The longest-lived rodent, the naked mole-rat (Ctenohystrica, Heterocephalus glaber) is recognized as an animal model of biogerontological interest (Buffenstein, 2005; Austad, 2010; Edrey et al., 2011; de Magalhães et al., 2007a) with a maximal lifespan of more than 30 years in our captive care (Lewis and Buffenstein, 2016). This maximum lifespan is five-fold greater than predicted allometrically for a 40 g rodent (Edrey et al., 2011). Even in the wild, naked mole-rats are also considered to be very long-lived rodents with reports of breeding females remaining 17 years in the same colony while non-breeders remain 2–3 years (Hochberg et al., 2016). In sharp contrast, other rodents generally last only a season in the wild, with their young-age deaths attributed to predation, inclement weather, parasites, pathogens and lack of food resources (Morgen, 2003; David and Jarvis, 1985; Boonstra and Krebs, 2012; Krebs et al., 1995; Krebs et al., 1973). Laboratory mice, cosseted in a protected environment with ad libitum resources, live almost an order of magnitude longer than their wild counterparts. Nevertheless, these small mammals live only half as long as expected on the basis on body size and lifespan is limited by age-related, exponentially increasing intrinsic risk of dying (Miller et al., 2002). Similarly, the difference between captive and wild longevity records for naked mole-rats likely reflects a lower incidence of extrinsic rather than intrinsic mortality in captivity. What determines naked mole-rat lifespans in captivity is currently unknown.

The naked mole-rat is a strictly subterranean, mouse-sized rodent and is one of only two known eusocial mammals; it lives in large family groups (colonies) of up to 300 individuals (average colony size = 60). Their underground lifestyle in the arid and semi-arid regions of sub-Saharan Africa poses numerous ecological and physiological challenges, such as difficulty locating food underground, impaired heat and gas exchange, low oxygen availability, and exposure to heavy metals and other chemicals in soil and plant-defense toxins (Buffenstein, 2000). But this milieu also protects against dangers such as predation and above-ground climate extremes (e.g., cold, wind and rain), thereby providing several survival advantages (Buffenstein, 2005).

Breeding in each colony is monopolized by only one female (the ‘queen’) and 1 to 3 males at a time, with most animals in the colony showing no sexual behaviors throughout their life, but rather helping with the overall maintenance and survival of the colony, including care of pups (Jarvis, 1981). Queen status is primarily maintained through physical intimidation of subordinates and should the queen die or a non-reproductive subordinate be removed from the colony, subordinates can become reproductively active (Clarke and Faulkes, 1997). Attainment of breeder-status for either sex, regardless of age, is accompanied by morphological, physiological and behavioral changes, including changes in body size, brain volume and reproductive organ morphology (O'Riain et al., 2000; Holmes et al., 2007; Peroulakis et al., 2002). These differences are pronounced and obvious in the breeding female (O'Riain et al., 2000).

While the underlying determinants of species’ longevity remain unknown, several physiological traits correlate with longevity (Harvey and Purvis, 1999). Across vertebrates, adult body mass is a strong correlate, with larger species living longer than smaller species. Naked mole-rats live exceptionally long vis-à-vis this metric: almost five-fold longer than expected (Hulbert et al., 2007). Species’ ages of reproductive maturity (T_sex) are also predictive of their lifespans (Hamilton, 1966; Rose et al., 2007; Prothero, 1993). The definition of T_sex is more nuanced than that of body weight: ambiguity exists around how the age of sexual maturity should be marked, whether T_sex should include gestation time, and how T_sex relates to other developmental milestones. T_sex also lacks independence from both body weight and phylogeny. Nonetheless, it retains predictive power even when those variables and nuances are taken into account (de Magalhães et al., 2007b). Relative to T_sex, naked mole-rats are once again long-lived outliers: despite a long gestation length (66–76 days) and a six-month elapse from birth to reproductive capacity (Edrey et al., 2011), they live over three-fold longer than expected by this metric (de Magalhães et al., 2007b).

