Five years later, with double the demographic data, naked mole-rat mortality rates continue to defy Gompertzian laws by not increasing with age

Reviewer #1 (Public Review):

Ruby et al. have investigated patterns of age-specific mortality in the exceptionally long-lived naked mole-rat (NMR), under captive conditions. The authors first visited this topic five years previously with an unprecedently large data set and concluded that naked mole-rats are 'non-aging': because analyses of their survival did not detect an increasing mortality hazard with age. This result has obvious applied interest in humans because of its implications for maintaining health into later life. One criticism directed at this previous work was that a limited number 'old-aged' individuals in their data set (individuals in what might be expected to be the latter half of the life course) reduced the power with which to detect an age-related increase in mortality - or to convincingly demonstrate its absence. The current study revisits this topic with a larger sample across the life course. The authors also provide additional analyses that explore various predictors of mortality, including breeding status, body weight and colony size, and now also make direct comparisons to mortality patterns in other species of African mole-rat from the Fukomys clade (which share many convergent social and life history features). I found the analyses of Fukomys mortality particularly illuminating. However, while these additional analyses provide some useful context and can generate interesting discussion points about ageing patterns in an extremely unusual species, the principal issue at hand whether the absence of Gompertzian mortality in NMR is a robust pattern.

In this respect, a major limitation of the current study is that only 11% of the animals (n = 755) had died at the point of its conclusion- the remaining 89% being right-censored (n = 6138). This means that, as in the previous analysis, there are still relatively small numbers of individuals that have died in the older age classes (see Fig 1 for the high level of right-censoring between 15-20 years and the low numbers of deaths after this point, also Supp 1 for the raw data): the part of the life course where one would predict mortality rates to increase from an evolutionary perspective. Thus, while the authors claim very generally that the "demographic data has doubled", this in no way reflects whether the new data is informative to the question at hand, which relies on an ability to estimate death rates in older individuals accurately. If one looks more closely at the numbers which do matter, then one can see that the number of deaths in the data set has shifted from 447 in the former treatment (Ruby et al. 2018) to 755 currently, but that the number of later-stage deaths remains somewhat modest (and that this is probably reflected in the large confidence intervals for the mortality hazards at this time). I therefore remain unconvinced that the current study can rule out an exponential increase in hazard in older individuals.

The authors have also not provided any statistical evidence that the mortality hazard changes with age (or not), instead relying on visual comparisons of aggregated data. This is a fundamental problem and demands a more thorough treatment that compares survival models with different shape profiles. If anything, it seems that the hazard rate is declining with age - see Figures 1B & 2C, and while this may strengthen the authors argument if supported statistically, I would still wonder whether the higher mortality in early life - say 6 months to 3 years of age - is a consequence of the costs of early life development and that this is not a useful baseline against which to compare 'adult' mortality. It would also not overcome the data limitations identified above.

An additional concern is that the paper is selective in its presentation of previous work, with the authors focussing on results which support their main interpretations and glossing over those that don't. For example, the study refers to the fact that NMRs are resistant to various age-related diseases and do not show many age-related declines in physiology. Yet, while this argument of negligible senescence might hold generally, the literature contains various reports of later life declines in NMR physiology (Andziak et al. 2006; Edrey et al., 2011). Referring to work from your own group, Braude et al. (2021) write "several typical mammalian age-related lesions of muscles, bone, heart, liver, and eye, including sarcopenia, osteoarthritis, a decline in articular cartilage thickness of the condyles, lipofuscin accumulation in several organs, eye cataracts, and kidney fibrosis have been described in naked mole-rats older than 26 years (Edrey et al., 2011)". A more balanced treatment of physiology in extremely old individuals would prove constructive.

Another way in which the study fails to fully represent the literature is with respect to the divergence in ageing rates between breeders and non-breeders. This pattern has proved seductive for various mole-rat researchers because of its similarities to social insects and the suggestion that it is reproduction itself which delays ageing. While this is a clear possibility with some empirical support, it is important to also consider the question from the other way: which is to ask why non-breeders die at higher rates than breeders. For other cooperative breeders such as meerkats, the answer is clear: dominant, breeding individuals evict subordinates and once evicted from the group, the chances that these individuals will survive plummets (e.g. Cram et al. 2028). Is it possible that a similar form of dominance control might contribute the shorter life span of non-breeders in captivity? You reference Toor et al. (2020) elsewhere and this is relevant here again.
Captivity also prevents non-breeders from dispersing when they would otherwise ordinarily do so (Braude 2000): is it possible that this also affects their mortality in captivity? Perhaps not being able to disperse induces chronic stress (see for example the discussion in Novikov et al. 2015). The idea that breeders show a lower intrinsic rate of aging is attractive, but many factors could contribute to this and alternatives should be considered unless they can be strongly refuted.

