Abstract
Most living organisms age, as determined by species-specific limits to lifespan1–6. The biological driving force for a genetically-defined limit on the lifespan of a given species (herein called “lifespan setpoint”) remains poorly understood. Here we present mathematical models suggesting that an upper limit of individual lifespans protects their cohort population from infection-associated penalties. A shorter lifespan setpoint helps control pathogen spread within a population, prevents the establishment and progression of infections, and accelerates pathogen clearance from the population when compared to populations with long-lived individuals. Strikingly, shorter-living variants efficiently displace longer-living individuals in populations that are exposed to pathogens and exist in spatially structured niches. The beneficial effects of shorter lifespan setpoints are even more evident in the context of zoonotic transmissions, where pathogens undergo adaptation to a new host. We submit that the selective pressure of infectious disease provides an evolutionary driving force to limit individual lifespan setpoints after reproductive maturity to secure its kin’s fitness. Our findings have important public health implications for efforts to extend human’s lifespan.
As early as 18891, theories attempted to explain the evolution of the paradoxical phenomenon of aging2–5. The majority of theories can be organized in two classes. Non-optimality2 theories argue that aging is an inevitable property of life due to somatic6 or genetic7 damage. Whereas optimality theories propose that aging results from the trade-off between maintenance and reproduction (disposable soma theory)8, or that aging is neutral because extrinsic causes of death precede the lifespan setpoints (selection shadow)7. Further, aging has also been proposed to result from detrimental side effects of genes that are beneficial in early stages of development (antagonistic pleiotropy)9. Additional theories proposing that aging itself is adaptive have not been well supported by either theoretical or experimental evidence5.
Taking together these theories are consistent with many lifespan phenomena, however each of them, if taken individually, only explain a subset of observations. For example, the existence of single gene mutations that individually can extend lifespan10 is not consistent with non-optimality theories given that both somatic or genetic inevitable damages are unlikely to be controlled by a single “master” gene. On the other hand the current optimality theories cannot explain why the ecological cases that favor the biological immortality are so infrequent, that it is almost never observed. If aging itself is adaptive, and therefore genetically programmed, immortal individuals should be detected due to mutations in genes responsible for aging mechanisms. Another general problem with adaptive aging theories – benefits from individual’s death allocated to its kin should exceed the price of its own life. Some examples of abnormally long-living species (e.g. tuatara, bowhead whale, proteus) can be explained by most existing theories, while some (birds, bats, naked mole rats) – only by few of them (see Extended Data Table 1 for detailed discussion). Attempts to integrate different aging concepts did not yet resulted in a comprehensive unifying theory4. Here we propose a kin-selection evolutionary theory, whereby limiting the lifespan-setpoints of a population provides a selective advantage that helps control the impact of infectious diseases and reduces the likelihood of zoonotic transmission where pathogen adaptation to a new host is required to establish epidemics. The theory proposed here is general in the sense that explains the majority of the lifespan-related phenomena (Extended Data Table 1), provides a rational for the absence of immortal organisms, as well as how specific lifespan setpoints are selected to benefit individual kin.
To examine whether lifespan setpoints are linked to protection from infection, we developed a agent-based in silico model that incorporates lifespan into a previously developed host-pathogen theoretical framework11. In the initial simulation experiments, we considered populations of individuals with a range of defined lifespans. Time units we use are arbitrary and might reflect days, months or years depending on a given organism. All of our conclusions are nicely scalable along the time axis since pathogens tune the length of their life cycles according to the host’s longevity. These were exposed to ten pathogen species that are able to infect susceptible individuals independently of each other (Fig. 1, Extended Data Fig. 1). For simplicity, efficiency of transmission and the fitness penalty produced by each of these ten pathogens were assumed to be identical. The fitness of each infected individual declined gradually up to a 20% maximum penalty for a single pathogen infection. Therefore, an individual’s fitness was reduced to zero if infected with five pathogens (20×5=100), leading to its death. The model assumes that there are no other reasons for death except disease caused by infection or reaching the maximum age span, there is no recovery from diseases, neither vertical pathogen transmission. In addition, an individual’s reproduction efficiency is set to correlate linearly with its fitness, i.e. uninfected individuals have more progeny (Fig. 1a). We also assumed a maximum population number for a single ecological niche of ten thousand individuals. Infection efficiency depends directly of density of individuals in a population, which is deemed to be uniform and ideally mixed using previously described conditions11. The model examines the effect of different pathogen transmission rates and assumes that pathogens are never fully eliminated from the system: when the last infected host dies, pathogens are reintroduced from another host species or from the environment. In this manner, our model not only considers the progression of existing infections, but also acquisition of new epidemics. Using this model and starting from an uninfected population, we observe that both the population size and the number of pathogens fluctuate in cycles, until an equilibrium is reached overtime (Fig. 1b, c), consistent with previous models and simulations11. The oscillation can be rationalized in terms of infected individuals dying reducing the availability of uninfected hosts. We monitored the number of individuals in the population and the pathogen load, as well as the total population fitness calculated as the sum of the fitness of all its members.