Beyond lifespan, the physiological declines that accompany advancing age in most mammals fail to manifest in naked mole-rats (Buffenstein, 2008). Breeding females show no menopause, retaining high fertility even at ages past 30 years (Lewis and Buffenstein, 2016). Neurogenesis is also prolonged and may continue for at least two decades (Holmes, 2016), and over a similar time course, no significant changes in cardiac function (Grimes et al., 2014), body composition, bone quality, and metabolism (O'Connor et al., 2002) are evident. Age-associated chronic diseases such as cancer are also rare (Edrey et al., 2011; Lewis and Buffenstein, 2016). Within the cell, proteasome function, as well as mitochondrial mass, gene and protein expression are maintained with age (Pérez et al., 2009; Kim et al., 2011). These molecular and physiological observations reflect broader phylogenic trends with respect to mortality and life history traits: species from safer habitats tend to live longer; those from more dangerous habitats tend to mature rapidly, reproduce early and die young (Ricklefs, 1998; Pianka, 1970).

The concepts of mortality and physiological decline associated with aging can be connected within the mathematical framework of the Gompertz-Makeham law of mortality (Gavrilov and Gavrilova, 1991). Age-specific hazard h(t) is defined by the equation h(t) = αe^βt + γ. The first term (αe^βt) describes the Gompertzian component of hazard, originally derived from examination of human life tables (Gompertz, 1825). This hazard increases exponentially with age, presumably due to intrinsic age-related physiological declines. In this framework, β defines the rate-of-aging with respect to mortality: its value determines the doubling time for mortal hazard (for humans, ~7–8.5 years; [Finch et al., 1990]). The second term (γ) describes the Makeham component: a constant, extrinsically-imposed minimum hazard that can obfuscate Gompertzian hazard at younger ages (Makeham, 1860). The coefficient of the Gompertz term (α) influences the age at which intrinsic hazard overtakes extrinsic hazard.

While naked mole-rats are already noted as exceptionally long-lived (Buffenstein and Jarvis, 2002), this status relies on small-sample-based estimates, leaving much uncertainty as to how exceptional their longevity may truly be and how they differ from other mammals with respect to the Gompertz-Makeham aging framework. Here, we compiled a large, historical dataset of naked mole-rat lifespans using records kept throughout the ~35 year maintenance of our collection (described in [Edrey et al., 2011]). With over 3000 data points, we constructed survival curves and performed analyses of age-specific hazard. In these analyses, this mouse-sized rodent exhibited no increase in mortality hazard, that is, no Gompertzian aging, across its full, as-yet-observed, multi-decade lifespan. This life-history trend is unprecedented for mammals.

Aging, defined as the inevitable physiological decline over the lifespan of an organism that weakens homeostasis and increases vulnerability to environmental challenge, is typically observable in mammals in the form of an increase in mortality hazard as organisms get older. A decrease in the rise-rate of hazard has been reported in multiple studies involving experimental interventions that extend lifespan (e.g., caloric restriction), and is consistently interpreted as a slowing of aging itself (Fok et al., 2014; Yen and Mobbs, 2008; Simons et al., 2013). By that metric, ‘aging’ was not observed at all in our analysis of naked mole-rat mortality, regardless of sex or breeding status. This apparent lack-of-aging agrees thematically with a large body of literature documenting negligible systems-based senescence in naked mole-rats (Edrey et al., 2011; Buffenstein, 2008). It places this species in a unique demographic position among mammals: as mammals get older, even long-lived species conform to Gompertzian laws of mortality (Jones et al., 2014; Cohen, 2017).