Lastly, it would be very beneficial to have more information on how individuals become breeders in the captive population/s. For the purposes of the analyses, individuals have been categorised as a breeder or a non-breeder based on whether they bred or not at some point in their life (i.e., they are a "breeder" for their whole life for the purposes of the Kaplan Meier curves and the estimation of mortality hazards). I think it is therefore important to rule out the possibility that only high-quality individuals become breeders and that this is what drives the contrast in breeder and non-breeder mortality. In short, is it the case that most breeders are created through the random pairing of a male and a female? Or do new breeders inherit the position once the old queen dies? The latter could lead to breeders being of generally higher quality, which might affect their mortality hazard independently of status.

Overall, I think that the authors can confidently conclude that any onset of actuarial senescence is heavily delayed in naked mole-rats, but the main conclusion that naked mole-rats "defy Gompertzian mortality" is based on inadequate evidence. It seems very possible that the inability to detect an increasing mortality hazard in such a long-lived species arises from data limitations. The central finding of the study should therefore be viewed very critically.

Refs:
Anziak et al. (2006) Aging Cell 5:463-471.
Braude et al. (2021) Biological Reviews 96: 376-293.
Cram et al. (2018) Current Biology 28: 1-6.
Edrey et al. (2011) ILAR Journal 52:41-53.
Novikov et al. (2015) Biogerontology 16: 723-732.
Toor et al. (2020) Animal Behaviour 168: 45-58.

Reviewer #2 (Public Review):

Ruby et al. investigated whether demographic aging was absent in the naked-mole rat (Heterocephalus glaber); an exceptionally long-lived small mammal that appears to challenge Gompertzian patterns of increased mortality hazard with age. In particular, this study replicates a previous one in which the authors show that the mortality hazard does not increase with age as it is expected for mammals, especially small ones. The main motivation of this replication is to address the current controversy surrounding the "perpetual neoteny" reported by the authors. The study also extends to the exploration of the role of social factors on the observed patterns in mortality hazard across age and to a meta-analysis comparing mortality hazards across species of mole-rats which highlights the unique pattern of demographic aging (or the absence of) in naked mole-rats. This study is of broad interest to readers in the field of demography, aging, and life history evolution. The key claims of the manuscript state that naked-mole rats avoid an increase in mortality hazard as they age. Although this work raises new evolutionary questions concerning the unexpected gradual (or fully absent) increase versus Gompertzian increase in hazard among mammals, I also identified weaknesses that I discuss below.

Strengths:
Sample sizes - The sample sizes across analyses are vast and the data curation described demonstrates careful thought during the data analysis processes.

Social factors - The analysis testing associations between body mass (as proxy for dominance) and colony size (as proxy for social competition) are novel and provide insights into potential evolutionary drivers for the observed lack of increase in mortality hazard.

Across species comparison - The analysis using Fukomys mole-rats offered a novel phylogenetic comparison of the mortality hazard across age and raises new evolutionary questions concerning the unexpected gradual versus Gompertzian increase in hazard. This study encourages new ones exploring alternative life histories among mammals.

Weaknesses:
Censored data - A significant number of individuals remained alive (~50%) at the end of the study, and thus I wonder how much can the authors say about increased hazard if the individuals have not reach old ages. Maybe the individuals do live long and show increased hazard are very old ages.

Independence between studies - The study provides the replication of a prior study using the same captive population, but I understand that many observations are not independent across studies given repeated measurements. Although this provides reliability, I wonder how independent the conclusions are. This represents a weakness to me because we still do not know whether this is a unique evolutionary trait of this particular captive population. If this is the case, I agree this makes the population a great model for aging studies but do the authors findings have further implications across populations or species? I wonder if populations raised under different conditions would present similar patterns of mortality hazard across age.

