BioSystems, 17 (19815) 245--258 245 Elsevier Scientific Publishers Ireland Ltd.

EVOLVE II: A COMPUTER MODEL OF AN EVOLVING ECOSYSTEM

MICHAEL CONRAD a and MICHAEL STRIZICH b

aDepartments of Computer Science and Biological Sciences, and bDepartment of Computer Science, Wayne State University, Detroit, M148202 (U.S.A.)

(Received May 2nd, 1984) (Revision received September 18th, 1984}

The Evolve II program is a model of an ecosystem in which organisms are allowed to evolve. Organisms are subject to a changeable environment and competi t ion from other organisms for a limited food supply. The gene structure may change through mutation. A feature of Evolve II is that the magnitude of phenotypic change resulting from mutation is itself a property of the gene. The system was studied under a number of environmental variation schemes. We report three significant findings. Two species (lineages with distinctly different survival strategies) evolved and coexisted in the same environmental conditions. Organisms developed a resistance to phenotypic change in response to mutation in slowly varying environments. However, traits which favor survival of the individual at the expense of reproduction could in some cases undergo phenotypic change in response to mutation despite the fact that this did not favor the survival of the offspring. This demonstrates that gene struc- tures can evolve whiich are advantageous from the standpoint of the lineage, but not advantageous from the stand- point of individual offspring.

Keywords: Computer evolution model; Computer ecosystems; Competitive exclusion; Existential game.

1. Int roduct ion

AlgorithmicaUy specified models of eco- systems provide a means for testing theories of evolution and ecological relationships. In the present model (to be caned Evolve II) highly simplified bacteria-like organisms are represented with array entries. These entries represent the genes, the phenotype , and history of each organism. An algorithm simulates the environment and organisms interact with this environment through two principles. The first is that the organisms can reproduce with variation. The second is that the environmental conditions select which organisms reproduce.

The first model of this t ype (Evolve I) also represented organisms in a fashion somewhat reminiscent of bacteria and also operated on the same two principles (Conrad, 1970, 1981a; Conrad and Pattee, 1970). The organ- isms and environment in Evolve I were represented as list structures using the LISP language and were somewhat more complex

than those in Evolve II. An alternative algorithmic specification of evolution has also been implemented by Martinez (1979). Martinez's model was directed to elucidating the emergence of fundamental biological properties necessary for Darwinian evolution, whereas the Evolve models are directed to studying whether evolutionary principles as currently understood are sufficient to generate an evolutionary process and to dis- covering qualitatively new features of evolu- t ionary dynamics. Evolve II is wri t ten in PL1 and is as a consequence much more efficient than Evolve I. It also possesses a number of important features not present in the earlier model. On of these is the inclusion of evolu- t ionary amenability. Genes which express the same phenotypic proper ty may be more or less amenable to evolution (see Conrad, 1983}. This paper will consider both the evolutionary dynamics of the genotype and the amenability proper ty in the context of the dynamics of an ecosystem.

Once such a model is built it is investigated

0303-2647/85/$03.30 © 1985 Elsevier Scientific Publishers Ireland Ltd. Published and Printed in Ireland

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experimentally, just like a natural system. The main discovery which has been made with Evolve II is the surprising one that it is possible for species with alternative life strategies to coexist in the same environment. The model also exhibited features which illustrate in a striking way the opposing effects of selection acting on traits advanta- geous to the individual and traits advantageous to the lineage.

Evolve II originated as a software develop- ment project in the Computer Science Depart- ment at Wayne State University (Conrail, 1981b). The model was significantly modified for the experiments reported here (for details of the program see Strizich, 1982).

2. Specifications of the model

2.1. System structure

Evolve II is a model of an evolving ecology system. Such a system consists of organisms and the abiotic environment, the air, tempera- ture, light, etc. The overall organization is illustrated in Fig. 1.

The abiotic environment was modelled with two arrays. One array holds the values of light and temperature. Temperature is allowed values from 0 to 9 and light is allowed values from 10 to 19. These values may

Driver Module

Performance Evaluation

Aging Cycle $

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Fig. 1. Flow of control.

change after each cycle (time unit). The other arrayis for mass. In order to simplify the model, mass is considered to be food. If mass is avail- able organisms may consume it. Organisms pass mass back to the environment both in the form of waste and their "dead bodies". This mass is placed in a decaying mass array which works in a bucket brigade fashion. The mass becomes available for consumption after a number of cycles called the decay rate which is specified by the user before a simulation. It may take from 0 to 5 cycles for mass to become available for consumption once placed in this array. The mass that the system starts with is also specified by the user. Total mass is a conserved quant i ty throughout the evolution of the system.

The organisms are modeled with three arrays. Each organism has an entry in each array. The arrays are called genotype, pheno- type and history. Genotype has an entry for each gene of each organism. We have worked with three genes per organism but the program may be modified to accommodate more. Phenotype has an entry for each trait of each organism. The traits are determined from the genotype. History has 11 entries per organism, which are as follows:

(1) The mass required to reproduce. This is a function of the genotype of the organism.