Delayed (as opposed to non-existent) Gompertzian aging possibly could also explain our observations. The non-increasing hazard could have simply reflected the Makeham component of the Gompertz-Makeham law, a background level of extrinsic hazard that obscures Gompertzian intrinsic hazard early in life. Such a model describes human mortality until age ~40 years (Bell and Miller, 2005) (Figure 5C) and horse mortality until age ~6 years (Figure 5D). We cannot reject the possibility of an as-yet-undetectable Gompertzian component to naked mole-rat mortality. And in fact, this alternative model is not formally falsifiable: any observational extension of constant hazard would simply delay the earliest point at which Gompertzian hazard might take effect. However, given the extremely low baseline hazard rate of 1/10,000 per day for non-breeders and ~1/100,000 for breeders, it seems unlikely that the Gompertzian hazard is being overwhelmed. But even under a delayed-aging model, naked mole-rats profoundly distinguish themselves from other mammals: in this context, through an unprecedentedly-long adulthood prior to the emergence of Gompertzian hazard.

Indeed, naked mole-rat mortality was less consistent with a typical Gompertz model of hazard than it was with an exponential decay model, with a constant probability of decay (death) defining a species’ half-life. For naked mole-rats, even the high estimate for per-day hazard of ~1/10,000 that was obtained for non-breeders (Figure 3A) would correspond to a half-life (i.e., median lifespan) of ~6900 days (19 years). Under an exponential decay model, the concept of a ‘maximal lifespan’ loses relevance: at no point does mortality hazard grow into an insurmountable obstacle. One could try and force the concept of ‘maximal lifespan’ onto an exponentially-decaying species by defining it in terms of a high percentile of lifespan (say, 95%) – and by that definition, the maximal lifespan of the naked mole-rat would be very long indeed! But that definition ignores the implicit meaning of the term: as an age beyond which biological wear and damage has become insurmountable.

Demographic aging is defined by the increase of intrinsic hazard with age (Gavrilov and Gavrilova, 2015). Our analyses of captive naked mole-rats confidently revealed a lack of demographic aging up to at least 4400 days of life (~12 years) and strongly suggested no demographic aging far beyond that age (Figure 1 and 2). That twelve year stretch of time can be considered from several perspectives. In Figure 5, it is considered from the perspective of T_sex, that is the minimum lifespan allowable for an organism to reproduce. Most mammals live beyond that age, as is required to provide progeny with support and nurturing (Lee, 2003), but show signs of demographic aging within a few fold of T_sex; from this perspective, the naked mole-rat is exceptional, showing no signs of demographic aging many dozens-of-fold beyond T_sex (Figure 5). Twelve years can also be considered in the context of the expected total lifespan of a naked mole-rat based on its body size (de Magalhães et al., 2007b): this 35-gram rodent would be expected to live up to six years, but instead has not shown the first sign of demographic aging at twice that age. Twelve years could finally be considered from the perspective of natural lifespan in the wild, which is estimated to be 2–3 years for the naked mole-rat (Hochberg et al., 2016).

Senescence is difficult to observe in wild rodent populations (David and Jarvis, 1985; Krebs et al., 1995; Krebs et al., 1973; Slade, 1995) with most rodents living less than a year (Stueck and Barrett, 1978) Nonetheless, senescence is easily observed for those rodent species (rats and mice) in captivity, not far beyond their typical natural lifespans (Figure 5B; [Gavrilova and Gavrilov, 2015]). For the naked mole-rat, demographic aging is absent 4-to-6-fold beyond their natural lifespans.

In summary, naked mole-rats fail to exhibit any evidence for intrinsic hazard contributing to their mortality, even at ages far beyond their expected maximum lifespans based on multiple other aspects of their biology or their full lifespans observed in the wild. In doing so, they establish themselves as a non-aging mammal.

The progenitors of the naked mole-rats used in this study were collected by Jennifer Jarvis, Kate Davies, Mike Griffin and Rochelle Buffenstein in Kenya in 1980 and have been housed and cared for at several institutions in South Africa (University of Cape Town and The Medical School of the University of the Witwatersrand) and the USA (City College of New York, University of Texas Health Center at San Antonio and the Buck Institute). Naked mole-rats were housed in multi-chambered plexiglass burrow systems in rooms maintained at 28–30°C and 30–50% relative humidity, in keeping with climatic conditions in their native habitat. The animals were fed ad-libitum with fruit and vegetables (bananas, apples, oranges, butternut squash, red bell pepper, romaine lettuce, cucumber, green beans, corn, carrots and red garnet yams) and supplemented with a high protein and vitamin enriched cereal (Pronutro, South Africa).

