Comparative and meta-analytic insights into life extension via dietary restriction

Comparative and meta-analytic insights into life extensionvia dietary restriction

Shinichi Nakagawa, Malgorzata Lagisz, Katie L. Hector andHamish G. Spencer

Department of Zoology, National Research Centre for Growth and

Development, University of Otago, PO Box 56, Dunedin 9054, New Zealand

Summary

Dietary restriction (DR) extends the lifespan of a wide range of

species, although the universality of this effect has never been

quantitatively examined. Here, we report the first comprehensive

comparative meta-analysis of DR across studies and species. Over-

all, DR significantly increased lifespan, but this effect is modulated

by several factors. In general, DR has less effect in extending life-

span in males and also in non-model organisms. Surprisingly, the

proportion of protein intake was more important for life exten-

sion via DR than the degree of caloric restriction. Furthermore, we

show that reduction in both age-dependent and age-independent

mortality rates drives life extension by DR among the well-studied

laboratory model species (yeast, nematode worms, fruit flies and

rodents). Our results suggest that convergent adaptation to labo-

ratory conditions better explains the observed DR–longevity rela-

tionship than evolutionary conservation although alternative

explanations are possible.

Key words: age-dependent mortality; age-independent mor-

tality; caloric restriction; comparative analysis; evolutionary

conservation; evolutionary convergence; meta-analysis; pro-

tein restriction.

Introduction

It is generally accepted that dietary restriction (DR, a reduction in food

intake without malnutrition) has health benefits such as prolonging life-

span and protection from various diseases (diabetes, cancer and cardio-

vascular disease; Fontana et al., 2010; Partridge, 2010; Piper et al.,

2011). Such benefits have been demonstrated in a wide diversity of spe-

cies, across several animal phyla (Mair & Dillin, 2008). Much of the evi-

dence concerning DR comes from five laboratory model species (Le

Bourg, 2010): yeast (Sacchromyces cerevisiae), the nematode (Caenor-

habditis elegans), the fruit fly (Drosophila melanogaster), the mouse (Mus

musculus) and the rat (Rattus norvegicus), in which the effects of DR were

first reported in 1935 (McCay et al., 1935; hereafter, we will refer to

these five species as the ‘model species’). The phylogenetic diversity rep-

resented by these five species has underpinned a widely held belief in an

evolutionarily conserved mechanism that mediates the relationship

between DR and longevity (Le Bourg & Rattan, 2006; Mair & Dillin, 2008;

Le Bourg, 2010). A recent report on the effect of DR on lifespan in long-

lived rhesus monkeys (Macaca mulatta; Colman et al., 2009) reinforces

this view, raising the hope that DR has the same beneficial effects for our

own species (Fontana et al., 2010; Partridge, 2010). Nevertheless, the

beneficial effects of DR do not appear to be universal: studies of house-

flies and several species of rotifers (Kirk, 2001; Cooper et al., 2004), for

example, failed to detect any life-extending effect of DR. Such studies call

into question the possibility of any evolutionarily conserved mechanism.

Evolutionary explanations for DR effects on lifespan invoke a life history

trade-off. Among and within species, fecundity negatively correlates with

longevity, the so-called cost of reproduction (Williams, 1966). Dietary

restriction results in increased longevity, but also in decreased fecundity,

at least in laboratory animals (Partridge et al., 2005a). In the wild, many

organisms encounter periods of starvation during which they should

devote energy to somatic maintenance and repair, prolonging lifespan to

survive until a nutritionally richer period when they can afford to repro-

duce (Kirkwood & Shanley, 2005). Findings on sex differences in the

effects of DR support this cost-of-reproduction view. In Drosophila and

several strains of mice, the life-prolonging effect is much more pro-

nounced in females than in males (Partridge et al., 2005a). Such a sex dif-

ference is expected, because males are generally thought to invest less

into reproduction.

