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Keywords:

  • body mass;
  • comparative biology;
  • oxidative stress;
  • phylogenetic contrasts

Summary

  1. Top of page
  2. Summary
  3. Introduction
  4. Problem one: co-variation of lifespan and physiological traits with body mass
  5. Problem two: species do not represent statistically independent data
  6. Conclusions
  7. Acknowledgments
  8. References

Comparative differences between species provide a powerful source of information that may inform our understanding of the aging process. However, two problems regularly attend such analyses. The co-variation of traits with body mass is frequently ignored, along with the lack of independence of the data due to a shared phylogenetic history. These problems undermine the use of simple correlations between various factors and maximum lifespan potential (MLSP) across different species as evidence that the factors in question have causal effects on aging. Both of these problems have been widely addressed by comparative biologists working in fields other than aging research, and statistical solutions to these issues are available. Using these statistical approaches, of making analyses of residual traits with the effects of body mass removed, and deriving phylogenetically independent contrasts, will allow analyses of the relationships between physiology and maximum lifespan potential to proceed unhindered by these difficulties, potentially leading to many useful insights into the aging process.


Introduction

  1. Top of page
  2. Summary
  3. Introduction
  4. Problem one: co-variation of lifespan and physiological traits with body mass
  5. Problem two: species do not represent statistically independent data
  6. Conclusions
  7. Acknowledgments
  8. References

The maximum lifespan potential (MLSP) has been used widely as a conceptual expression of the physiologically attainable lifespan by a given species. The problems with this concept have been fully explored by Carey (2003). Nevertheless, MLSP remains a frequently used trait in comparative biology, where it is generally equivalent to the lifespan of the oldest observed specimen of any particular species. Species differ enormously in their MLSPs, even when the comparative database is restricted to single classes of organism. The shortest lived mammals (class Mammalia), for example shrews, with MLSPs of around 12–15 months (Brambell, 1935; Hutterer, 1976), have lives that are two orders of magnitude shorter than the current estimates of maximum longevity for the longest lived mammalian species (whales living up to 200 years; George et al., 1999). These differences in MLSP have evolved within the different ecological contexts in which the different species live, but must also have an underlying physiological, biochemical and molecular basis. Studies examining the differences in the physiology of species that vary in their MLSP may therefore provide insights into the mechanisms that underlie the physiological basis of aging in specific creatures – such as humans (Austad, 1996, 1997; Barja, 2004). This comparative approach for understanding the physiological basis of the aging phenomenon has been used since at least the early 1900s (e.g. Rubner, 1908).

In this paper I will highlight two problems with this approach that, despite several previous papers highlighting them (Promislow, 1991, 1993, 1994; Speakman et al., 2002), have been, and continue to be, widely ignored by the community of scientists working on aging. Although not the only difficulties with the comparative method, they are among the more serious issues. The problems are generic and they attend utilization of the comparative method in all fields of study, and are not restricted to using such data to study aging phenomena. Fortunately, in several other fields these problems have been well appreciated (e.g. studies of life histories of animals; Harvey & Keymer, 1991) and statistical methods have been developed to overcome them (Felsenstein, 1985; Garland et al., 1993). I suggest these alternative methods can be profitably utilized in the study of comparative biology of aging. Unfortunately, however, the apparent lack of familiarity with these issues to date has led to the publication of many fundamentally flawed and potentially misleading papers in the field of aging research.

Problem one: co-variation of lifespan and physiological traits with body mass

  1. Top of page
  2. Summary
  3. Introduction
  4. Problem one: co-variation of lifespan and physiological traits with body mass
  5. Problem two: species do not represent statistically independent data
  6. Conclusions
  7. Acknowledgments
  8. References