Analysis - Another weakness concerns the analysis used. Authors make the claims that social hierarchy may affect mortality hazards and decide to explore associations between body mass and hazard. I wonder if a Cox regression model is more appropriate for the available continuous data, relative to a Kaplan-Meir method. A Cox regression will allow the authors to control for several continuous variables simultaneously, without the limitation of categorical assumptions. A Cox model could also be extended to time-varying covariates allowing for the hazard to change over time (if that is the case). If the authors understand that their approach is equivalent, I suggest a discussion on it. This also applies to the analysis on colony size.

In summary, I see value in this study. There is vast evidence for the penalty of becoming old among mammals. Thus, studies like this one reporting novel patterns are of high impact. I agree that such findings must be replicated and validated. I also see a lot of potential for the use of the available data for more extensive meta-analyses comparing life histories across social mammals or across species with similar use of habitat (underground). Such analyses may allow the authors to move beyond descriptions and discuss why such life history traits may have evolved. Yet, I am not sure how much novelty this study brings, relative to prior studies. It seems the authors may need more than 5 years to allow their individuals to reach older ages.

Reviewer #3 (Public Review):

As a follow up from a manuscript previously published (Ruby et al. 2018), the authors use basic survival analysis methods to estimate hazard rates on an extended dataset of naked mole rats. They conclude that naked mole rats do not show the common exponential increase in mortality that has been typified in most mammals.

In fact, this species has attracted great interest due to their extreme longevity, and the physiological mechanisms that have been associated with slower aging. As the authors show, this species shows unprecedented longevity, particularly considering their body size and phylogenetic location.

However, the data available and the methods used cannot support the conclusion of an absence of increase in mortality for adults. As the authors show, the survivorship curves, calculated using Kaplan-Meier estimators, do not reach below values of 0.5. In short, nothing can be said about hazard rates after the age of median life expectancy. What the authors show is that, up to a certain age (when at least 50% of the individuals are still alive), the hazard rate is relatively constant. Beyond that age, the authors cannot draw any conclusions.

In addition, here is a summary of the methodological limitations I could find based on their limited description: 1) their survivorships do not go below 0.5 and thus cannot make any statements about actuarial senescence; 2) ignoring this last, to test whether the hazards follow a Gompertz mortality it would be more appropriate to use maximum likelihood and test alternative models (e.g., exponential, Siler), and not visually as they show in fig 1; 3) they seem to be confusing left-censoring with left-truncation; 4) given the left-truncation, they should be using product limit estimators and not Kaplan-Meier estimators (which they might, but it's not possible to know based on the limited description of the methods); 5) their treatment of the effects of colony size, breeding status, and body weight should be at least by means of a proportional hazards, not a simple visual inspection on arbitrary age intervals.

In light of these limitations, I would rank the significance of the study as not more than useful, and the strength of evidence inadequate. Still, and as I've stated above, this species is of great interest for ageing research, and the extensive work that the authors have done maintaining this captive colony is to be commended.

Author Response

We thank Dr. Carlos Isales and Dr. Jenny Tung as well as the peer Reviewers for their critiques and comments concerning this manuscript and respond here to their key concerns. Some of the Reviewers’ questions raised fascinating points about naked mole-rat biology and social habits, which we are also curious about, but which are too far afield from the central themes of the manuscript to warrant new work or revision. The Reviewers also raised some concerns about our methodological assessments and data interpretation which may warrant further discussion and explanation. We address those comments below. In no case do we feel that the concerns raised undermine our conclusions, so we have not undertaken new analyses nor revised the manuscript.

Median survival and power.

A recurring theme in these reviews is that our conclusion that naked mole-rats do not experience actuarial senescence is spurious, as it is “incomplete for younger animals and inadequate for older animals” due to Kaplan-Meier survival failing to reach median lifespan. We counter that premise, for median survival is an arbitrary threshold with no special bearing on when the Gompertzian hazard increase (onset of actuarial senescence) should become apparent. This point is well illustrated in Figure 5 of our original manuscript (Ruby et al., 2018). For demographic data from lab mice, humans, and horses (panels B, C, and D, respectively), the Gompertzian hazard increase is readily apparent by the time median survival (indicated by vertical dotted lines) is reached.