Studies of single-gene mutations in the model species are now elucidat-

ing some of the molecular pathways of DR effects (Bartke, 2011). Muta-

tions that prolong lifespan are usually involved in slowing down nutrient-

signalling pathways. For example, down-regulation of the target of rapa-

mycin (TOR) pathway extends lifespan in yeast, C. elegans, drosophila and

mice (McCormick et al., 2011). Also, reduced activity in the insulin ⁄ insu-

lin-like growth factor signalling (IIS) pathway leads to longer lifespan in

C. elegans, Drosophila and mice (Kenyon, 2011). Dietary restriction is

thought to influence one or more of these nutrient-signalling pathways,

although how exactly DR acts on these pathways is still poorly understood

(Fontana et al., 2010; Partridge, 2010). The mutation studies have been

viewed as strong evidence against the DR effect arising from convergent

adaptation and strong support for its evolutionary conservation (Mair &

Dillin, 2008). Nevertheless, the unequivocal demonstration of the life

extension by DR in the five model species does not prove the universality

or conservation of the DR–longevity relationship (Le Bourg & Rattan,

2006; Le Bourg, 2010). For many generations, these model species have

lived under laboratory conditions, which usually provide constant food

supply, are free from pathogens, parasites and predators and select for

fecundity and appetite but against longevity (Miller et al., 2002; Austad &

Kristan, 2003). Thus, some researchers have controversially speculated

that the effect of DR could be a laboratory artefact, for example, by allevi-

ating the detrimental consequences of overfeeding (Le Bourg, 2010).

A second debate concerning DR studies is whether restriction of caloric

intake per se can extend longevity (Masoro, 2006). DR is often referred to

as ‘caloric restriction’ because a reduction in calories was believed to be

the key factor prolonging an organism’s lifespan. A series of recent stud-

ies, however, suggests that the balance between macronutrients (the

ratio between proteins and carbohydrate ⁄ fat) is more important than

caloric restriction (Simpson & Raubenheimer, 2009). In several insect spe-

cies (crickets and drosophila), fixed-calorie diets containing lower ratios

of protein to carbohydrates (‘protein restriction’) extended longevity (e.g.

Mair et al., 2005; Lee et al., 2008; Maklakov et al., 2008; Fanson et al.,

Correspondence

Shinichi Nakagawa, National Research Centre for Growth and Development,

Department of Zoology, University of Otago, PO Box 56, Dunedin 9054, New

Zealand. Tel.: +64 3 479 5046; fax: +64 3 479 7584; e-mail: shinichi.

[email protected]

Accepted for publication 10 January 2012

ª 2012 The AuthorsAging Cell ª 2012 Blackwell Publishing Ltd/Anatomical Society of Great Britain and Ireland

401

Aging Cell (2012) 11, pp401–409 Doi: 10.1111/j.1474-9726.2012.00798.xAg

ing

Cell

2009). Furthermore, a study on drosophila suggests that adequate ratios

of amino acids within protein intake are key for lifespan extension via DR

(Grandison et al., 2009), but there is limited experimental evidence as to

whether such clear effects of protein restriction apply to mammalian spe-

cies. Some researchers argue that caloric restriction is crucial for the

mammalian life-extending effect of DR (Masoro, 2006), although there is

indirect support for the effect of protein restriction in humans (Fontana

et al., 2008). It seems that both caloric and protein restriction may play a

role in producing life extension by DR.

Here, we attempt to resolve these two debates by conducting a com-

prehensive and comparative meta-analysis on a wealth of published stud-

ies, investigating the relationship between DR and survival. Importantly,

the comparative meta-analytic approach enabled us to combine a wide

variety of species from a great number of studies and to extract general

trend from what appears to be contradictory results while controlling for

species-specific and study-specific effects (Hadfield & Nakagawa, 2010).