Body mass is a pervasive trait that influences all levels of organismal biology. Apart from a few phenomena such as circadian cycles, almost every aspect of organismal biology differs as a function of body mass (e.g. Peters, 1983; Calder, 1984; Schmidt-Nielsen, 1984). This ‘allometry’ of relationships to body mass differences between species has formed one of the few bases for the development of fundamental biological laws that unify our understanding of function across life in general (West et al., 1997; West & Brown, 2004). Not surprisingly, MLSP is also a trait that is correlated with body mass of different species (for example in mammals –Fig. 1). The direct consequence of this pervasive role of body mass in organismal biology is that MLSP will be correlated with anything that is also related to body mass – which is just about everything. Figure 2 shows some examples of such relationships between biological traits and MLSP that have recently been published, and some additional relationships between MLSP that are newly generated here to illustrate the problem. Mammals that live longer have lower urinary excretion rates of DNA excision repair products (8-oxoGua and 8-Oxodg) (Foksinski et al., 2004), lower oxidative damage to mitochondria (8-Oxodg in mitochondrial DNA) (Barja, 2002a,b), lower levels of fatty acid desaturation in heart phospholipids and lower levels of DHEA in heart phospholipids (Pamplona et al., 1999). However, longer lived mammals also have lower activities of citrate synthase, combined with higher levels of both lactate dehydrogenase and pyruvate kinase (Emmet & Hochachka, 1981), lower mass-specific basal metabolic rates (Calder, 1984), and perhaps most revealingly concerning the spurious nature of such analyses, they also have longer legs and larger diameter eyeballs.

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Figure 1. The relationship between Loge MLSP (maximum reported longevity) and Loge body mass for 249 species of mammal.

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Figure 2. Relationships between physiological and other traits and Loge MLSP. (A) Urinary 8-oxo-7,8-dihydroguanine, (B) urinary 8-oxo-7,8-dihydro-2′-deoxyguanosine, (C) urinary 5-hydroxymethyl uracil, (D) mitochondrial oxidative damage (Mt 8OhdG), (E) lipid double bond index, (F) DHEA levels, (G) basal metabolic rate/gram body tissue, (H) citrate synthase, (I) lactate dehydrogenase, (J) pyruvate kinase, (K) limb length and (L) eyeball diameter. All traits are Log transformed. (A)–(C) from Foksinski et al. (2004); (D) from Barja (2004); (E) and (F) from Pamplona et al. (1999); (G) based on data in Speakman (2005); (H)–(J) from Emmett & Hochachka (1981); (K) and (L) based on data compiled from direct measurements of specimens in the University of Aberdeen zoological museum and animal house.

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Although we could construct some plausible mechanistic linkage for these latter two relationships – for example animals with bigger eyes can see dangers coming at greater distances and are therefore able to run away sooner, and longer legs enable them to run away faster, both potentially reducing their risks of mortality, most researchers would agree that there is no causal relationship between the size of an animal's eyeballs or its legs and its MLSP or its rate of aging. It is obvious that these relationships arise because MLSP is linked to body size and bigger animals have both bigger eyes and longer legs. The other relationships in Fig. 2(F–J) arise by generally similar mechanisms – animals that are bigger have lower metabolic rates and hence the enzymatic machinery attached to metabolism (citrate synthase, lactate dehydrogenase and pyruvate kinase) differs in consistent ways with body size and this leads to spurious associations between these traits and MLSP. Such relationships are not strong evidence for a causal link between these traits and the aging process. Because they are generated in exactly the same way, this criticism also extends to the other traits (Fig. 2A–E) where it is generally inferred that the associations do reflect some underlying causality.

Clearly, the differences in lifespan between large and small species must arise via some mechanism rooted in physiology (Barja, 2004). The problem is that simply correlating MLSP with aspects of physiology does not allow us to separate important traits where differences in the physiology cause differences in MLSP from trivial traits where the correlation arises only because both are related to body mass. If we interpret the relationship between variation of a given trait and MLSP as an important indicator of the process of aging, this reflects more our biases concerning the physiological basis of the aging process rather than anything inherent in the statistics.

