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The Journals of Gerontology Series A: Biological Sciences and Medical Sciences 59:B301-B305 (2004)
© 2004 The Gerontological Society of America

The Evolution of Programmed Death in a Spatially Structured Population

Justin M. J. Travis

Centre for Conservation Science, University of St. Andrews, Fife, United Kingdom.

Address correspondence to Justin Travis, NERC Centre for Ecology and Hydrology, Hill of Brathens, Banchory, Kincardineshire, AB31 4BW Scotland. E-mail: jmjt{at}ceh.ac.uk


   Abstract
Top
 Abstract
The Model
 Results and Discussion
 REFERENCES
 
Recent studies have identified a number of genes that regulate life span. When these genes are inactivated, organisms live longer, but suffer no obvious adverse effects. These results have generated considerable debate, largely because current evolutionary theory is unable to explain them. In this article, I report results from an individual-based spatial model in which a programmed age of death is allowed to evolve. In a freely mixing population with global dispersal, evolution selects for individuals with ever-increasing life span. However, in a spatially structured population with localized dispersal, a programmed age of death evolves. The exact age of death that evolves depends critically on the scale of dispersal. Within this model, individuals are genetically programmed to die, even though they are still able to reproduce. These results suggest that death can be adaptive and offer an explanation for the evolution of "death genes."

ALFRED Russel Wallace was the first to suggest that aging and death might be evolved traits. In the 1860s, he suggested that individuals are programmed to die so that they do not compete with their offspring (1). His idea had some early support, notably from the influential German biologist August Weismann (2), but by the 1920s it had been dismissed as a "perverse extension of the theory of natural selection" (3). By the middle of the last century, the focus of evolutionary theory on senescence had shifted to other theories such as mutation accumulation (4,5) and antagonistic pleiotropy (6).

Today, with just a few exceptions (7,8), most evolutionary biologists continue to believe that the way evolution works makes it impossible for genes to exist with the single function of causing death (9–11). Indeed, 51 international scientists recently drafted and endorsed a position statement that stated "... longevity determination is under genetic control only indirectly" and "... aging is a product of evolutionary neglect, not evolutionary intent" (12). In simple terms, the logic behind this view is that selection should favor those individuals that produce the greatest number of healthy offspring. Longer-lived individuals are expected to produce more offspring, or at least increase the survival of their offspring by providing longer parental support.

Recent discoveries in nematodes (13–15), insects (16,17), and mammals (18–20) of genes that, when mutated, increase life span, have increased interest in the evolution of aging. In this article, I show that within a spatially structured population, programmed death does evolve and suggest that it is time to reconsider the "perverse" theories of Wallace and Weismann.


   THE MODEL
Top
 Abstract
 The Model
Results and Discussion
 REFERENCES
 
Patch occupancy models are widely used within ecology to study spatial processes (21–24). Here, I extend this well-established framework by developing a patch occupancy model to investigate the evolutionary ecology of programmed organism death.

A patch occupancy model represents the landscape as a number of cells. Each cell can be in one of two states, occupied or unoccupied. There are two main uses of this type of model. The first (used here) assumes that each patch can sustain one and only one individual, and, in this form, the model is suitable for individual-based simulations of a single population. The second assumes that each patch can support a whole subpopulation, and, in this form, the model can be used to describe metapopulation dynamics.

In its simplest form, a patch occupancy model is spatially implicit. This implies that colonization of a patch is equally likely to occur from any other cell. Levins' metapopulation model (21) was the first spatially implicit patch occupancy model. This deterministic model tracks the total density of occupied and unoccupied patches. Occupied patches go extinct at rate e, and unoccupied patches are colonized at a rate determined by the species' colonization ability and the densities of occupied and unoccupied patches. Numerous authors have since used the model in this format (22,25), while others have made use of it in a stochastic form (26,27).