Our main aims are the followings: (i) to determine the universality of DR

effects on longevity between sexes and among species, especially focus-

ing on the model and non-model species, and (ii) to quantify the impor-

tance of both caloric restriction and protein restriction in the effect of DR

on longevity. Additionally, in the model species, we investigate whether

DR affects either age-independent or age-dependent mortality rate or

both (Partridge et al., 2005b; Phelan & Rose, 2005). An overall objective

of this study is to quantitatively synthesize the current state of knowledge

on this important topic for the first time, and thus, to present an overview

of the empirical evidence.

Results and discussion

Universality of life-extending effect of DR

We located 145 studies investigating the relationship between DR and

longevity in 36 species, which matched our selection criteria (see Experi-

mental procedures). We extracted 529 effect sizes from these studies

(Data S1); the effect size measure used is the natural logarithms of hazard

ratio, ln(HR) (Table S1). In short, a set of three ln(HR) values were

extracted from each pair of survival curves (consisting of the control

group and the DR group) at three relative time intervals (during which

0–25%, 25–50% and 50–75% of the control group died), and the overall

estimates from these three values constituted effect size values as ln(HR)

(Fig. S1; Parmar et al., 1998; Williamson et al., 2002). Negative ln(HR)

values mean that individuals in DR groups were less likely to die at a given

point on average than ones in the control groups.

Overall, DR reduced the risk of death by 60% (Bayesian mixed-effects

meta-analysis, BMM; Hadfield, 2010; Hadfield & Nakagawa, 2010;

b[meta-analytic mean] = )0.434, 95% credible interval (CI) = )0.704 to

)0.171; Table S2). This effect remains robust even when phylogenetic

non-independence among 36 species was accounted for (Bayesian phylo-

genetic mixed-effects meta-analysis, BPMM: b[meta-analytic mean] = )0.515,

CI = )0.953 to )0.093; Figs 1 and S2, Table S1 and Data S2). We

observed moderate to high heterogeneity (Higgins & Thompson, 2002;

BPMM: I2 = 53.73, CI = 41.15–66.00; Table S2; hereafter, results only

from BPMM are presented, see Table S2–S6 for equivalent results from

BMM); that is, the life-extending effect of DR is more apparent in certain

species and ⁄ or studies.

In meta-analysis, significant heterogeneity calls for moderators (e.g.

the effect of sex), which may explain such heterogeneity (Higgins &

Thompson, 2002). Thus, we tested the controversial suggestion that

the life-prolonging effect of DR is only true for the model species,

along with a less contentious idea that DR has more influence on

females than on males. We found that the life-extending effect of DR

was 20% smaller for male organisms than for females and also that

DR was nearly twice as effective in prolonging lifespan in the model

species than in the non-model species (BPMM: b[female ⁄ male difference] =

0.218, CI = 0.038–0.411 and b[non-model ⁄ model difference] = )0.666,

CI = )1.121 to )0.222; Fig. 2A,B and Table S3). Although the signifi-

cant sex effect is more or less expected from previous work (Partridge

et al., 2005a), our finding is, to our knowledge, the first quantitative

proof for the generality of the sex effect in the DR–longevity relation-

ship. The housefly study, where DR convincingly failed to induce life

extension (Cooper et al., 2004), has often been cited as evidence

against the universality of the DR–longevity relationship (Le Bourg,

2010). Nevertheless, we point out that all houseflies in this experiment

were males, so that the negative result could be predicted from our

meta-analytic result, and it is not conclusive evidence against a life-

extending effect by DR in this species. In contrast to the sex effect,

the significant and clear model species effect we discovered is unex-

pected and fascinating. This finding supports the idea that the life-

extending effect of DR is related to living in peculiar laboratory condi-

tions for many generations (Miller et al., 2002; Austad & Kristan,

2003; more discussion later).