We initially analyzed whether different lifespan setpoints impact the total fitness of populations upon infection. We examined pathogens with different transmission efficiencies (β) and individuals with different arbitrary lifespans (A). Total population fitness captured after reaching equilibrium was plotted as a function of lifespan and pathogen transmission efficiency (Fig. 1d, 1e). All lifespan ranges (excluding the biologically immortal control) were indistinguishable with respect to fitness when the pathogen transmission efficiency was very low (Fig. 1e, β = 0.005 to 0.01)). Interestingly, at slightly higher, but still low, pathogen transmission rates (β = 0.015 to 0.045), fitness of the population was negatively correlated with longer lifespans (Fig. 1d, e). Individuals with the longest lifespans render the population more susceptible to poorly transmitted pathogens, compared with a population of individuals with shorter lifespans (Fig. 1d, asterisk). Thus, as individual lifespan shortens, population fitness increases (Fig. 1d, red zone) when faced with low transmission infections. This analysis suggests that longevity decreases population fitness due to the increased susceptibility to epidemics outbreaks (Extended Data Fig. 2c).
An analytic solution to the model also supports these conclusions. The basic requirement for pathogens to spread in the population is that the number of susceptible individuals infected by pathogens shed by a single infected host (herein R0) – should exceed 1. R0 can be expressed as transmission efficiency (β) multiplied by duration of the infection, which we initially assumed to average half of the host lifespan . For simplicity, the population density-related component is considered to be 1 and it is omitted from the calculations. The interdependence or demonstrates that the establishment of infection at low transmission efficiencies is determined by lifespan (Fig. 1f). If the lifespan is shorter than the time required for transmission, pathogens are unable to establish an epidemic. Thus, populations composed of shorter-lived individuals are expected to be more protected from invasion of pathogens, particularly if pathogens have lower transmission rates (β = 0.005 to 0.045). These results suggest that the benefit of a limited lifespan is to protect populations from low or moderately transmissible diseases that establish persistent infections; for humans many such persistent infections are common, including AIDS, hepatitis B and C, leprosy, herpes, tuberculosis, and helminths.
Even if an epidemic is established, i.e. when pathogen transmission efficiency becomes high (β = 0.1 to 0.24), populations with shorter-lived individuals also experience a fitness benefit arising from the metastability of host and pathogen populations (Fig. 1d, e, light blue zones highlighted as “metastable populations”). The benefit results from the significant reduction in host population density caused by rapid spread of the infection, which, when combined with shorter lifespans, leads to a dramatic decline in pathogen numbers thereby allowing the population to recover from infection (Extended Data Fig. 3e-f).
Populations often migrate to colonize new environments. To further study the role of lifespan setpoints in controlling infection, we next examined the relationship between lifespan and pathogen load in the case of host populations dispersing to a new environment. In our modified simulation and analytical models, dispersal involves extreme population size reduction, “bottlenecking”12, whereby a small group (10) of random individuals from infected population colonize the new environment (Fig. 2a, b). Under these conditions, since the population density is low, pathogens will not spread efficiently soon after migration. The model predicts that in populations with shorter lifespans, the infected founders will die before the population density has reached a level that allows for efficient transmission. Consequently, populations composed by shorter lifespan individuals more efficiently clear pathogen than populations composed of longer-lived individuals (Fig. 2b-f). Of note, clearance efficiency also depends on the basal fecundity rate (B-number of progeny produced by 100% fit individual per time unit). Populations with highly fecund individuals will reach high densities faster and, thus, the probability of pathogen spread in a population by infected founders will increase accordingly (Fig. 2g, Extended Data Fig. 3h, i).