To overcome these problems, an approach is needed that statistically allows us to separate the alternative reasons that might generate an interspecific association between MLSP and a given trait of interest. Such methods are in widespread use in other fields of enquiry (e.g. Pearl, 2000; Shipley, 2000) and include several sophisticated approaches such as ‘path analysis’. Among the simplest methods to overcome this problem is to seek associations between residual variation in the trait and MLSP, once the effects of body mass have been statistically controlled (Promislow, 1991). This method is illustrated for a hypothetical trait in Fig. 3. As is generally the case, both this hypothetical trait and MLSP are related to body mass. The technique involves fitting an allometric relationship between the trait and body mass and between MLSP and body mass, for the same species. Several alternative regression models are available to fit allometric relationships. The most commonly utilised is model I regression or least squares. Least-squares regression makes the assumption that the error variation in the x-trait is zero. This is clearly unrealistic as no variable can be measured free of error. It is the most commonly used regression model in allometry, however, because it is widely acknowledged that although body mass cannot be measured free of error, the error variance is generally considerably lower than any other trait of interest. Consequently, although measurements generally violate the assumptions of least-squares regression, the most common alternative regression model [model II or reduced major axis (RMA) regression] makes the even less realistic assumption that the error variance in both traits is equal.

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Figure 3. The analysis of residuals. In (A) the relationship between MLSP and body mass is plotted for a sample of 29 species. In (B) the relationship of a hypothetical trait related to aging is also plotted against body mass for the same 29 species. Because the relationship between body mass and lifespan is positive and the relationship to the hypothetical trait is negative the relationship between lifespan and the trait is also negative (C). The residual MLSP is the vertical distance of each datum to the line of best fit in (A) and the residual trait is the same in (B). To test if the trait is associated to MLSP independent of the effects of body mass one examines the association of the residual MLSP to the residual trait (C). In this case the relationship revealed in the residuals is positive (D), exactly the opposite of the trend in the raw data (C), exposing how misleading the plots of raw data can be because of co-variation of traits with body mass.

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To remove the confounding effect of body mass, one calculates the residuals to this fitted regression. These residuals are in effect the vertical distances that each data point lies from the line of best fit. The nature of the least-squares regression fitting procedure is that the residuals must sum to zero and be independent of the x variable. This is another advantage of using least-squares regression to fit the line because the residuals to other fitted regression lines, like RMA, are not independent of the x variable (body mass in these cases). For any trait, therefore, there is a combination of positive and negative residual values. If a species has a high positive residual for MLSP then this value says that for its body mass the species lives a long time. Its actual maximum lifespan may be quite short relative to that of a whale or an elephant, but relative to other animals of the same size it lives a long time. For example, take a small insectivorous bat like the pipistrelle (Pipistrellus pipistrellus). This animal weighs 6 g and has an MLSP of 16.5 years (Hurka, 1986). In absolute terms its life is short. However, for its size it has a very long life. The pipistrelle data point lies well above the relationship of MLSP to body size and it therefore has a high positive residual. Similarly, a large negative MLSP residual value says that, independent of body mass, that species lives a relatively short life. By definition these residuals are not related to body mass. To see if the trait in question is related to MLSP, independent of any effects of body mass, one examines the relationship between the residuals. If the hypothesis is that high rates of mitochondrial oxidative damage lead to shortened lifespan one would anticipate that species with high residual rates of mitochondrial oxidative damage would have low residual lifespans. If this analysis is significant then one might infer that the relationship between the two occurs not because they are both related to mass, but because they are really related. However, if there is no relationship in the residuals, one might conclude that the association when body mass was not accounted for arose simply because both traits were correlated with body mass.

As a practical example of this approach, consider the relationship of basal metabolic rate (BMR) to MLSP. Many previous studies have addressed the question of whether metabolic rates of animals are related to their lifespans, dating back to the seminal work of Rubner (1908). As illustrated in Fig. 2, MLSP is negatively related to BMR. Animals with low rates of metabolism (per gram body tissue) live longer. The association in Fig. 2 is based on an analysis of 249 species for which both BMR and MLSP are currently available (Speakman, 2005). One hypothesis is that this association arises because low metabolic rate involves low rates of oxidative phosphorylation, correspondingly low rates of electron transport and hence lowered free-radical production. But it may equally arise because both BMR and lifespan are related to body mass. If we calculate the residual BMR and plot it against the residual MLSP (Fig. 4) then it is clear that mammalian species that have high metabolic rates for their body masses do not live shorter lives for their body masses, allowing us to reject the causal nature of the original correlation.