Importantly, the validity of estimates from meta-analysis relies on the

assumption that there is negligible publication bias in a particular research

topic (Egger et al., 1997). Inspection of funnel plot symmetries of our

data revealed no obvious signs of publication bias in our data set

(Figs 2C–H and S3; for the results of a regression approach (Egger et al.,

1997), consistent with the absence of publication bias, see Table S4 and

Dialog S1). Therefore, our estimates are likely to be reliable.

Caloric restriction or protein restriction?

We now build upon the above analyses to investigate the relative impor-

tance of caloric and protein restrictions. It is noted that, on the one hand,

the variable caloric intake (%) represents the relative percentage of calo-

ric intake for the DR group in relation to the control group where caloric

intake was 100%. One the other hand, the variable protein intake (%) is

the percentage of total food energy coming from protein in relation to

the other macronutrients, namely carbohydrate and fat for both groups

(see Dialog S1).

We found significant quadratic effects of both caloric and protein

intake on the risk of death, with the life-extending effect of caloric intake

peaking around 50% and that of protein intake about 30% (BPMM:

b2[caloric intake] = 1.785, CI = 0.664–2.907; b[caloric intake] = )1.702,

CI = )2.815 to )0.651; b2[protein intake] = 5.352, CI = 3.219–7.358; and

b[protein intake] = )3.088, CI = )4.440 to )1.389; Figs 3and S4 and

Table S5). Our results indicate that the effect of protein intake is larger

than that of caloric intake, illustrated in Fig. 3A,B. This result is remark-

able because, while most studies included in our data set explicitly chan-

ged the caloric intake between control and DR groups, very few studies

deliberately manipulated protein intake (Data S1 and Dialog S2). None-

theless, different studies covered a wide range of protein intake (0% up

to approximately 90%). The contours of the DR effect on longevity in

Fig. 3C show the importance of the balance between caloric intake and

protein intake for DR to be effective.

This bivariate action of DR may explain many equivocal results in the lit-

erature, where researchers usually focused on caloric intake rather than

protein intake for their interpretation. For example, animals that were

food-restricted by 50% would not necessarily show the benefit of DR, if they

were also fed a high-protein diet. Our results strongly support a recently

proposed protein restriction hypothesis (Simpson & Raubenheimer, 2007,

Dietary restriction and longevity: meta-analysis, S. Nakagawa et al.


402

2009) with an implication that this phenomenon may be general across

the animal kingdom.

Notably, when we used alternative values based on actual food con-

sumption as a measurement of caloric restriction, where available (32%

of all the data points; Model 14 in Table S6), the life-extending effect of

caloric intake disappeared but that of protein intake remained virtually

unchanged (BPMM: b2[caloric intake] = )0.087, CI = )0.441 to 0.227;

b[caloric intake] = )0.059, CI = )0.580 to 0.431; b2[protein intake] = 5.119,

CI = 2.937–7.264; and b[protein intake] = )2.976, CI = )4.467 to )1.386;

Table S6). Although this particular result is difficult to explain and recon-

cile, caloric restriction may not be the main determinant for the life-

extending effect of DR, as indicated in a series of insect studies (e.g. Mair

et al., 2005; Lee et al., 2008; Maklakov et al., 2008; Fanson et al., 2009).

How are aging trajectories changed?

We next examined the five model species in which the effect of DR was

apparent to reveal how DR exerted life-extending effects. There are two

ways that mortality rates can be reduced: (i) they are reduced by a con-

stant fraction across the lifespan of an organism (i.e. a change in the age-

independent mortality rate, also known as initial mortality rate) and

(ii) the rate at which mortality rates increase across the lifespan is reduced

(i.e. a change in age-dependent mortality rate; Partridge et al., 2005b;

Phelan & Rose, 2005). In our data set, the two mechanisms of life exten-

sion can be identified and distinguished by meta-analytically estimating

intercepts and slopes of ln(HR) values over the three relative time intervals

(0–25%, 25–50% and 50–75% of the control group being dead, as

described in Dialog S1 and Fig. S5). Our data set for the model species

included 290 estimates for both intercepts and slopes from 105 studies

(Data S3). Statistically speaking, we should observe a negative intercept

with a zero slope if only age-independent mortality change is at work,

whereas a significantly negative slope with a zero intercept if only age-

dependent mortality is occurring. If both types of mortality change occur,

a negative intercept and negative slope should be observed.

