The results of our analyses do not support the MTE. Only primates have a total development time scaling exponent that is consistent with the predictions of the MTE. The other three orders all have total development times that scale with body mass with a substantially shallower exponent of 0.15. The durations of the individual components of total development time—gestation and lactation—also do not scale with body mass in the manner predicted by the MTE. None of the orders has a gestation duration allometry that conforms to the predictions of the hypothesis; they all have gestation duration allometries that are shallower than predicted by the MTE. Only one order—Artiodactyla—has a lactation duration allometry that conforms to the predictions of the MTE. The lactation duration allometries for two of the other orders—Rodentia and Carnivora—are shallower than predicted by the MTE, while the lactation duration allometry for the fourth order—Primates—is steeper than predicted by the MTE.
The results of our analyses are consistent with those obtained by Dubman et al.  and Clauss et al.  but inconsistent with those obtained by Hamilton et al. . There appears to be a simple explanation for this discrepancy: Clauss et al.  found that gestation duration scales with an allometric slope of 0.25 when OLS regression was used but was much shallower when they corrected for phylogenetic autocorrelation. This suggests that the cause of the conflict between our results and those of Hamilton et al.  is likely their decision not to correct for the effects of phylogeny.
To evaluate this potential explanation, we followed Hamilton et al.  and subjected our combined dataset to mixed-effects linear modeling with Order treated as a random taxonomic effect using the lme4 package . The results were more consistent with the predictions of the MTE, especially in the analyses that focused on gestation duration and total development time (gestation duration: 0.20 < b < 0.24; lactation duration: 0.17 < b < 0.24; total development time: 0.24 < b < 0.25). That our dataset yielded results that are more consistent with the predictions of the MTE when analyzed with the method employed by Hamilton et al.  supports the idea that the discrepancy between our main results and Hamilton et al.’s results  is primarily due to the fact that we used full phylogenetic correction and they did not.
There are two reasons for thinking our slopes are more accurate than those reported by Hamilton et al. . One is that, while there has been some debate concerning the relative merits of model I vs model II regression approaches in allometric analyses , it is now generally accepted that phylogenetic correction produces more accurate estimates of allometric slopes ,. As illustrated by Clauss et al. , OLS models may miss underlying patterns, including grade effects where different taxonomic groups have the same slope but different intercepts.
The other reason for thinking our slopes are more accurate than those reported by Hamilton et al.  is an empirical one. We compared the log-likelihoods for the OLS model (λ = 0) and PLGS model (λ = ML), and the log-likelihoods for the former were consistently lower than the log-likelihoods for the latter, and the chi-square comparisons were all significant (p < 0.05). This indicates that the PGLS estimates provide a significantly better data fit than the OLS estimates for our sample, and therefore support the contention that the slopes we obtained are more likely to represent the true allometric slopes for the three maternal energetic investment durations than the slopes reported by Hamilton et al. .
The departure of allometries for total development time and its individual components from the predictions of the MTE has serious implications for at least one of two key claims of the MTE—that energy transfer is constrained by the structure of the internal resource distribution networks, and that natural selection has maximized the rate of resource transfer within the body. The 0.15 exponents for total development time in Artiodactyla, Carnivora, and Rodentia indicate that total development times are more alike in small and large species of these orders than is predicted by the MTE. Assuming that infants are the same relative size at weaning, this means either that large species develop for a shorter time, or that small species develop for a longer time, than the MTE predicts (Figure 1c). If durations are shorter at large body sizes, the implication is that large mammalian mothers transfer energy faster than they should be able to do so according to the MTE. This in turn implies that the structure of the internal resource distribution networks does not constrain energy transfer in the manner averred by the MTE. Conversely, if durations are longer than expected at small body sizes, this implies that, contrary to what the MTE contends, natural selection has not maximized energy transfer rates at small body sizes. Thus, the total development time allometries indicate that one or other of the claims is incorrect.
Using the same logic, the departure of allometries for gestation duration from the predictions of the MTE also indicates that at least one of the core claims of the MTE is incorrect. The fact that the gestation duration allometries for all four orders are shallower than predicted by the MTE could mean that large species develop in utero for less time than the MTE predicts, and therefore transfer energy via the placenta faster than they should be able to do so according to the MTE. That is, large mammals may have a higher growth rate compared to small mammals . Alternatively, it could mean that small species develop longer in utero than the MTE predicts, and therefore transfer energy via the placenta slower than expected based on BMR, which in turn implies that natural selection has not maximized the rate of within-body energy transfer in smaller species resulting in relatively slower growth rates.