We also observed a minor positive effect of lifespan limitation on the fitness of highly infected populations as shown previously13,14. Since older animals possess more chronic pathogens than younger ones, their removal could increase the total population fitness (Fig. 1d, diamonds, 1e, “epidemics reduced”; Extended Data Fig. 3a-d). Importantly, our model suggests that this is a minor effect, compared to the more significant consequences resulting from epidemics prevention and pathogen clearance following host population bottleneck dispersal (Fig. 1d-f, and Fig. 2).
Individuals that live longer should reproduce for longer times and be more effective in passing on their genes. Thus, the evolution of traits that limit lifespan, common to most organisms, is counter-intuitive. We thus examined the whether long-living variants can displace a population of short-living individuals. To this end, we modified our simulation to allow for variants with a very long lifespan (A=∞) to emerge in a population of individuals with a defined lifespan (e.g. A=60). Under conditions where all individuals in a population intermix evenly, and thus long and short lifespan individuals have equal probabilities to interact with each other, the longer-living variants efficiently outcompete shorter-living individuals (Fig. 3b), even if this leads to establishment of epidemics (Extended Data Fig. 4a). However, under conditions of severe epidemics, premature death caused by pathogens equilibrated the number of short and long-lifespan individuals, thus limiting the advantage of long-lived variants (Fig. 3c, blue zone, Extended Data Fig. 4b, c). Populations located in the region of parametric space with short lifespan-associated benefits, i.e. the region where epidemics can’t get established and metastable populations (Fig. 1e), were susceptible to displacement by longer-living individuals (Fig. 3c, Extended Data Fig. 4b, c, area below the dashed line). Thus, in ideally mixed populations long-living variants will displace short-living individuals.
The conclusions are different when populations are composed of sub-populations or clusters that are spatially separated, for instance by living in different niches. These spatially separated sub-populations may interact by exchanging individual members that move from one sub-population to another. We studied competition between longer-lived and shorter-lived organisms in this context of clustered populations, by modifying our model and introducing barriers between subpopulations (Fig. 3, Extended Data Fig 5). We based our analysis on a previously proposed computational model used to explain the seemingly altruistic effect of programmed cell death in unicellular organisms15. We observe that in the context of infection of clustered populations, the shorter-lived individuals outcompete long-lived variants. As a result of infection, the density of individuals in uninfected clusters is higher than in infected clusters. Accordingly, uninfected individuals from overcrowded clusters are more likely to migrate to infected clusters where the density is lower. This “asymmetric dispersal” model proposes that the direction of dispersal indirectly depends on the fitness of the individuals in a given cluster, which is linked to infection (Fig. 3a).
Using this model, we initially performed a source-sink density-dependent dispersal simulation16,17 consisting of a 10 x10 grid of niches with capacities for three hundreds individuals each (Extended Data Fig. 5b). We introduced additional fitness penalties on reproduction to simulate the overpopulation effects and density pressures more adequately (Extended Data Fig. 5a for details). As mentioned, asymmetry in population densities between clusters forces migration of individuals from high density niches to a less populated cluster. At the start of the experiment all clusters were populated with individuals of a given limited longevity. Then a small group of long-lived (A=∞) mutants was introduced into one of the central clusters (Fig. 3d, e, Extended Data Fig. 5b) and the competition between genotypes was simulated. Our analysis revealed that when pathogen activity is low (β=0.005) (Fig. 3d) long-lived mutants displace the short-lived individuals with efficiencies comparable to those in uniform populations (Fig. 3b). If we examine this process considering density-independent dispersal, with individuals migrating at a high frequency (e.g. birds or bats, Fig. 3f, mobility 10−1), we find that clusters behave as a well mixed environment (similar to Fig. 3b-d). Thus, longer lifespan will also be selected in populations of highly mobile individuals (Fig. 3f, Extended Data Mov. 1). In contrast, when we consider a density-dependent dispersal under higher pathogen transmissibility conditions (β=0.03), shorter lifespan individuals displace long-lived variants (Fig. 3e, Extended Data Mov. 1). Our analysis further revealed an area where the short lifespan is beneficial and long-living strains are not able to prevail (Fig. 3g, *). Our model also suggest that upon infection, the emergence of longer-lived mutants also leads to extinction of the shorter-lived individuals in that cluster (Fig. 3e, dashed with yellow); as a result, the generation of longer lived mutants is detrimental to all individuals within the cluster.
