brown et al. offer some empirical evidence to support 508

509 Body mass and reproductive power their idea, but their paper called for more tests on taxa of small mammals. Jones & Purvis (1997) were the first to carry out such work using data from bats. Their analyses showed that there was no support for the idea that the regressions of life histories on body mass change sign in bats, either at 100 g or any other body size. This paper tests Brown et al. s (1993) prediction using data from insectivores. Insectivores, like bats, are an ideal taxon for this work in that they cover a range of small body sizes, from approximately 2 g to 1 kg. Using a comparative method to remove the effect of phylogeny (Harvey & Pagel 1991), this paper tests whether in insectivores, life histories and reproductive power scale with body mass as modelled by Brown et al. (1993). Because this paper uses much of Jones & Purvis s (1997) methodology, the analyses and results are presented in a similar format to that used by those authors to provide a closely complementary study. Materials and methods Life-history data from the mammalian order Insectivora were collected from the literature. The data set, and the sources and methodological regimen employed in its compilation, will be published elsewhere (Symonds, in press). Although data from 63 species of insectivores were collected, complete lifehistory data do not exist for many species. Therefore, the actual number of species values for most variables is considerably less than 63. The variables are largely the same as those used by Jones & Purvis (1997) in their study, with the exception of mass at weaning, for which there are insufficient data for insectivores. The variables are (with number of species included in brackets): A, average adult body mass (63); B, average neonatal mass (38); C, age at weaning (38); D, litter size (60); E, gestation length (35); F, maximum life span (29); G, age at sexual maturity (26); H, number of litters per year (30); I, litter mass (D B) (38); J, annual fecundity (number of female offspring born per adult offspring per year assuming a sex ratio at birth of 0 5) ((D H)/(2) (30); K, prenatal maternal investment rate (I/E) (30); L, postnatal maternal investment rate ((A B)/C) (33); M, overall maternal investment rate ((D A)/(E + C)) (30). The last three variables are taken to represent reproductive power (Brown et al. 1993), in other words, the rate at which females transfer energy into offspring. For these variables, it was only possible to achieve estimates by the equations given above. Owing to the lack of data on mass at weaning, further estimation of these variables (as made in Jones & Purvis 1997) was not possible. It should be noted therefore that in the case of variables L and M, adult body mass is assumed to be equivalent or proportional to body mass at weaning. While it seems that for insectivores this may be likely, if there were differences in the extent of postweaning growth between different species (especially between large vs small species), this may affect the outcome of the analysis. Data from the Soricidae, for example, indicate that there may be some variation in the relationships between mass at weaning and adult body mass (Innes 1994). All data were logarithmically transformed before analysis (Harvey 1982). These include data on litter size, which have not been so transformed in some other analyses (e.g. Read & Harvey 1989) because of the high number of mammalian species that produce singletons. Since this does not apply to insectivores (virtually no species have litter sizes of one), it was decided to transform these data also. Because closely related taxa share characteristics as a result of descent from a common ancestor, they cannot be considered as independent data points in analysis. Therefore, it is necessary to remove the effect of phylogeny (Felsenstein 1985). The data were transformed by an independent contrasts technique of pairwise comparisons (based on Felsenstein 1985) to produce data (standardized independent contrasts) that were independent of phylogeny. This was done using the computer package CAIC (Comparative Analysis by Independent Contrasts) developed by Purvis & Rambaut (1995). This technique requires knowledge of the phylogeny of the group for use in the transformation. The phylogeny used in the analyses is shown in Fig. 1 and comprises the phylogeny of interfamilial relationships produced by Butler (1988), with the intrafamilial phylogenies shown below inserted at the appropriate branches: 1. Erinaceidae: Frost, Wozencraft & Hoffman (1991). 2. Talpidae: Yates & Moore (1990). 3. Tenrecidae: Eisenberg (1981). 4. Chrysochloridae: Bronner (1995). 