Another concern raised in the reviews is uncertainty about the true increase in power for these updated data since our 2018 report. The Reviewers correctly point out that the distribution of those data, and not just their scale, are relevant to power. The distribution of all data, old and new, are clearly illustrated as a function of age in Figure 2A. The ~doubling of available observation data is consistent across age groups, with one exception: at ~8,000-10,000 days of age. However, we do not agree that is a shortcoming of the new data’s power for hazard calculation among older animals, given that the animals that formerly occupied that age bin have continued to age, without greater hazard, across the next five years. In other words, the lack of N increase in that particular age bin is balanced by the massive increase in available data at ~10,000-12,000 days of age - an advanced age bin that was previously almost empty.

More surprisingly is the insinuation that for an approximately 40 gram rodent species, median survival on an order of 30+ years, with no sign of an increase in age-related mortality hazard, is considered a reasonable expectation. Both here and in our 2018 manuscript, we have conservatively used Tsex (180 days) as our benchmark for allometric scaling. Alternatively, one could scale this to the predicted lifespan based on average body weight for the species. According to the equation of de Magalhaes et al. (2007), the maximum lifespan of H.glaber is expected to be merely six years. Here, the Reviewers suggest that we are under-powered to make any statements about demographic aging because we have not reached median lifespan - despite the fact that our observations extend out to seven times the expected maximum lifespan. This is the precise nature of our argument that Gompertzian demographic aging is defied: that the onset of actuarial senescence is not apparent even at ages many-fold beyond when one would expect Gompertzian trends to have wiped out the entire population.

Ironically, the Reviewers seem to have focused on the most striking manifestations of Gompertzian defiance - not reaching median lifespan after decades of population observation, or having few death events after tens of thousands of days of individual lifespan observation - as reasons to doubt the conclusions. Even if we quadrupled the number of sample points and included data for another 35 years, if we still did not detect the onset of actuarial senescence, the same critiques would still apply - and would be similarly illogical.

The appropriateness of Kaplan-Meier, with left & right censorship

Objections were raised about the appropriateness of Kaplan-Meier survival analysis for our data. Reviewer #3 asserts that “a Kaplan-Meier estimator can only take right-censored and uncensored records”, which is incorrect. This perhaps reflects a wider misunderstanding of Kaplan-Meier statistics that warrants further explanation.

Reviewer #3 asserts that “left-censoring occurs when your event can be repeated and some events occur before the start of the study”. This is an oversimplified and far too-limited description of when left-censoring should be applied. We will further explain how left-censorship is applied in various analyses of our data, but for further reading on how this practice can produce unbiased estimates, we recommend the Reviewers consult (Cain et al 2011). We will discuss left and right truncation and censorship in terms of the diagram from Figure 2 of that manuscript, which illustrates a study in which the timing of event Y after event X in an individual’s life is being analyzed, given enrollment in a study at age A and exit from the study at age B. We also remind the Reviewers that methods used previously by us are in the papers (Ruby et al, 2018 & 2019) which were referenced and cited in our manuscript and should also be consulted for a full description.

For our study, ages A and B from (Cain et al 2011) are akin to the edges of our hazard estimation windows: appropriate application of censorship and truncation allows us to accurately, unbiasedly estimate hazard within each age bin, allowing fair evaluation of changes (or lack thereof) as a function of age. For full Kaplan-Meier survival, age A is uniformly defined as Tsex (day 187), and B is not globally defined - rather, it is defined for each animal if observation ended due to exit from the collection (i.e., used in research studies (KFR), donated to another researcher, or continuing to be alive at the time of the study). Since none of the Reviewers seemed confused or concerned about our use of right-censorship in these cases, we will focus this discussion on left-censorship.

In our original analysis (Ruby et al., 2018), we did not apply left-censorship because Dr. Buffenstein had maintained the animals since they were born, therefore no events occurred (i.e. observations of an animal being alive or dead on a day) prior to the beginning of the study. In the parlance of (Cain et al, 2011): we knew when the initiating event X had occurred (Tsex), and the animals had been continuously observed thereafter, up until either their death or rightcensorship point. Animals were right-censored if they were removed from the study, e.g. due to sacrifice for research or donation to other researchers. Doing so reduced the population size moving forward (to the right) without modifying the survival value, allowing the impact of individual death events to be appropriately amplified (i.e. Kaplan-Meier analysis).