At 90 days of age, individual mole-rats were sexed, weighed and microchipped, using 12 mm Avid MUSICC microchips, and thereby assigned a unique 9-digit identifier. The microchips were implanted just underneath the dorsal skin in non-anesthetized animals. Thereafter, all animals were weighed regularly at 3 month intervals.

Animal welfare checks were conducted daily. Animals deaths observed during these checks were recorded, the individuals identified from their microchips and necropsies performed. Records were aggregated into three spreadsheets. For each spreadsheet, the dates-of-censorship for naked mole-rats currently alive and in the collection were set to the date of completion for the spreadsheet in which they were recorded (April 14, 2016; April 20, 2016; and May 17, 2016). Those three spreadsheets are provided as a single file (Supplementary file 1), with the date of compilation indicated. Censorship status was additionally applied to ‘dead’ animals labeled as ‘SOLD/GIVEN AWAY’ (409 animals) or ‘KFR’ (killed for research; 867 animals). Lifespan was calculated in days as the difference between the two specified dates, using the python ‘datetime’ module. Animals with dates of birth or death/censorship with less-than-single-day-resolution (e.g., month- or year-of-birth available) were excluded from the initial analysis and from analyses based on sex and breeding status, but were included in the ‘expanded’ analyses from Figure 2. Animal-by-animal data is provided in Supplementary file 1 (see Legend for details).

For our first expanded analysis, we included data that was only recorded at month-resolution (blue, Figure 2A and B). We used the 15th day of each month as our midpoint ‘guess’. Month-of-birth was reported for 38 individuals. For an additional 22, approximate month-of-birth was recorded: we treated these the same as unambiguously recorded month-of-birth. For one individual, month-of-death was reported. Of those 61 animals added to our dataset, 19 died and 42 were right-censored.

For our second expanded analysis, in addition to the 61 animals from above, we included 139 more animals with lower-resolution data or other modalities of ambiguity (yellow, Figure 2A and B). For two animals, year and season of birth was recorded, in both cases as ‘Fall’. We used November 7 as the seasonal mid-point of Fall. For 36 individuals, ranges of possible dates were given, with the endpoints given at the resolution of years for 24 of those. For each range, we took the middle date of the full timespan described by the range. The year-of-birth alone was recorded for 40 individuals: we used July 2 as the year mid-point. For an additional 57 animals, an approximate year was recorded: we treated those in the same manner as specific years. Two optional dates were provided for four individuals: we treated each of these as a range, using the mid-point between the two options. Of those 139 animals added to our dataset, 28 died and 111 were right-censored. Including the 61 added above (200 animals added in total versus the original analysis), 47 died and 153 were right-censored.

For our third expanded analysis, in addition to the 200 animals from above, we added 69 animals for which birth was recorded as occurring either before or after a date, month, or year (cyan, Figure 2A and B). This is the worst-case scenario in terms of data reliability: the indicated time-of-birth was un-bounded in one direction (or bounded by the present), making it impossible to assign an average of the possibilities as was the case for ranges. Nonetheless, to include these animals in the analysis, we used the closest date satisfying each inequality (e.g. treating ‘>1997’ as January 1, 1998). Of those 69 animals added to our dataset, 8 died and 61 were right-censored. Including the 200 added above (269 animals added total versus the original analysis), 55 died and 214 were right-censored.

For Figures 1–4, survival was calculated using the Kaplan-Meier method (Kaplan and Meier, 1958). For Figures 1–3, mortality hazard for each block of days/group of animals was calculated as the number of observed death events (i.e., number of days on which a naked mole-rat was observed to have died) divided by the total number of days that naked mole-rats were under observation (for individuals who were alive across an entire interval: the number of days in the block; for individuals who died or were censored during a block: the number of days in the block prior to and including the death/censorship event). Confidence intervals were calculated using the Wilson score interval with continuity correction (Newcombe, 1998).