Overall, both age-dependent and age-independent mechanisms con-

tributed to the DR life-extending effects (BMM: b[intercept] = )0.516,

CI = )0.686 to )0.354; b[slope] = )0.181, CI = )0.252 to )0.120; Fig. 4,

Table S7). Previous studies have claimed that in drosophila, DR reduces

the age-independent mortality rate but not the age-dependent mortality

rate, whereas for rodents, much of the life extension by DR stems from

decreasing the age-dependent mortality rate (Partridge et al., 2005b;

Phelan & Rose, 2005). However, our meta-analytic results show that the

Fig. 1 A forest plot of effect size, logarithm of hazard ratio [ln(HR)], estimates for the relationship between dietary restriction (DR) and survival. An overall meta-analytic

posterior mean and posterior means for 36 species (as random factors; see Dialog S1 and Fig. S1) with 95% credible intervals (CIs) are shown (Table S2). Control n and DR n

represent the numbers of independent animals (or colony numbers for Sacchromyces cerevisiae and Podospora anserina) used (in 145 studies). The overall mean supports the

life-extending effect of DR, and also, for the model species, this effect is consistently supported (95% CIs are not touching or crossing zero).



403

DR effects generally result from the dual actions of age-dependent and

age-independent mortality changes. How DR brings about these two

effects simultaneously will be an important future question.

Peculiarly, yeast seemed to be the only species where we did not find

convincing evidence for age-dependent mortality change (BMM;

b[intercept] = )0.695, CI = )1.263 to )0.144; b[slope] = )0.006,

(C) (D)

(E) (F)

(G) (H)

(A) (B)

Fig. 2 The effects of sex and species status on the relationship between dietary restriction (DR) and survival. (A, B) The model species consistently support the relationship

between DR and longevity [i.e. negative ln(HR)] in all types of sex categories (red: females, blue: males, purple: mixed sexes or males and females, and green: hermaphroditic

organisms), whereas the non-model species consistently fail to support this relationship. Also, males responded less to DR than females. Data shown are posterior means and

95% credible intervals (Table S3). (C to H) Funnel plots with posterior means (solid lines) with different sex types and species statuses (model species: C, E and G and non-

model species: D, F and H). No obvious signs of publication bias can be seen.



404

CI = )0.254 to 0.225; Table S7). This result could be due to the limited

sample size in this species (note that the slope for yeast is not statistically

different from the other species). Alternatively, it is possible that a biologi-

cal reason can account for this observation. Longevity of a single-celled

organism, yeast, is measured by ‘replicative’ lifespan (i.e. how long a set

number of mother cells can keep generating daughter cells; Lin & Sinclair,

2008) rather than actual age as in multicellular organisms. In other words,

how DR ameliorates aging may differ between single and multicellular

organisms.

Evolutionary conservation or laboratory convergence?

Bayesian phylogenetic mixed models can provide an index, termed phylo-

genetic heritability (H2; Hadfield & Nakagawa, 2010), which quantifies

the amount of phylogenetic signal (Lynch, 1991) in the data set and

ranges from 0 to 1 (for details, see Dialog S1). Our first BPMM, which only

included the intercept (i.e. meta-analytic mean) as a fixed factor, had a

reasonable amount of phylogenetic signal (BPMM: H2 = 0.351,

CI = 0.004–0.512; Table S2), suggesting that the DR–longevity relation-

ship was only apparent in some species but not others. However, our final

BPMM, which accounted for the sex effect, the model species effect and

the effect of protein and caloric intake, had much less phylogenetic signal

(BPMM: H2 = 0.003, CI = <0.001–0.450; Table S5). Therefore, these

four variables seem to explain most of the phylogenetic signal (i.e.

between-species differences) in the original analysis. Given that the evi-

dence for life extension by DR is weak in the non-model species (Fig. 2)

and that the five model organisms represent four distantly related animal

phyla, we suggest that the life-extending effect of DR is a response only

evident when animals have been housed in laboratory conditions for a

number of generations. There are a number of explanations why this may

be the case.