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Figure 4. Analysis of residuals of MLSP plotted against residual basal metabolic rate (BMR). Although MLSP is strongly negatively related to BMR (Fig. 2H) there is no significant association in the residuals indicating that this relationship arises because of the relationships of both MLSP and BMR to body mass.

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In Fig. 5, I have re-plotted several recently published relationships between MLSP and various traits related to oxidative damage using this residuals approach. From these plots several interesting things emerge. In the original plots between lifespan and the absolute values of these traits, all the relationships were highly significant (Fig. 2). However, when the shared effects of body mass are removed most of these significant relationships disappear. Nevertheless, some relationships remain significant. For example, the negative association between urinary levels of the DNA excision repair product 8-oxo-7,8-dihydroguanine and MLSP remains significant (P = 0.026, r2 = 78.5%: Fig. 5A), and the negative association between levels of DHEA and MLSP also remains significant (P = 0.038, r2 = 83.5%, Fig. 5F), after the shared effects of body mass are removed. I suggest that using this approach may give us a much better indication of the traits that are significantly related to the aging process. However, it is important to remember that even after removing the effects of body mass, the relationship between residual variation in a trait and residual variation in MLSP is still only a correlation. This may give us some insight into processes that are linked to aging, but it cannot be used to infer causality. This is because the correlation may arise as a result of causality in the opposite direction, or as a result of other shared covariations apart from body mass. So, simply because levels of residual variation in DHEA are lower in individuals that have greater residual MLSP does not mean these low levels cause the extended life. The low levels of DHEA may themselves be a consequence rather than a cause of MLSP, or low levels of DHEA may be a consequence of a separate process that itself drives, or is caused by, the MLSP.

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Figure 5. The relationships in Fig 2(A–F) re-plotted using residuals of MLSP and the traits in question to body mass. In most cases the highly significant relationships disappear, although some remain, possibly indicating their significance for the aging process.

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There is one additional caveat. Many of the comparative studies published thus far are based on limited data sets. Typical numbers of species included in such studies are less than 20. These small samples are prone to bias in residual analyses by occasional outlying values. Naturally outlying values may be of important biological significance: an example is the pipistrelle bat mentioned above. However, where the factor driving the value to be an outlier is not biological, then in a small sample such data may cause problems – either generating spurious associations of residual traits or negatively interfering with the detection of significant associations. The most important example of this is the inclusion of data of MLSP for humans. The main problem with the MLSP for humans is that MLSP is generally quoted as 120 years. This estimate is presumably a rounding of the longest authenticated human longevity record (122 years 164 days in 2004 – Jeanne Calment) to the nearest decade. But, estimates of MLSP are very dependent on sample size contributing to the sample (Carey, 2003), and this human longevity record emerges from hundreds of millions of accurate birth and death records. No other species comes even remotely close to matching this sample size. For example, records for longevity of different dog strains that are derived from pet insurance schemes currently include fewer than 10 000 estimated lifespan records for most dog breeds (e.g. Speakman et al., 2003) and these are among the better lifespan data available for mammals. Hence, MLSP for humans is an outlier in most analyses, not because humans are exceptionally long lived, but mostly because they are exceptionally well documented and have an enormous sample size. This might cause some additional complications if the human datum reflects the largest body weight included in the analysis, because this would bias upwards the regression linking MLSP to body size and hence compromise the estimated residual calculations. Identifying outliers in data is a difficult problem for which there are many available and sophisticated techniques. However, in this case one has a good a priori demographic reason to exclude the human datum before analyses commence (as suggested by Promislow, 1994). In the example in Fig. 5(A), omitting the human datum reduces the significance of the relationship of residual MLSP to residual 8-oxo-7,8-dihydroguanine such that it is no longer significant (F = 3.85, P = 0.145, r2 × 100 = 56.2%), but does not bring the other non-significant relationships (Fig. 5B,C) up to the P < 0.05 significance criterion, and the significant association to residual levels of DHEA (Fig. 5F) is unaffected because humans were not included in the sample generating those data.