In the last 10 years, an increasing number of authors have been making use of spatially explicit patch occupancy models (23,24,28,29). This is the form of the model used here. Now, the landscape is represented as a lattice of habitat patches, with each cell on the lattice able to support one individual (Figure 1). In all the simulations shown in this article, the lattice is a 200 x 200 square. Thus, if every patch were occupied, the population size would be 40,000. The model works in discrete time: In each time-step, deterministic death, stochastic death, and reproduction occur. Individuals vary in a discrete quantitative character d that determines their programmed age of death. When an individual reaches age d it immediately dies, and the patch within which it was living becomes available for colonization by another individual. There is a probability e, which is independent of age, that each individual suffers stochastic death (as opposed to programmed death). A key assumption of this model is that individuals are less likely to have offspring as they grow older. The reduction in fecundity with age is modelled using the geometric progression Pa = {gamma}(a–1), where P is the probability that an individual aged a produces an offspring. {gamma} is a constant specifying the rate at which fecundity decays with age. Offspring inherit their age of death gene from their parent with a probability m of mutation. When a mutation occurs, the programmed age of death parameter d is, with equal probability, either increased or decreased by 1.



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  		Figure 1. A schematic of the model. Each patch on the lattice can be in one of two states, either occupied by an individual (indicated by a cross) or unoccupied. With global dispersal, offspring disperse with equal probability to any cell on the lattice. With local dispersal, offspring disperse to a patch within a specified neighborhood of their parent. Three possible neighborhoods are shown around a focal individual (black cell). For nearest neighbor dispersal, movement occurs with equal likelihood to the 8 nearest neighbors (darkest grey cells). If longer dispersal is incorporated, offspring move with equal likelihood to any cell within a certain distance. For example, they may move up to 3 cells in both dimensions. In this instance, dispersal occurs with equal likelihood to the nearest 48 patches (all the grey cells)

 
Following birth, offspring immediately disperse. In most of the simulations for which results are presented, dispersal is to the nearest neighbor: Dispersal occurs with equal likelihood to the 8 adjoining patches (see Figure 1). Later, results are presented where dispersal occurs over a longer distance. Here, dispersal occurs with equal likelihood to any patch within a certain distance of the natal patch (see Figure 1 for examples). Absorbing boundary conditions are assumed: If an individual disperses off the edge of the lattice, it dies. When global dispersal is implemented, offspring are equally likely to move to any patch on the lattice. There is no loss of individuals off the edge of the lattice with global dispersal. Offspring successfully establish at the patch to which they disperse only if it is unoccupied. Otherwise, they die.

Simulations were carried out to investigate how different patterns of dispersal influence the evolution of d. Initially, two sets of simulations were run. In the first batch, offspring disperse to any patch on the lattice with equal likelihood (global dispersal). In the second, offspring disperse at random to 1 of the 8 cells that neighbor their parent's location (nearest neighbor dispersal). Each batch contained simulations with different values of {gamma} and e, so it is possible to ascertain how important these two parameters are in determining the results. Global dispersal and nearest neighbor dispersal are extremes, and most organisms exhibit movement behavior that is better represented by something in between. Further simulations are conducted where the scale of dispersal is gradually increased from nearest neighbor to global through a number of intermediate scales.


   RESULTS AND DISCUSSION
Top
 Abstract
 The Model
 Results and Discussion
REFERENCES
 
In a freely mixing population with global dispersal, evolution selects for individuals with ever-increasing life span (Figure 2A). Regardless of the initial value of d, evolution proceeds relentlessly in the same direction, although the rate of change in d declines as d increases. In a simulation that lasted 1,000,000 time-steps, d evolved to 193.4. As d increases, the intensity of selection acting to drive it higher declines. This is due both to the limited number of individuals that survive stochastic death to reach older ages, and to the decline in fecundity that occurs with age.