It is possible that life extension by DR is a laboratory-induced con-

vergence among the model species. This laboratory convergence

explanation, however, runs counter to recent findings that the same

or homologous nutrient-signalling pathways (e.g. TOR, IIS) are involved

in prolonging lifespan among these distantly related model species

(Fontana et al., 2010; Partridge, 2010; Bartke, 2011; Kenyon, 2011;

McCormick et al., 2011). It is more parsimonious to think that such

pathways are evolutionarily conserved and the life extension by DR is

an ancestral response incurred by the nutrient-signalling pathways

shared by contemporary animals. Therefore, we speculate that there

may exist a neglected pathway, which reduces lifespan in animals,

cancelling the life-extending effects associated with nutrient-signalling

pathways. This neglected pathway may be less functional in the model

species after many generations of cosseted laboratory life. It is also

possible that such a pathway does not exist, but the life-extending

effects of nutrient-signalling pathways are somehow more pronounced

in the model laboratory species, which have been inadvertently

selected for such a ‘positive’ response (Harper et al., 2006). A recent

study revealed significant heterogeneity in the response to DR among

(A) (C)

(B)

Fig. 3 The effect of caloric intake and protein intake on the relationship between dietary restriction (DR) and survival. (A, B) Both caloric intake and protein intake show

significant quadratic effects, supporting important roles of these factors in the DR–longevity relationship (the original data points, N = 529, weighted by the inverse of their

variances are shown accordingly; Table S5). (C) The bivariate effects of protein and caloric intake in different sexes and species status, showing that optimal conditions in both

variables are a key to maximize the effect of DR on lifespan.



405

(A) (B)

(C) (D)

(E) (F)

(G) (H)

Fig. 4 Mechanism by which dietary restriction (DR) increases longevity. (A) Significant intercepts of the overall estimate and of each model species (dark blue: rats, light blue:

mice, red: fruit fly, green: nematode worms, yellow: yeast and black: overall estimates) support that DR decreases the age-independent mortality rate (posterior means and

95% credible intervals, CIs, are shown; see Fig. S5 and Table S7). (B) Significant slopes of the overall estimate and of the model species support that DR also decreases the

age-dependent mortality rate, except yeast [the unit of logarithms of hazard ratio (ln(HR)) for slopes is converted to % for interpretability]. (C to H) Negative intercepts and

negative slopes of ln(HR) against age (% control dead) suggest that changes in both age-independent and age-dependent mortality are responsible for the life extension by

DR in general; specifically in rats, mice, fruit flies and nematode worms but not in yeast. (n indicates the number of studies where intercepts and slopes were estimated, and

grey lines represent these regression lines.)



406

41 inbred straits of mice; DR even shortened lifespan in some stains

(Liao et al., 2010). This observation indicates that laboratory selection

of different sorts could result in a variety of responses to DR. Yet,

another possibility is that researchers are able to control extraneous

factors such as housing conditions and fine-tuning of experimental

diets for the model species much better than for non-model species,

so that the life-prolonging effect is exaggerated in the model species.

If so, it would seem that life extension via DR is less effective and less

general than previously supposed and, therefore, might be less appli-

cable to humans.