For left-censored data, the same operation occurs but in reverse order: for example, if an animal is left-censored at 457 days of age, then the population size is increased by one on that day, without modifying the survival value. In Kaplan-Meier survival estimation, for each observation period, the current survival value is multiplied by the fraction of animals surviving at that time interval divided by the number of animals in the population in that interval. Since the animal in question was not observed prior to 457 days of age, it would not be counted in the population size prior to that day: had it died, it would not have been in the study population at all. However, once it has entered the population, each day-of-age on which it is observed to be alive is included in the population size tally, since each day it could also perish and thereby impact the survival curve. If any of the Reviewers received animals from Dr. Buffenstein should they wish to extend this data set in the future using those animals, left-censoring them at their age when they were received (or after some acclimation period) would be the proper method to do so.

As stated above: in our original analysis (Ruby et al., 2018), we did not generally apply leftcensorship because Dr. Buffenstein had maintained the animals since they were born (although beginning the analysis at Tsex qualifies as population-wide left-censorship). In their commentary, Dammann et al. (2019) pointed out that loss of records could modify the hazard distribution through bias towards longer-term survivors: in other words, counting long-lived animals as part of the population in early life is unfair because the death events from the truly larger population at that time had been lost (in that case: perhaps back in the 1980’s). In the parlance of (Cain et al, 2011): loss of records would have been the equivalent of left truncation, which if unchecked could produce bias. For our reply (Ruby et al., 2019), we address this problem by applying a drastic left-censoring of all animal data on a date where we could be highly confident that all records had been securely maintained, thus removing any potential bias introduced by old, lost records - as illustrated by (Cain et al, 2011). That re-analysis does not change our results, negating loss of decades-old records as a confounder of our conclusions. In this new manuscript, we used this technique again, only analyzing data collected since those data reported in our prior publications. Again, our original conclusions were confirmed: quoting Reviewer #3, “the main figures are virtually the same, with some minor changes due to the extended dataset”.

Independence between studies

In this new manuscript, with substantially more data, we applied left-censorship again in order to conduct an analysis of just the newly-provided data. Importantly, no datum - i.e. no day of observation of an animal being either alive or dead - overlapped between that analysis and those from our original reports (Ruby et al., 2018 & 19), and data were collected across nonoverlapping periods of time. Reviewer #2 questions the independence of this analysis from the original, correctly citing that it is still our own collection whose demographic data we are surveying. We reply that it is as independent of a dataset as we could possibly provide: greater independence would require the publication of substantial demographic data from other members of the H.glaber research community, which we would be happy to see. We also want to remind the Reviewers that Sherman and Jarvis (2002) also reported negligible demographic senescence for animals >15 years of age under their care: a fully-independent observation that concurs with our conclusions, albeit with substantially fewer animals and less statistical power.

“Glossing over” reports of aging phenotypes

Reviewer #1 suggests that our review of our own prior publications in this manuscript has “glossed over data that don’t support our main interpretations”, specifically mentioning the papers by Edrey et al., (2011) and Andziak et al., (2006). However, this is not an accurate reflection of the content of those published papers. The reviewer highlights data pertaining to case studies of two animals, aged 29 and 30 years, exhibiting pathologies that are commonly associated with aging in the Edrey et al., (2011) paper that was entitled “Successful aging and sustained good health in the naked mole-rat……”. But, as per the title of that paper, those were atypical cases. Indeed, we reported that the majority of animals maintained good health and activity well into their third decade. The Andziak et al., (2006) paper revealed that young (2y), healthy naked mole-rats have higher levels of oxidative damage to lipids, proteins and DNA than observed in young mice; but the follow up paper Andziak and Buffenstein (2006) reported that unlike that observed in mice, in naked mole-rats the levels of such damage do not further increase with advancing age, supporting the premise of sustained tissue homeostasis. Routine pathological assessments undertaken by our group and from zoological specimens in the 12 years since Edrey et al., (2011) have revealed many more instances of “aging phenotype pathologies” - but again, with similar frequency across all age groups (Delaney et al., 2021). We have not “glossed over data that don’t support our main interpretations”: in fact, the data brought up by the Reviewer support our conclusions. Like natural death, “age-associated disease phenotypes” occur stochastically across all age groups of H.glaber, rather than being exponentially enriched in elderly animals as in other species.