5. Soricidae: Several phylogenies were combined. Firstly, the two major subfamilies (Crocidurinae and Soricinae) were each assumed to be monophyletic. For the relationships between the genera in the Soricinae, George s (1988) most parsimonious cladogram was used. Additional information, on the positions of Neomys and Cryptotis, was taken from George & Sarich (1994) and Ducommun, Jeanmaire-Besançon & Vogel (1994), respectively. For relationships within the genus Sorex, George s (1988) phylogeny was used with additional information, on the position of S. coronatus and S. cinereus, supplied by Dannelid (1991). For the relationships between the three genera of the Crocidurinae used in the analysis, information was taken from Ducommun et al. (1994). Finally, the relationships within the genus Crocidura were taken from Maddalena & Ruedi (1994) (the position of Crocidura mariquensis is unresolved), with the relationships between the Palearctic species of Crocidura resolved using the

510 M. R. E. Symonds phylogeny produced by Maddalena that is illustrated in McClellan (1994). With all phylogenetic comparative methods it is clearly desirable that the phylogeny used is accurate and known without error (Harvey & Pagel 1991). Since this will rarely, if ever, be the case it is stressed that the results below are predicated on the topology of the phylogeny used. All branches were assigned the same length (= 2). While this is certainly not an accurate reflection of the evolution of the Insectivora, given the lack of true branch length data this is an accepted default procedure (Purvis, Gittleman & Luh 1994) The y-variable contrasts were then regressed against the body mass contrasts, with the regression line forced through the origin (for justification of this procedure see Garland, Harvey & Ives 1992). In order to test the hypothesis that the relationship between reproductive output and body mass will change at an optimum body size, the regression coefficients between the variables for species below 100 g and above 100 g (Brown et al. s 1993 prediction) were calculated. In addition, following Jones & Purvis (1997), two additional possible thresholds were tested: the mean body size ( 155 g) and the median body size (41 5 g). This procedure involved splitting the species into two groups about the threshold under test, and performing the analysis individually on each group data set (similarly splitting the main phylogeny into the two group phylogenies). t-tests were used to test whether the differences in the regression slopes either side of the thresholds were significant (see Zar 1996, p. 355). Because of the possibility that the phylogeny used in the analyses may be inaccurate, ordinary least squares regression analyses were also performed on the untreated species values (i.e. not involving independent contrasts). The tests on optimum thresholds were likewise carried out on these untreated data. In order to test the possibility that none of the three thresholds is correct, two further tests were used as in Jones & Purvis (1997). The average body mass at each node (given by CAIC) and the contrast slope (the y-contrast divided by the body size contrast) at each node were calculated and ranked. Spearman s rank correlation was then used to test whether these two variables were linked. Secondly, runs tests were used on the signs of the contrast slopes, once the average body mass was ranked. This determines whether there is a change of sign at some untested body mass. According to the predictions of Brown et al. s (1993) model, there should be a change from a run of positive values to a run of negative values, or vice versa. Finally, because of the problems of increasing Type I error rates as one performs large numbers of statistical significance tests, it is sometimes recommended that Bonferroni s inequality test be used (Rice 1989). However, the Bonferroni correction is often overly conservative with large numbers of tests, and consequently it may result that no tests appear significant (as was the case with Jones & Purvis 1997). Bonferroni s test was not used in this analysis. Any significant results should therefore be considered to be possible examples of Type I error. Results Fig. 1. The phylogeny of the Insectivora as used in the analyses (see text for details). The regression coefficients of the slopes and the results of the t-tests are shown in Table 1. They show that few life-history variables have significant relationships with body mass after the effect of phylogeny is removed. Of the main variables, maximum life span appears to be significantly linked to body size: larger insectivores seem to have longer lives. Neonatal mass and litter mass are also strongly linked as would be expected. The three measures of reproductive power (maternal investment rates) are also strongly positively linked.