Problem two: species do not represent statistically independent data

  1. Top of page
  2. Summary
  3. Introduction
  4. Problem one: co-variation of lifespan and physiological traits with body mass
  5. Problem two: species do not represent statistically independent data
  6. Conclusions
  7. Acknowledgments
  8. References

The second problem with using comparisons of different species that has been widely ignored by biogerontologists (but see Kapahi et al., 1999; Speakman et al., 2002) is the problem that extant species are the products of the process of evolution. As such, all mammals, for example, share part of their evolutionary history with some common ancestor, which renders them non-independent data. Because independence of the individual data included in any analysis is a prerequisite of most statistical procedures, for example, the least-squares regression used in the preceding analyses, using the raw data may be a problem. The nature of this problem can perhaps be best appreciated by a practical example. It is well established that the order Chiroptera have much longer lifespans than expected for their body sizes (high residual lifespans) (Austad & Fischer, 1991; Wilkinson & South, 2002; Brunet-Rossinni & Austad, 2004). The Marsupalia show the converse pattern of low lifespans for their body masses (Austad & Fischer, 1991). Consider then a comparative study that includes three bat species, three marsupials and three rodents. A plot of their respective lifespans as a function of body mass is shown in Fig. 6(A). Now consider a hypothetical trait we believe is related to aging also plotted against body mass for the same species (Fig. 6B). If we plot the raw data we have a significant relationship of this trait to MLSP (Fig. 6C), and if we calculate the residuals we also have a significant relationship (Fig. 6D). However, it is also clear that the data in Fig. 6(D) are clustered by their order of origin. A phylogenetic tree showing the interrelationships of these species is shown in Fig. 7. A single mutation at point A in the tree that conferred low levels of the trait in question would be shared by all the animals downstream of that point in the phylogeny. This includes all the marsupials. Equally, a mutation at point B would affect all the bats. Although we have sampled three species of bats and three species of marsupials we are really pseudo-replicating the analysis because in reality only two mutational events occurred in the evolutionary history. The ‘true’ sample size in this analysis is not nine but closer to three, which reflects the three different genotypes: carrying mutation A, carrying mutation B but not A, and carrying neither A nor B. Another way to think about this is that one would not include the data for each individual animal within a species as independent data in such an analysis, as two individuals of the same species share their physiology because of a shared phylogenetic history – not because each has been the product of a unique special act of creation. Data for different species cannot be included for the same reason.

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Figure 6. (A) Hypothetical relationship of loge MLSP in three bat (open circles), three rodent (open squares) and three marsupial (open triangles) species to Loge body mass. (B) Hypothetical relationships of a trait believed to be related to aging in the same species plotted in (A) also plotted against body mass; (C) raw values of the trait in (B) plotted against MLSP; (D) residual variation in the trait in (B) plotted against residual MLSP.

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Figure 7. Hypothetical phylogenetic tree relating the species plotted in Fig. 6. Mutations at A and B affect all the species downstream of that point. Sampling several species downstream of the mutation points does not give an independent sample with respect to the mutations because the samples are not independent.