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  		Figure 2. Trajectories showing how programmed age of death evolves. A, Global dispersal. Evolution always selects for individuals with a longer life span. B, Local dispersal. Selection favors individuals with an intermediate programmed age of death. The parameters used are the same in both: {gamma} = 0.9, e = 0.01, m = 0.001. Trajectories are each for a single run of the model and are shown for 5 different starting values of d (10, 20, 50, 75, and 100)

 
A dramatically different result is found when local dispersal is incorporated (Figure 2B). Evolution selects for individuals that have an intermediate programmed age of death. In the example shown in Figure 2B, an evolutionary stable strategy (ESS) exists such that individuals are genetically programmed to die when they are aged 27. For all starting values of d, over time d converges to an ESS. By dying at 27, individuals in these simulations reduce their potential individual lifetime fitness by about 6%. How can this result be explained?

The result is due to the spatial population structure that arises when dispersal is localized. I suggest that the kin selection (KS) theory and the concept of inclusive fitness provide the likely mechanism, although, as discussed below, further work will be needed to verify this. Inclusive fitness includes both the direct fitness an individual obtains through its own reproduction, and the fitness obtained indirectly through reproduction of its kin. According to KS, a particular behavior is favored by natural selection if it results in the increase in an individual's inclusive fitness. Since KS was developed by Hamilton in the 1960s (30), it has provided an evolutionary explanation for a range of different behaviors including dispersal (31) and altruism (32). Let us consider how KS can explain the evolution of programmed death. When organisms have limited dispersal, the population develops a spatial structure in which individuals are likely to be located close to their kin. The patch vacated when an individual dies is likely to be reoccupied by a relative. If fitness declines with age, then an individual can increase its inclusive fitness by dying, and thus making room for its younger and fitter kin, once it reaches some critical age. When dispersal is global, an individual can never increase its inclusive fitness through dying, as kin are no more likely to benefit from the newly available patch than nonkin.

To be certain that kin selection is the mechanism behind the result, and that it is not another feature of the spatial structuring within the population, further work is required. Hamilton's theory is the notion that rB – C > 0 in order for an altruistic act to be favored, where r is the relatedness, B is the benefit to the recipient, and C is the cost to the donor. There is not a straightforward way to calculate these three values in the patch occupancy model developed here. However, methods for obtaining analytical approximations to patch occupancy models have been developed in recent years (33). If these methods can be extended to incorporate age structure, they have the potential to provide the mean values of r, B, and C that are required to ascertain whether KS really is important.

What are the effects of {gamma} and e on d? Programmed death occurs earlier if {gamma} is increased (see Figure 3A). This result makes intuitive sense: If individual fitness declines more rapidly with age, then inclusive fitness is enhanced by dying at a younger age. If reproductive fitness does not decline with age, programmed death does not evolve. The model does not explain the evolution of senescence from a nonsenescing state. Instead, it provides an explanation for the evolution of a programmed age of death in organisms that already exhibit reproductive aging. Evolution selects for a later programmed death when the probability of age-independent stochastic death e is higher (Figure 3B). This result may seem somewhat counterintuitive, but can be explained by considering the effect of e on spatial dynamics. When e is low, the population size is high, and therefore most patches are occupied resulting in fewer empty sites available for colonization by offspring (Figure 3B). When e is large, most dispersing offspring find an empty site, and this dilutes the benefits from older relatives dying. Another way of viewing this is that a large e lengthens the time between an individual dying and its patch being reoccupied. This has the effect of increasing the age at which an individual increases its inclusive fitness through dying, and therefore d evolves to a higher ESS.