511 Body mass and reproductive power Table 1. Regression coefficients of each life-history variable with body mass for all contrasts, above and below the three tested thresholds (100 g, 155 g and 41 g). The t-values for each of the slope comparisons are also shown. Ns is the number of species for which there are data. Nc is number of contrasts included in the analysis, below and above the threshold value. MI is maternal investment. Significance indicated as follows: * P < 0 05, ** P < 0 01, *** P < 0 001 Variable Ns Nc Slope (SD) Nc 100 g < 100 g > 100 g t Nc 155 g < 155 g > 155 g t Nc 41 g <41g >41g t Neonatal mass 38 36 0 78 (0 049)*** 23/12 0 72 0 65 0 60 25/10 0 74 0 57 0 81 19/16 0 75 0 85 1 92 Age at weaning 38 36 0 00 (0 033) 25/10 0 04 0 03 0 66 27/8 0 00 0 06 1 44 18/17 0 01 0 01 0 91 Litter size 60 55 0 03 (0 051) 37/17 0 05 0 17 0 63 40/14 0 04 0 13 0 37 26/29 0 04 0 02 1 29 Gestation length 35 33 0 04 (0 020) 21/12 0 01 0 01 0 46 23/10 0 02 0 00 0 76 15/17 0 03 0 06 1 62 Maximum life span 29 27 0 20 (0 078)* 18/8 0 23 0 08 0 37 20/6 0 25 0 34 0 49 13/13 0 17 0 19 0 17 Age at sexual maturity 26 24 0 02 (0 173) 14/10 0 34 0 40 0 03 16/8 0 22 0 61 0 63 8/15 0 49 0 03 1 35 Litters per year 30 28 0 00 (0 045) 14/13 0 11 0 07 0 02 16/11 0 09 0 05 1 03 8/19 0 33 0 05 1 49 Litter mass 38 36 0 81 (0 061)*** 23/12 0 69 0 98 1 57 25/10 0 73 0 88 1 25 19/16 0 78 1 04 1 17 Annual fecundity 30 28 0 04 (0 082) 14/13 0 18 0 30 1 01 16/11 0 10 0 25 0 13 8/19 0 41 0 14 1 36 Prenatal MI rate 30 29 0 82 (0 077)*** 19/9 0 78 0 93 1 12 21/7 0 79 0 82 0 90 15/13 0 98 0 99 0 34 Postnatal MI rate 33 31 1 00 (0 028)*** 21/9 1 01 0 93 1 13 23/7 1 03 0 88 1 71 17/13 1 02 0 91 1 88 Overall MI rate 30 29 1 08 (0 065)*** 19/9 0 95 1 41 2 20* 21/7 0 97 1 39 1 38 14/14 1 04 1 38 0 85 There is little evidence for changes in sign around a threshold mass. Eight of the results do show changes in sign; but only two (with maximum life span at 100 g and with gestation length at 41 g) in the predicted direction (positive to negative in the first case, negative to positive in the second case), and none of these differences is significant. Indeed, of all the t- tests between regression slopes, only one appears to be significant (overall maternal investment rate at 100 g). In this case, though, the difference does not involve a change in sign and is not even in the direction predicted by the BMT model. Table 2 shows that none of the runs tests is significant. However, the Spearman s rank correlation coefficient of the relationship between body mass and the contrast slope for litter size is significant. The coefficient is positive though (0 28), implying that litter size is at a minimum at some intermediate body size, and not at a maximum as would agree with the predictions of Brown et al. (1993). Table 3 shows the results obtained from using raw species data (i.e. the effect of phylogeny is not removed). In contrast to the results presented in Table 1, these results indicate strong relationships between body mass, and age at weaning and gestation length. However, most of the t-tests are again not significant, agreeing with those performed on the independent contrasts. Two variables show significant changes in sign (gestation length around 100 g, litter size around 41 g), but are the opposite to the predictions of the BMT model. The other two significant t- tests (overall maternal investment rate at 100 g and 41 g), do not involve changes of sign and are also in the opposite direction to the predictions of the model. Discussion There is little evidence from insectivores that there are changes in the relationship between body mass and reproductive power around a threshold body size as Table 2. Non-parametric tests of the model. Number of runs in the y-contrast data and Spearman s rank correlation coefficients between the contrast slope and average body mass (taken at each node, see method). * is P < 0 05. None of the runs tests was significant Variable Nc No. runs r s Neonatal mass 36 22 0 11 Age at weaning 36 18 0 29 Litter size 55 31 0 28* Gestation length 33 17 0 14 Maximum life span 27 15 0 04 Age at sexual maturity 24 13 0 16 Litters per year 28 13 0 03 Litter mass 36 12 0 16 Annual fecundity 28 13 0 17 Prenatal MI rate 29 10 0 04 Postnatal MI rate 31 5 0 24 Overall MI rate 29 7 0 29