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This problem in comparative biology has been appreciated for at least 20 years (Felsenstein, 1985) and a whole series of sophisticated statistical approaches have been developed that aim to transform raw interspecific data into what are generally termed phylogenetically independent contrasts (Pagel & Harvey, 1988; Harvey & Keymer, 1991; Purvis & Garland, 1993; Diaz-Uriarte & Garland, 1998; Garland et al., 1999, 1993; Freckleton et al., 2002). These contrasts are constructed using known phylogenies for the interrelationships between the different species and this whole area has been facilitated by the development of molecular methods for diagnosing phylogenetic interrelationships of different organisms. Sensitivity analyses for errors in the phylogeny have been widely performed and it has been shown that the methods are generally robust to such errors (Freckleton et al., 2002; Purvis & Garland, 1993; Diaz-Uriarte & Garland, 1998). The net result of performing a phylogenetically independent contrasts analysis is that the significance of relationships tends to decline because the lack of independence in the data is corrected for. To illustrate the use of this method I have taken the one relationship in Fig. 5 that remained significant after the residuals analysis excluding data for humans (Fig. 5F the negative association of residual MLSP with residual levels of DHEA). This plot is redrawn in Fig. 8(A) with the individual species shown. The data comprising this analysis conveniently divide into the rodents/lagomorphs (closed symbols) and the artiodactyl/perissodactyls (open symbols). Visual examination of Fig. 8(A) suggests the data are not clumped in the manner of those in Fig. 6(D), indicating that lack of independence from phylogeny may not be too serious a problem, although obviously the datum for the rabbit exerts a large leverage on this regression and its inclusion might be questioned. The phylogeny of the species involved in this analysis reconstructed from molecular sequence data for the mammals in general (Graur, 1993; Graur et al., 1997; Robinson-Rechavi & Graur, 2001) is shown in Fig. 8(B). Sophisticated data analysis packages utilize the data that are encapsulated in this phylogeny along with the original data to generate the phylogenetically independent contrasts. The equivalent phylogenetically independent contrasts plot is shown in Fig. 8(C) to illustrate how these compare. This plot was derived using the Felsenstein (1985) method for deriving the phylogenetically independent contrasts (PICs) using the PDAP program (Garland et al., 1993). Note that each point in the contrasts plot represents the contrast at each node in the phylogeny. As there must be n − 1 nodes in the phylogeny relative to n original data, the sample size is one lower for the PIC plot than the original data. Individual contrasts are indicated by numbers next to the individual points and refer to the nodes in Fig. 8(B). The relationship in Fig. 8(C) was not significant (F = 1.6, P = 0.162). The original trend is, however, preserved and the failure to reach the 0.05 criterion may reflect a power issue at the low sample size. Alternatively, much of the significance was due to the contrast at node 5, between rabbit and the rodents, which may occur because of the strong leverage that the rabbit point had in the original plot (Fig. 8A). Removing this point would completely remove any correlation. Using phylogenetically independent contrasts in studies of interspecific data for traits related to MLSP is highly desirable, particularly when relationships using the raw data are only marginally significant.

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Figure 8. Phylogenetically independent contrasts analysis. In (A) the tip data are shown for the relationship of residual MLSP plotted against residual DHEA (as in Fig. 5F), but with the individual species shown and the division into rodent/lagomorphs (closed symbols) and artio/perissodactyls (open symbols). The phylogeny of the eight animals in this sample reconstructed from molecular data is shown in (B) with the seven nodes numbered. The phylogenetically independent contrasts analysis for the same data in (A) using the phylogeny from (B) is shown in (C). The contrasts at each node are numbered. The resultant relationship was not significant (F = 2.6, P = 0.152).

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Conclusions

  1. Top of page
  2. Summary
  3. Introduction
  4. Problem one: co-variation of lifespan and physiological traits with body mass
  5. Problem two: species do not represent statistically independent data
  6. Conclusions
  7. Acknowledgments
  8. References

Comparative biology provides a rich source of variation in animal lifespans that are the substrate of many comparative studies aiming to elucidate features of the aging process. However, attractive as it may seem, comparative biology has lots of pitfalls into which many previous studies in biogerontology have fallen. This is despite the numerous excellent previous papers that have sought to alert readers to the salient problems (e.g. Promislow, 1991, 1993, 1994). The present paper has aimed to highlight just two of the most common mistakes that still litter the biogerontological literature. The first is the problem of not accounting for the shared variability in given traits and MLSP by differences between species in body mass. The second is not accounting for the phylogenetic dependence of comparative data. Fortunately, these problems have been long recognized in other fields that use the comparative method extensively (such as evolutionary biology), and statistical methods are available to overcome these problems. I suggest that greater insights into the process of aging will emerge from the comparative method if these well-established approaches from other fields are used rather than ignored.

Acknowledgments

  1. Top of page
  2. Summary
  3. Introduction
  4. Problem one: co-variation of lifespan and physiological traits with body mass
  5. Problem two: species do not represent statistically independent data
  6. Conclusions
  7. Acknowledgments
  8. References

I am grateful to Wayne van Voorhies and Don Thomas for useful discussions of these issues and to Ted Garland for the copy of PDAP. Colin Selman and two anonymous referees made extremely helpful comments on previous drafts of the manuscript.

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  2. Summary
  3. Introduction
  4. Problem one: co-variation of lifespan and physiological traits with body mass
  5. Problem two: species do not represent statistically independent data
  6. Conclusions
  7. Acknowledgments
  8. References
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