Comparative and meta-analytic insights

There have been numerous qualitative papers discussing the universal-

ity and ⁄ or specificity of the life-extending effect of DR across species

(Partridge & Brand, 2005; Phelan & Rose, 2005; Le Bourg & Rattan,

2006; Mair & Dillin, 2008; Le Bourg, 2010). Our meta-analytic

approach goes significantly beyond these verbal assessments, however,

and shows that, given the right dietary conditions, DR could extend

lifespan of any species, although the effect may be modulated by

important factors such as sex. Our work represents the first formal

meta-analysis on the topic of the DR–longevity relationship. We see a

number of fertile avenues for future meta-analytic research, which will

offer quantitative answers to controversies in the field of nutrition-

related gerontology (which are summarized in Table 1). Notably, the

statistically robust results revealed by our meta-analysis cannot be

extrapolated directly to individual species (Nakagawa & Cuthill, 2007);

real differences among species remain.

To conclude, our study reaches several significant findings that may

resolve many conflicting results from previous studies: (i) DR is gener-

ally more effective at increasing female longevity than male longevity,

(ii) the balance between protein and caloric restriction is a key factor

to maximize the effect of DR in extending lifespan, (iii) DR induces life

extension generally by reducing both age-independent and age-

dependent mortality rates, and (iv) the effect of DR on longevity

seems only apparent in the model species, but not in the non-model

species, supporting the laboratory convergence explanation of the

DR–longevity relationship. Although alternative explanations are possi-

ble for the last point (see above), future investigation into this

hypothesis is warranted.

Experimental procedures

The data for meta-analysis were collected using ISI Web of Science and

Google Scholar with the search string ‘calorie* ⁄ diet* ⁄ energy ⁄ food’ +

‘restrict*’ + ‘longevity ⁄ lifespan’. Backward and forward searching was

also carried out primarily using review articles that focused on non-

rodent or non-mammalian studies to locate smaller studies on less com-

mon species which may not have been conducted with a focus on calo-

rie restriction and longevity in mind. Papers published at any date up to

December 2009 were included. Of over 2000 studies this search

yielded, papers were selected that contained a graphical survival curve

or, in the case of some older studies, that gave the complete data set

from which a survival curve could be constructed. Papers were also

excluded from analysis based on a number of methodological criteria

that are detailed in Dialog S1. From the included studies, we extracted

effect size measures: we used survival curves to quantify the natural

logarithms of hazard ratio, ln(HR) (Table S1). In short, a set of three

ln(HR) values were extracted from each pair of survival curves (consist-

ing of the control group and the DR group) at three relative time inter-

vals (during which 0–25%, 25–50% and 50–75% of the control group

died), and the overall estimates from these three values constituted

effect size values as ln(HR) (Fig. S1; Parmar et al., 1998; Williamson

et al., 2002). To analyse the collected data, we used standard proce-

dures associated with meta-analysis and meta-regression, as described

in Dialog S1. BMM and BPMM were implemented in the R package,

MCMCglmm (Hadfield, 2010; Hadfield & Nakagawa, 2010).

Acknowledgments

We thank J. Hadfield, S. Morgan, D. Raubenheimer, L. Tain, S.

Gronke, M. Piper, P. Dearden, the SN lab members and two

anonymous referees for their comments and advice, which

improved the earlier versions of this paper. We are also grateful

to K. Miller for helping with figure production and J. Hadfield for

statistical advice. This project was supported by funding from

National Centre for Growth & Development, New Zealand, and

funding from the Department of Zoology, University of Otago,

New Zealand. SN is supported by the Royal Society of New Zea-

land Marsden Fund.

Author contributions

SN conceived the idea for the study, all authors contributed to design

the study, SN, ML and KLH collected data, SN conducted data analy-

sis, SN and ML wrote the first version of the manuscript, and all

authors contributed to the final draft.