For naked mole-rats in Figure 5A, hazards were calculated as described above across non-overlapping 200 day windows, starting at day 200. Hazard was also calculated across the shorter interval between the day of reproductive maturity and the beginning of the first full window (days 183–199). For mice in Figure 5B, the same method was applied to non-overlapping 50 day windows starting at day 50, with hazard additionally calculated for the partial window starting at reproductive maturity (days 42–49). Mouse data was the combined male-and-female control-mouse survival data reported by Miller (Miller et al., 2014), collected for the NIA Intervention Testing Program (Miller et al., 2007; Nadon et al., 2008). Raw data for control mice used in Figure 5 (Miller et al., 2014) was provided by the authors.

A model for survival for breeders versus non-breeders was constructed by calculating the hazards for death or censorship using data from either females-only or males-and-females, and for windows of age, as-specified in Figure 4A. Mortality hazard was calculated as described above; censorship hazard was calculated as described for mortality hazard but reversing the treatment of censorship versus death events.

Lifespan simulations were performed using custom python scripts. For each simulation, an initial population was created with the indicated-in-the-figure number of breeders and non-breeders. For each day starting at day 183 (i.e. T_sex), for each surviving and uncensored individual, a pseudo-random float in the half-open interval [0.0, 1.0) was generated using the python ‘random’ module. If that number was less than the probability of censorship given breeding-status and day-of-life, the individual was marked as ‘censored’ on that day and removed from the population. Otherwise, a second pseudo-random float was generated: if that number was less than the probability of death given breeding-status and day-of-life, the individual was marked as ‘died’ on that day and removed from the population. The simulation continued until the population had been exhausted or day 12,000 was reached, in which case all surviving individuals were marked as ‘censored’ on that day.

Parameters of our model are provided in Supplementary file 2. The exact demographic data for panels B-E of Figure 4 (100 simulations per panel) are provided as Supplementary file 3–6, respectively. A python script for running additional simulations as described above is provided as Supplemental Python Script.

For human in Figure 5C, hazards were plotted as calculated and reported for females of the 1900 birth cohort by Bell and Miller (Bell and Miller, 2005). For horse in Figure 5D, hazards were calculated using two insurance life-tables from Valgren (Valgren, 1945): data from Table 1 and 2 were combined, and hazard estimated as the total dead divided by the total insured for each year-of-life. Median and percentile survivals were calculated through iterative multiplication of age-specific survival (one minus age-specific hazard), starting at T_sex.

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Author details

1. J Graham Ruby

   Calico Life Sciences LLC, South San Francisco, United States

   Contribution

   Conceptualization, Data curation, Formal analysis, Visualization, Writing—original draft, Writing—review and editing

   Competing interests

   The research was funded by Calico Life Sciences LLC, where all authors were employees at the time the study was conducted. The authors declare no other competing financial interests

2. Megan Smith

   Calico Life Sciences LLC, South San Francisco, United States

   Contribution

   Data curation, Investigation

   Competing interests

   Megan Smith: The research was funded by Calico Life Sciences LLC, where all authors were employees at the time the study was conducted. The authors declare no other competing financial interests

3. Rochelle Buffenstein

   Calico Life Sciences LLC, South San Francisco, United States

   Contribution

   Conceptualization, Resources, Data curation, Supervision, Investigation, Methodology, Writing—original draft, Project administration, Writing—review and editing

   For correspondence

   rbuffen@calicolabs.com

   Competing interests

   Rochelle Buffenstein: The research was funded by Calico Life Sciences LLC, where all authors were employees at the time the study was conducted. The authors declare no other competing financial interests

   "This ORCID iD identifies the author of this article:" 0000-0003-3285-8311

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