We next examined the role of fertility. Asymmetry in population numbers between healthy short-lived and infected long-lived population strongly depends on their fecundity (Fig. 3h-j). Thus, using deterministic equations (Fig 3h), we modeled growth of short-lived and longer-lived populations with arbitrarily distinct birth rates (B). We propose that short-lived individuals outcompete long-lived ones in a birth rate-dependent manner, because high fertility allows asymmetry in density between clusters to develop more rapidly (Fig. 3i). We further propose the existence of an equilibrium when the population growth of healthy short-lived individuals approach that of infected long-lived individuals (Fig 3j, black circle). Our model predicts a simple interdependence between fecundity, lifespan and pathogen effects on fitness (P) (Fig. 3j, equation). This dependency, together with fecundity effects during bottleneck dispersal (Fig. 2g, Extended Data Fig. 3h, i) explains the negative correlation between longevity and fecundity, as previously proposed in the context of the disposable soma theory8.
An important source of new pathogens in natural populations is the horizontal transmission between species, also called zoonotic transmission. The species-to-species barrier often requires that pathogens undergo several cycles of replication in the new hosts before adapting and gaining optimal transmissibility (Fig. 4a). We next considered how longevity impacts the ability of zoonotic infections to become established in a population, by modeling how populations with short-lived or long lived individuals influence pathogen adaptation to the host. We used a model similar to that used in Fig. 1e, with the exception that the pathogens are initially attenuated with a 10-fold transmissibility reduction; adaptation requires the pathogen to be passaged between ten host individuals to reach higher transmission efficiency. Under these “zoonotic infection” conditions, we observed that the range of efficiency of pathogen transmission in which epidemics cannot get established is increased dramatically for populations with shorter lifespan individuals (Fig 4b zone below the dashed line), while the invasion of populations with long-living mutants (A=∞) remains unaffected (Fig. 4c). This suggests that the advantage of short lifespan is particularly important in the context of zoonotic epidemics. Thus, our model suggests that asymmetric dispersal and pathogen adaptation to a new host are two critical factors enhancing the benefits and evolutionary stability of shorter lifespan.
Taken together, our analyses indicate that host–pathogen coexistence and coevolution played a key role in determining the lifespan setpoints of a species. A population of longer-lived individuals is more susceptible to introduction of pathogens from other species, less effective to clear the infection following bottlenecking, and is less fit than a population of shorter-lived individuals when epidemics progress. Extension of the lifespan setpoint is beneficial only in the absence of pathogens, which for most species is not a realistic scenario in an evolutionary context. However, tolerance to pathogens (e.g. in bats) might alleviate selection pressure resulting in expansion of lifespan. The asymmetric dispersal from uninfected highly populated niches to infected less populated ones disfavors the emergence of longer lived individuals (Fig. 3). A series of asymmetric dispersal events should then lead to fixation of lifespan-setpoints optimized for the elimination of pathogens from a given population. Importantly, during epidemic outbreaks following asymmetric dispersal, we find that longer-lived individuals place even shorter-living individuals in the same cluster under the risk of extinction (Fig. 3e). Thus, infection is likely to be a major evolutionary force dictating the puzzling near-absence of immortal or extremely long-living individuals in nature. Indeed, subpopulations able to produce such long-lived variants are exposed to the catastrophic risk of being decimated during outbreaks. We thus conclude that lifespan of a species is a result of a trade-off between the pressure produced by pathogens and the pressure towards life extension and fecundity.