Breeding status

Reviewer #1 also states that “this study fails to fully represent the literature with respect to the divergence in aging rates between breeders and non-breeders” This section of our discussion (lines 326-367) addresses the survival advantage in many cooperative breeding mammals in the wild and in captivity including other mole-rats and meerkats (Sharp and Clutton-Brock, 2010; Dammann et al., 2011, Cram et al., 2018). The lower survival of subordinates in captivity may be due to chronic stress associated with bullying by the dominant animals and their inability to disperse and avoid such unpleasant activities; often being injured and dying after losing fights for a more dominant position in the social hierarchy. Braude et al., (2021) similarly report that compared to subordinates who undertake the more precarious activities of burrow extension, foraging or dispersal, the breeding females remain in their study site for far longer periods.

In captivity, subordinates have two paths to becoming a breeder: If the breeding female dies, some subordinate females within the colony will fight to the death to establish breeding status and inherit the dominant role in the colony. This could imply that they are “higher-quality” individuals as suggested by Reviewer #1 with molecular and physiological mechanisms in place to outlive their “poorer- quality” conspecifics. However, the majority of breeding females in our colony arise through random pairing of a female and a male that has been isolated for a few days from their colony. As such there is no selection for “higher-quality” individuals with concomitant inheritance of better somatic maintenance mechanisms. Rather, breeding status appears to be accompanied by a phenoplastic switch, as suggested by the lower levels of DNA methylation in tissues of breeding females (Horvath et al., 2021) and altered growth patterns when a female changes her status to that of a breeder (O’Riain et al., 2000). This is possibly linked to moving up the dominance hierarchy with concomitant changes in stress, somatotropic, and reproductive hormones as well as augmented tissue repair pathways for the maintenance of homeostasis.

We have not undertaken in depth studies on behavior and social habits and the effect of age, but agree these would be of interest in future studies.

Analysis initiation at 6 months

Mortality rates are highest in the first three months of life, in keeping with increased mortality during the developmental period. While it is true that in captivity most animals continue to grow for the first eighteen months to two years of life and some individuals may continue to gain weight well into their third decade, we and others have shown that animals can successfully breed at 6 months of age, if given the opportunity to do so. Other demographic studies similarly use the age at which animals can reproduce as the starting point for their analyses. Nevertheless, even if we were to use 2 years as the starting point, the same trends will be evident for there was no increase in mortality risk even at ages beyond 30 years.

Colony size effects

It is intriguing that smaller colonies had higher mortality risk than larger colonies. In many cases smaller colonies represent younger colonies with possibly less well established breeders and a higher degree of social instability. In other cases, the breeding female may not be very successful in raising her young, and possibly is not producing “high-quality” offspring. We agree with the Reviewer, behavioral assessments are needed to evaluate if there is more fighting and competition for dominance or if other social dynamics or ‘poorer-quality’ offspring are at play, nevertheless these findings are intriguing and we have speculated as to why this is the case. Further work is needed to definitively tease out why this is indeed the case.

References cited here

Andziak et al., (2006) doi: 10.1111/j.1474-9726.2006.00237

Andziak and Buffenstein (2006) doi: 10.1111/j.1474-9726.2006.00246

Braude et al., (2021) doi: 10.1111/brv.12660

Cain et al (2011) doi: 10.1093/aje/kwq481

Cram et al., (2018) doi: 10.1016/j.cub.2018.07.021

Dammann et al., (2011) doi: 10.1371/journal.pone.0018757

Dammann et al., (2019) doi:10.7554/eLife.45415

Delaney et al., (2021) doi: 10.1007/978-3-030-65943-1_15

De Magalhaes et al., (2007) doi: 10.1093/gerona/62.6.583

Edrey et al., (2011) doi: 10.1093/ilar.52.1.41

Horvath et al., (2022) doi:10.1038/s43587-021-00152-1

O’Riain et al., (2000) doi: 10.1073/pnas.97.24.13194 Ruby et al., (2018) doi: 10.7554/eLife.31157

Ruby et al., (2019) doi: 10.7554/eLife.47047.

Sharp and Clutton-Brock,(2010) doi: 10.1111/j.1365-2656.2009.01616.

Sherman and Jarvis (2002) doi: 10.1017/S0952836902001437