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Table 1 Potential meta-analytic topics in nutrition-related gerontology

Quantifying and ranking the usefulness of biomarkers as longevity indictors

(e.g. oxidative damage, body temperature, glucose levels in blood)

Quantifying the effects of dietary restriction (DR) on health benefits

(e.g. protection against cancer and cardiovascular disease)

Quantifying and comparing the effects of DR on a range of different traits, such

as physiology, behaviour, life history and cognition

Quantifying the effects of and heterogeneity among different single-gene

mutations, which mimic DR in extending lifespan

Quantifying the efficiency of life-extending compounds, such as the target of

rapamycin (TOR) inhibitors, sirtuin-activating compounds (STACs; e.g.

resveratrol) and antioxidants

Quantifying the effects of immune challenges and pathogen ⁄ parasite infections

on immune responses and lifespan under DR

Quantifying the effects of stressors (e.g. heat shocks, pollutants) on lifespan and

longevity biomarkers under DR

These meta-analyses may be carried out within specific species or across

different species.



407

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Supporting Information

Additional supporting information may be found in the online version of

this article:

Fig. S1 A schematic showing typical survival curves for the control group

and the DR group and time points we used to obtain information for calcu-lating effect size values, ln(HR).

Fig. S2 A phylogenetic tree of the 36 species used in the analysis.

Fig. S3 Funnel plots of effect size, ln(HR), against its precision (the inverse

of standard error, 1 ⁄ SE). (A) The original effect sizes against the corre-

sponding precision values. (B) Corrected effect sizes (from Model 6) against

the precision. Asymmetry in the funnel shape is less obvious for the cor-

rected data (B) than the original data (A).

Fig. S4 The effect of caloric intake and protein intake on the relationship

between DR and survival. (A-B) Identical to Fig. 3 except that three addi-

tional outlier values are shown.

Fig. S5 Visualizing age-independent and age-dependent changes in mortal-

ity rate due to dietary restriction (DR) in terms of the natural logarithms of

mortality rate and hazard ratio. (A, B) Age-independent mortality ratechange. (C, D) Age-dependent mortality rate change. (E-F) Both types of

mortality rate changes at work.

Table S1 Conversions among the natural logarithm of hazard ratio, ln(HR),

hazard ratio, HR and percentage (%) difference.

Table S2 Estimates from Bayesian mixed-effects meta-analysis (Model 1)

and phylogenetic mixed-effects meta-analysis (Model 2) for the relationship

between DR and longevity, measured as ln(HR).

Table S3 Estimates from Bayesian mixed-effects meta-regression (Model 3)

and phylogenetic mixed-effects meta-regression (Model 4) examining ‘sex’

effect and ‘model species’ effect on the relationship between DR and lon-

gevity, measured as ln(HR).

Table S4 Estimates from Egger’s regression analysis for the original data

(Equations 14–16) and the adjusted data from Model 6 (Equations S17–

18).

Table S5 Estimates from Bayesian mixed-effects meta-regression (Model 5)

and phylogenetic mixed-effects meta-regression (Model 6) examining the

effects of caloric and protein intake on the relationship between DR and

longevity, measured by ln(HR).

Table S6 Estimates from meta-regression models (Models 7–14), testing

additional predictors (for the details of each model, see Dialog S1) by build-ing upon Model 6 (Table S4).

Table S7 Estimates from Bayesian mixed-effects meta-regression for exam-

ining the age-independent mortality rate (Models 15 and 17 with the for-

mer having ‘species’ as a fixed factor and the latter species as a random



408

factor) and the age-dependent mortality rate (Models 16 and 18) among

the five model species.

Data S1 Main data file.

Data S2 Phylogenetic tree.

Data S3 Data with slope and intercept estimates.

Dialog S1 Additional experimental procedures and their details along with

additional references.

Dialog S2 Details of Data S1–S3 files.

As a service to our authors and readers, this journal provides supporting

information supplied by the authors. Such materials are peer-reviewed and

may be re-organized for online delivery, but are not copy-edited or typeset.

Technical support issues arising from supporting information (other than

missing files) should be addressed to the authors.



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Comparative and meta-analytic insights into life extension via dietary restriction