The implications of the lactation duration allometries for the MTE seem to be even more serious. The shallower-than-predicted allometries for Rodentia and Carnivora can be explained using the same logic as for gestation—either large-bodied mammals are transferring energy faster than predicted by the MTE, or small-bodied mammals are not transferring energy at the maximum possible rate, contrary to the MTE. In contrast, the steeper-than-predicted allometry for primate lactation indicates that either large species develop ex utero for longer than the MTE predicts, and therefore transfer energy via the mammary glands slower than they should according to the MTE, or small species develop for less time ex utero than the MTE predicts, and therefore transfer energy via the mammary glands faster than the MTE suggests they should be able to do. Viewed together, the lactation duration allometries raises the possibility that both the claim that energy transfer is constrained by the structure of the internal resource distribution networks and the claim that natural selection has maximized the rate of resource transfer may be wrong.
Dubman et al.  proposed a revised version of the MTE hypothesis in light of the allometries they obtained for primates. Because they found that total development time scales as predicted by the MTE, but gestation duration and lactation duration do not, Dubman et al.  suggested that gestation duration and lactation duration in primates are coupled traits evolving under the constraint of BMR such that species can trade-off the lengths of gestation and lactation but have to do so within a total development time dictated by BMR. This “coupled-traits hypothesis” is also not supported by our data. While primate total development time scales with the expected 0.25 exponent, the other three orders all have total development times that scale with body mass with an exponent of 0.15. So, the proposed BMR constraint on total development time does not hold for Artiodactyla, Carnivora, and Rodentia. More problematically still, our data also do not support the trade-off part of the coupled-traits hypothesis. The allometries of gestation duration and lactation duration are more variable across the four orders than the allometries for total development time, as expected under a trade-off scenario. However, the coupled-traits hypothesis predicts a negative relationship between the residuals of the allometry of lactation duration and the residuals of the allometry of gestation duration, and this prediction is also not supported by our data. The relationships between the two sets of residuals are generally positive rather than negative, but highly variable across the orders, with the only strong relationship being in the Primates (0.12 < b < 1.24; n = 106; Artiodactyla: −0.01 < b < 0.98; n = 100; Carnivora: −0.24 < b < 0.3; n = 146; Rodentia: −0.02 < b < 0.42; n = 105). Thus, it appears that the coupled-traits hypothesis is also not a good explanation for the variation in the duration of the key components of the mammalian maternal energetic investment cycle.
The failure of our analyses to support the predictions of both the original MTE hypothesis and Dubman et al.’s  modified version has some important implications for future research on the factors governing energetic investments in offspring by mammalian mothers. One is that it suggests the influence of BMR on gestation duration and lactation duration is more complicated than suggested by the MTE and coupled-traits hypotheses. Metabolic rate must constrain gestation duration and lactation duration in some way, because gestation and lactation involve the transfer of energy and therefore can only be afforded once demands of the mother’s basal metabolism have been satisfied. But our results indicate that the constraint must be indirect rather than direct. Another important implication for future research on the factors governing energetic investments in offspring by mammalian mothers stems from our finding that gestation duration and lactation duration allometries are so different one from the other within and across orders. This suggests not only that we need to allow for the possibility that different factors drive gestation duration and lactation duration, but also that we must take into account the possibility that the drivers of variation in the two durations differ among clades.
With regard to future work, total development time and its components are not the only biological times whose scaling exponents have been found to be inconsistent with the predictions of the MTE. Several others can be identified in the recent literature. For example, Duncan et al.  investigated the scaling of age at first reproduction in 1197 species of mammal, and obtained an exponent that is significantly lower than the 0.25 predicted by the MTE. Similarly, Müller and colleagues  examined food-in-gut retention time in 77 herbivorous mammals and found that it does not scale with an exponent of 0.25. Lemaître et al.  provide a third example. These authors examined the scaling of longevity in a sample of 1213 mammalian species, and also obtained a scaling exponent that was significantly different from 0.25. The fact that several, diverse biological times do not scale in the manner predicted by the MTE clearly raises questions about the MTE’s general applicability. It would seem, then, that an important task is to determine whether the MTE’s failure to predict scaling exponents for biological times is matched by a failure to predict scaling exponents for other types of trait. Another worthwhile undertaking would be to investigate the statistically indistinguishable slopes and intercepts for total development time in Artiodactyla, Carnivora, and Rodentia. That the slopes and intercepts for total development time are the same for three such diverse orders is intriguing. Could it be that their development is in fact constrained by a common factor, just not by basal metabolic rate?