It is now generally accepted that host-pathogen interactions constitute major driving force during evolution18. The limitation of lifespan, leading to aging, may be one of the earliest and more robust population-level defense mechanisms against the spread of new pathogens and clearance of those that have been already established. A crucial role in the evolution of lifespan may be played by chronic low-transmissible diseases that persist for a significant part of a host’s life and cannot be cleared by immune system. A major selective pressure towards shorter lifespans may also arise from prospective pathogens that are present in the environment but did not yet adapted to a given hosts or established epidemics.
Our work does not negate but complement and extend previous evolutionary theories of aging. For example, our model is consistent with selection shadow and antagonistic pleiotropy theories (Fig 4d, Extended Data Table 1). However, we identify host-pathogen interactions as a major selective pressure driving evolution of lifespan setpoints. It should be also emphasized that our study does not invoke group selection19, but rather proposes the selection of shorter lifespan depends on the inclusive fitness of the individuals in the context of the population. Hence we consider evolution of lifespan a kin selection strategy that favors the reproductive success of an organism's relatives, even at a cost to the organism's own survival. Finally, considering lifespan termination as an adaptive trait, our theory does not provide mechanistic insights of aging. The lifespan setpoints likely exploit similar mechanisms across different species, such as the modulation of DNA and protein damage responses, stress responses and senescence pathways6,20–22.
Research on aging, searching for lifespan determinants may lead to an effective increase in human and animal lifespans. Our ability to describe and model aging as an evolutionary process linked to infection, provides a new paradigm to identify lifespan mechanistic programs which can be prevented or even reverted. On the other hand, our theory also alerts to potential epidemiological risks associated with extended lifespan (Extended Data Fig. 6h). Conversely development of efficient mechanisms to limit or tolerate infections weakens the evolutional pressure towards lifespan shortening. We propose this as an explanation for abnormal longevity in bats, mole rats (Extended Data Tables 1) and humans.
Methods
Data collection and presentation
All simulation scripts were coded and compiled with Python 2.7 (Python Software Foundation). Data was plotted with Excel (Microsoft) and MatLab (Mathworks).
Models
While our infectious catastrophe theory is well supported by previously published empirical evidence (see Extended Data Table 1a), this manuscript does not include any original experimental data supporting its predictions. Therefore it is crucial to demonstrate that our models are adequate and the values of parameters we use are realistic.
Our models are based on classical host-pathogen interaction models1, adapted to agent-based simulations to better account for the individual life-history effects on how epidemics proceed. The basic algorithm is presented in Extended Data Fig. 1. The values and main processes are listed in Extended Data Table 2a, b.
The host’s population sizes we used (10 thousand individuals in uniform simulations and 300×100=30000 in clustered metapopulations) were big enough to exclude any effect of stochastic factors on our final results.
In the beginning of simulations the niches were filled with maximum number of individuals with randomly generated ages (a) and replication values (r). Generation of uniformly distributed random numbers in all cases was performed with random.py Python library (Python Software Foundation) which uses standard Mersenne Twister algorithm.
Host’s reproduction was simulated the following way. Each round a value has been added to the replication value in each host: where B is birth rate (0.05 in all simulations, 0.075 and 0.1 in Extended Data Fig. 3h, i) and f-individual’s fitness (fmax=100 for an uninfected animal). When r was reaching value of rmax=100, the individual gave birth to another genetically identical individual. r of both parent and daughter individuals were set to zero. One generation of healthy individuals in typical simulation could therefore be calculated as:
arbitrary time units. New born animal was always considered to be uninfected. If population has reached its maximum (Nmax) in simulations of uniform populations, the newborns were considered to be aborted or expelled, while the r of the parental animal was still set to zero. For metapopulation experiments we used a fitness-dependent algorithm of population limits. To increase the pathogen effect on birth rate and to simulate overcrowding effects more adequately, the progeny was delivered to an individual only if . We assume that under conditions of resource shortage only the fittest individuals could leave progeny. However results similar to ours could be obtained with increase of pathogen’s adverse effect on birth rate without changing its effects on lifespan (unpublished).
Dying due to reaching the lifespan setpoint was simulated by incrementing the age of individuals (a) each round and comparing it to the preset age of death (A). For simplicity we assumed no visible fitness declines were preceding the individual’s death: very first “symptoms” of aging were considered to be lethal.
As mentioned in the main text, time units we use are arbitrary and might reflect days, months or years depending on a given organism. All of our conclusions are nicely scalable along the time axis since pathogens tune the length of their life cycles according to the host’s longevity.