512 M. R. E. Symonds Table 3. Regression coefficients of each life-history variable with body mass, above and below the three tested thresholds (100 g, 155 g and 41 g), for uncorrected (i.e. effect of phylogeny not removed) species values. The t-values for each of the slope comparisons are also shown. Ns is the number of species for which there are data. Significance indicated as follows: * P < 0 05, ** P < 0 01, *** P < 0 001 Variable Ns Slope (SD) Ns 100 g < 100 g > 100 g t Ns 155 g < 155 g > 155 g t Ns 41 g <41g >41g t Neonatal mass 38 0 80 (0 034)*** 25/13 0 84 0 62 1 36 27/11 0 87 0 67 1 00 21/17 0 88 0 71 1 04 Age at weaning 38 0 10 (0 027)** 27/11 0 12 0 13 0 05 29/9 0 09 0 01 0 55 20/18 0 07 0 05 0 21 Litter size 60 0 02 (0 035) 42/18 0 13 0 10 1 42 45/15 0 12 0 04 0 73 28/31 0 25 0 09 2 22* Gestation length 35 0 13 (0 030)*** 22/13 0 16 0 17 2 40* 24/11 0 21 0 10 1 68 16/19 0 16 0 02 1 03 Maximum life span 29 0 20 (0 046)*** 20/9 0 36 0 17 0 92 22/7 0 38 0 48 0 36 14/15 0 31 0 16 0 73 Age at sexual maturity 26 0 12 (0 108) 15/11 0 44 0 50 0 13 17/9 0 28 0 66 0 61 9/17 0 43 0 06 0 95 Litters per year 30 0 08 (0 042) 16/14 0 16 0 12 1 65 18/12 0 15 0 21 1 60 9/21 0 33 0 07 1 39 Litter mass 38 0 76 (0 043)*** 25/13 0 69 0 65 0 18 27/11 0 76 0 73 1 83 21/17 0 82 0 84 0 09 Annual fecundity 30 0 13 (0 063) 16/14 0 30 0 15 1 78 18/12 0 26 0 26 0 13 9/21 0 35 0 13 0 71 Prenatal MI rate 30 0 67 (0 054)*** 20/10 0 70 0 68 0 07 22/8 0 66 0 51 0 43 16/14 0 76 0 71 0 18 Postnatal MI rate 33 0 92 (0 023)*** 23/10 0 92 0 80 0 93 25/8 0 94 0 94 0 34 19/14 0 95 0 88 0 62 Overall MI rate 30 0 91 (0 049)*** 20/10 0 73 1 31 2 74* 22/8 0 74 1 29 1 97 15/15 0 78 1 22 2 23* predicted by Brown et al. (1993). This conclusion agrees with that of Jones & Purvis (1997) in their study of bats. The variables supposedly most associated with reproductive power (maternal investment rates) show no change in sign: in fact, the results often show the opposite of what is predicted (an increase in positive relationship for both prenatal and overall investment rate). In addition, none of the life-history variable contrasts shows a significant change around any threshold. There may be confounding factors that are causing the results not to accord with predictions. First, the phylogeny used in the comparative analysis is likely to contain some errors, which may consequentially affect the results. However, it appears that a small number of errors in phylogenetic reconstruction are not likely to affect results (M. R. E. Symonds, unpublished observations). It is possible that there could be major errors, especially if the Insectivora are not in fact a monophyletic clade as a recent paper has suggested (Stanhope et al. 1998; where the Chrysochloridae and Tenrecidae were separated from the other Insectivora). In defence, the results in Table 3, when phylogeny is not taken into account, largely show support for the same conclusions. That said, the non-independence of species data points means that some of the results obtained may be examples of Type I error (falsely significant results). A second potential confounding factor is that the sample sizes may not be large enough to provide a sufficiently strong test of the life-history predictions of the BMT model. Thirdly, it may be that, as suggested by Jones & Purvis (1997) for bats, insectivores all lie below the optimum body size for mammals. If this were the case, then we would expect to see that the signs of the regressions between life-history variables and body mass for insectivores were the opposite of those that have been found within and between other orders of mammals (see, e.g., Read & Harvey 1989). This situation does not occur. However, unlike in other studies (e.g. Read & Harvey 1989; Purvis & Harvey 1995), age at weaning, litter size, gestation length, age at maturity, litter per year and annual fecundity do not appear to be significantly linked to body size. The results from the runs tests and the Spearman s rank correlation coefficients (with the possible exception of the case of litter size, see Results) indicate that this is not due to a change in sign at any point in the relationship between these variables and body mass, contrary to the BMT model. It is possible that the results are examples of Type II error (falsely non-significant results), especially given concerns over the phylogeny used and the relatively small sample sizes. In conclusion, as with bats (Jones & Purvis 1997), insectivores do not show the relationships between life-history variables and body size that would be predicted by the BMT model of optimum body size for mammals. There are undoubtedly other factors affecting life histories within this order of mammals. These

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