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  		Figure 3. The evolution of age of death (d) depends on both the rate at which fecundity declines with age ({gamma}) and the probability that an individual suffers stochastic death (e). A, Evolution selects for a later programmed age of death when fecundity decays less rapidly. Here, e = 0.01 and m = 0.001. B, Evolution selects for earlier programmed death when the probability of stochastic death is lower (squares). This result is explained by the population density (triangles) (see text). Here, {gamma} = 0.8 and m = 0.001. In both A and B, the results show the mean and standard error of 10 simulations. In each simulation, the model is implemented for 100,000 time-steps and the population mean d is averaged over the final 500. Standard errors are only shown when they exceed 0.5

 
Global dispersal and nearest-neighbor dispersal are at the opposite ends of a spectrum of all possible dispersal behaviors. Most organisms will exhibit dispersal that is better represented by something between these two extremes. To assess how robust the results for nearest-neighbor dispersal are, some further simulations have been run with increased neighborhood sizes (see Figure 1). Increasing dispersal distance has the effect of increasing the age at which programmed death evolves to occur (Figure 4). This is explained by the reduced probability that closely related kin will colonize an individual's patch after its death. Interestingly, programmed death does evolve even with relatively long distance dispersal. With the parameters used to produce Figure 4, death is still adaptive with a maximum dispersal distance of 32, although when it is increased to 64, the result is very similar to that obtained with global dispersal. These results indicate that a suicide gene may be found in organisms with a range of dispersal abilities.



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  		Figure 4. Trajectories showing the evolution of d with different dispersal distances. Evolution selects for a later programmed death as maximum dispersal distance increases. However, even for moderately long dispersal distances, d has stabilized after 100,000 generations. Only when maximum dispersal distance is increased to 64 does the result resemble that for global dispersal. For the results presented here, e = 0.01, {gamma} = 0.9, m = 0.001, and the initial value of d was set to 30

 
In all the results described in this article, the mutation rate, m, was set at 0.001. Further simulations show that altering the mutation rate has the effect of changing the rate at which the equilibrium age of death is obtained: increasing m increases the rate. Increasing the rate also has the effect of increasing the variability within the population for the age of the death gene; however, it does not change the main conclusions.

Populations may be spatially structured at different scales. Within a single population, spatial structure can develop when dispersal is limited. This is the type of spatial structure present in the model described in this article. Spatial structure can also be found when a number of subpopulations are linked by occasional dispersal, thus forming a metapopulation. An obvious avenue for future work will be to investigate under what conditions a programmed age of death can evolve within a metapopulation. It has already been shown that pathogen-mediated selection can influence the evolution of host longevity within a metapopulation (34), but it remains an open question whether a programmed age of death can evolve in the absence of a pathogen.

The results presented in this article demonstrate that a programmed age of death can be adaptive. The "death genes" recently identified in several species may have evolved specifically to allow younger and more fecund relatives to gain a greater share of limited resources. This spatial population theory for the evolution of aging should not be considered as an alternative to either Peter Medawar's mutation accumulation theory (4,5) or George William's antagonistic pleiotropy theory (6), but rather as a natural expansion. Indeed, both of these well-established theories predict the decline in fecundity with age that is required in order for a death gene to evolve through the mechanism described in this article. Future work seeking to unify the mutation accumulation, antagonistic pleiotropy, and KS theories of aging and death is expected to prove valuable. It would also be interesting to investigate the behavior of a spatial version of a model incorporating the ideas of intergenerational transfer discussed recently by Ronald Lee (35).

Conclusion
Alfred Russel Wallace's early ideas about the evolution of aging and death may have been dismissed too soon. For now, the final word is his:

"... for it is evident that when one or more individuals have provided a sufficient number of successors they themselves, as consumers of nourishment in a constantly increasing degree, are an injury to those successors. Natural selection therefore weeds them out, and in many cases favors such races as die almost immediately after they have left successors."

—Alfred Russel Wallace


   Acknowledgments
 
I thank John Harwood, Jason Matthiopoulos, Mike Lonergan, Charles Paxton, and Angela Stewart for their critical reading of the manuscript. Two anonymous referees provided valuable comments.


   Footnotes
 
James R. Smith,, PhD, Decision Editor

Received July 21, 2003

Accepted January 20, 2004


   REFERENCES
Top
 Abstract
 The Model
 Results and Discussion
 REFERENCES
 

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