In this study we considered only chronic pathogens that cannot be cleared by the immune system. Such diseases are numerous and well known. We suggest long-lasting diseases, but not ones with rapid recovery, are contributing to the selection pressure towards lifespan shortening. Simulations in Extended Data Fig. 7d shows that introduction of recovery degrades the benefit produced by lifespan setpoint.
Infections were simulated in the following way: in the first step the infection load of the population (Lpi) has been estimated for each pathogen as a number of individuals infected with this pathogen. If this value was declining below 1, we assumed the presence of zoonotic pathogen reservoir and set as Lpi=1. Next the infection efficiency was estimated as β•Lpi, where β is transmission efficiency analyzed in a broad range of values of 0.005-0.24. To calculate number of pathogen attacks β•Lpi has been transformed into integer using stochastic rounding algorithm (e.g. 4.89 was giving 5 in 89% of cases and 4 in 11% of cases). Then these attacks were then randomly firing in the population. If the attack was hitting the susceptible individual it was infected, however if it hit an empty slot or an individual already infected with this pathogen, the attack was considered to have no consequences. Therefore numerically number of newly infected individuals in each round was equal to classical models: β⋅Lpi⋅Hpi=0, where Hpi=0 is a number of susceptible animals in population. The non-canonical algorithm of infection was used to simulate multiple independent infections and pathogen’s evolution (Fig. 4) more easily.
We have used multiple (10) pathogen species in all our simulations. In each experiment all of them had the same parameters. We assumed no interactions between pathogens; so they were able to infect hosts in any combinations. It was important to show that selective pressure towards shorter lifespan could be produced by the cumulative effect of several different pathogens with relatively mild pathogenesis. Multiplicity of pathogens also allowed us to minimize a number of disease parameters and still simulate fertility decline, long chronic infections as well as disease-inflicted death with a true stochastic component. It was also technically convenient, since it reduced noise in our simulations. Usage of a single pathogen with very strong adverse effects (e.g. developing its fitness penalties non-linearly over time, similarly to HIV, hepatitis or syphilis) would immediately raise questions about the universality of the simulation results. Using the parameters of humans diseases listed above would also require introducing vertical transmission as well as many additional conditions and parameters that would further complicate the model. Nevertheless all our conclusions are also clearly valid for such a single “terminator superpathogen” (unpublished). It should be also noted that vertical pathogen transmission (infection of the progeny by the parent immediately upon birth) will strongly increase key effects observed in Figs. 1 and 3 (unpublished).
A penalty that limits a host’s fertility due to disease (P) is an accepted fact: resources to be invested in reproduction are hijacked by pathogens and/or reallocated into deployment of immune responses. For analytical experiments (Fig. 2e to g, 3 h to j) we have used a 50% penalty, while in simulations a 20% (elsewhere stated) decrease in fitness per pathogen was used. The latter, more moderate number was selected so as to allow for several pathogens in the system. We did not introduced lifespan shortening by the single pathogen as it would complicate the interpretation in regions with low β. The gradual development of disease severity within 15 time points should be considered as a minor factor, introduced to eliminate some unaesthetic oscillations. In Fig. 1f we assume population density-dependent component to be equal to 1, and therefore . We consider this as an adequate simplification in the region of parametric space, where R0 ≈ 1. Adverse effects of epidemics are minimal in this region and proportion of susceptible animals in the population is ≈ 1. If the ages in population are distributed evenly, average age of infecting, as well as its duartion is . It should be noted that tiny fading outbreaks are happening in stochastic models even if R0 < 1 (not shown).
In Fig. 2 we demonstrate how infection can be cleaned following the bottlenecking of the host populations. To simulate highly infected starting populations, we have run the long-living individuals (A=∞) until they have reached the steady state adapting all 10 pathogen species. Then 10 random individuals were selected from this population and their lifespan setpoints were changed to the indicated value. Therefore the initial sampling was not affecting the pathogen composition immediately after the bottleneck. It was made from analogous moieties and usually retained all 10 diseases. For simplicity in the main text we discuss the dispersal of small population of founders to a new niche (Fig. 2), free from external pathogens. However taking in account the concept of pathogen adaptation (Fig. 4) it is clear that efficient cleaning from pathogens might follow the population decreases caused by diseases or predator-prey interactions occurring on the same territories: individuals might clean up the well-adapted pathogens, while the exposure to external non-adapted ones will not result in immediate restart of epidemics.
Simulation of competition between long-lived and short-lived individuals was performed in two ways that gave similar results (Extended Data Fig. 4). First, in situ generation of long-living mutant was simulated. Populations of short-living animals were run until reaching the steady state. Next, 25 random animals were transformed into long-living mutants (A=∞) and simulations have been running until the new steady state was reached and data was collected. Second, extrinsic invasion of long-living mutants was studied. Two isolated populations of short-living and long-living (A=∞) mutants were run in parallel under identical conditions. Upon reaching the steady-state, 25 slots were randomly swapped between two compartments with period of 100 rounds.
Source-sink density-dependent dispersal simulation (asymmetric dispersal) is one of the key results of the paper (Fig. 3, Extended Data Movie 1). Both empirical and theoretical studies show that dispersal as well as the underlying movement behavior are condition-dependent and informed processes. Local population density is considered to be a major factor affecting dispersal2–5. It should be emphasized that activation of a specific program for dispersal upon overcrowding was reported even in bacteria (swarming and quorum sensing)6,7 leaving no doubt that our assumption for universality of density-dependent dispersal is valid. Intraspecific competition and resource shortages push excess individuals into neighboring, less populated regions. We also note that purging the long-living mutants occurs rapidly in the course of epidemics progression. We suggest this to be much faster than most of evolutionary processes, since it does not require rare events (mutations) to happen. Taking this into account, we consider that the minimal stringency of physical barriers that separate different parts of population is less than in most other evolutionary models. Therefore our simulations (Fig 3d to g, Extended Data Movie 1) are based on adequate presuppositions. Simulations for clustered metapopulations (Extended Data Fig. 5) were performed first for each cluster as it would be a uniform population, and after density-dependent and density-independent dispersal were simulated. To exclude potential artifacts coming from the same order of cluster analysis, the sequence of cluster calculations was randomized at each round.
Equation if Fig. 3j was obtained from: . Under these conditions (and if density-independent dispersal is insignificant) the evolution of lifespan does not go neither towards lifespan elongation, nor shortening since the equilibrium between populations is reached. Thus from equations shown in Fig. 3h we obtain: , and the birth rate in the equilibrium point: . Decrease in birth rate will result in evolution towards longer lifespan and will move B’ to the left, while an increase in birth rate will lead to lifespan shortening and increase B’.
The concept of pathogen adaptation to new species is widely accepted. We can illustrate this with an example of HIV-2. Closely related viruses are persisting in sooty mangabeys (Cercocebus atys atys). While most serotypes of HIV-2 are known from single human hosts only, some can also be transmitted from human to human8. Thus it seems while most HIV-2 variants that infect humans result in a dead-end, a few are taking an opportunity to adapt enough to establish epidemics. Since HIV pathogenesis occurs in prolonged periods of time comparable to human’s lifespan, we suggest that longevity could assist pathogen adaptation in the end resulting in epidemic outbreaks. To simulate pathogen adaptation (Fig. 4b, c), each pathogen in each host obtained an additional parameter – passage number (x). For pathogens coming from the environment x was set as zero. At the stage of infecting the program assembled an array of passage values from a pathogen’s populations. Representation of each passage in the array was calculated as the number of individuals infected with the pathogen at the given passaging age multiplied by the relative transmission efficiency of this pathogen (βn or βa). Next for every successful pathogen attack, the algorithm randomly selected a passage number from this array and incremented it with 1 to assign to a newly infected host. Therefore the composition of a pathogen’s metapopulation was carefully simulated.
Simulation data was collected upon the epidemics was reaching steady-state. In experiments with uniform populations 3×103 of rounds were sufficient. For simulations of lifespan variants competition in uniform populations we used 9×103 rounds after mutant introduction. In clustered metapopulations the run was stopped after one of the variants was winning.
Number of replicate simulations is at least 10 per data point in all heatmaps presented. In panels 3f and g number of simulations is 40 per data point.