(2) Mass collected. The amount of mass that this organism has collected since its birth or last reproduction.

(3) Aging number. A number that deter- mines the likelihood of the survival of this organism after each cycle of the system.

(4) Age of organism. How many cycles this organism has lived.

(5) Number of reproductions. The number of offspring this organism has produced.

(6) Readiness to reproduce. The module that determines readiness sets a flag here for the module that effects the reproduc- tion.

(7) Match to temperature. The absolute value of the difference between the

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(s)

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current value of temperature and this organism's temperature trait. Match to light. Same as match to temperature. Average match to environment. The average of item 7 and 8. Relative efficiency. The quotient of item 9 and the average of all item 9s. Normalized relative efficiency. A distri- bution of the relative efficiencies over a unit interval.

2.2 System function

(i) Flow of control: the driver module. The program calls the initialization routines to set the initial values of the environment and create the initial organism. The population in the experiments reported always evolves from one organism, though it is possible to read in a list of initial organisms. After these values are set a loop of calls is entered. This loop simulates time. One pass through the loop models the minimum time for reproduction. During this time an organism gets a chance to eat and if it consumes enough food it reproduces. After it reproduces or does not reproduce its survival is decided upon based on its food reserves and its aging number.

( ii) Performance evaluation. The amount of food allocated to an organism depends on how well it matches the environment and how well other organisms match the environment. Rather than just passing out food from the top of a list of organisms until no food is left, we wanted to develop an algorithm that modeled the parallel distribution of food in nature. That is, all organisms get to eat some food until no food is left. Some organisms may eat enough to meet their needs, some may not, but they all get a chance.

Food is distributed on the basis of norma- lized relative efficiency. An organism is allocated either an amount of mass (food) equal to the product of the mass available and its normalized efficiency (a "fair share" of the available mass} or the sum of the mass it needs to reproduce and the mass it

needs for serf-repair, which ever is less. Note that no organism can ever collect more than the mass it needs to reproduce on any cycle. Also note that the less food that an organism needs to reproduce the easier it wil be for reproduction to be accomp]ished.

The mass that is available for distribution is the mass that has reached the top of the decaying mass array multiplied by the frac- t ion of maximum light intensity that is in effect on that cycle. This is intended to model changing seasons or changing climates. As the amount of light incident on an environment changes, the food supply should change correspondingly. In the case of plants or plankton their ability to produce food decreases as light decreases and in the case of animals there is less plant or plankton material to eat.

(iii) Aging. After all the organisms have had a chance to eat we make life, death and birth decisions. Each organism has a trait which we call the aging number. This number serves two purposes. It defines the amount of mass that must be collected in order that an organism receives its full chance of survival. This survival mass models the food that an organism must eat for self repair. The aging number also defines the chance of survival that the organism has. For example an organism with an aging number of 2 can have no more than a 20% chance of surviving each cycle. If this organism collects 2 mass units it gets the full 20% chance of surviving. An organism with an aging number of 8 may have an 80% chance of surviving a cycle. If it only has 6 mass units collected, from this or past cycles, its chance of surviving this cycle is 6/8 × 80% or 60%. A random number is then chosen and compared to this chance of survival. The organism dies if the number exceeds the chance of survival. If the organism survives its age is increased by one, if not it is flagged for later cycling into the decaying mass array. Organisms that still have enough mass to reproduce are flagged.

(iv) Mass cycle. This module checks the list of all organisms for those that have been

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flagged as dead. Mass cycle adds the mass of these to the decaying mass array and then produces updated arrays with these organisms removed.

(v) Gene cycle. The gene cycle is the module that creates the new organisms. The list of all organisms is checked for those that have been flagged as ready to reproduce. When such an organism is found its offspring is entered at the bot tom of the lists.

A new organism may have the same genes as its parent or one or more of its genes may mutate from those of its parent. Each gene is given a one third chance of mutating. A random number is chosen and if it is less than one third, the offspring has a different gene than its parent. This mutat ion rate is arbitrary. We have done no experiments with different rates but these experiments should be interesting.

Mutation is one of the key aspects of this model. Each gene is composed of two values. The first codes for the trait that gene deter- mines and the second for that gene's amena- bility to evolution. Amenability is an expres- sion of the likelihood of mutat ion to a gene that codes for a similar function. If the amenability is low it is more likely that a mutat ion to a functionally dissimilar gene would occur than if the amenability is high. A gene of trait value 6 and amenability 2 has a higher probability of mutating to a trait value of 3 than a gene with trait value 6 and amenability value 8. If a mutat ion takes the value of a gene outside of the allowed values, 0--9, the offspring is considered non-viable. Mass is deducted from the parent for this still-born child and the mass is added to the bot tom of the decaying mass array.

There is a charge associated with amena- bility. High amenabilities cause the mass that an organism must collect to reproduce to be higher.

(vi) Development. This module interprets the genotype into the phenotype. In the version of this project with which the experi- ments have been done this only involves copying the trait part of each gene to the

appropriate place in the phenotype array. There are provisions to allow the traits that make up the phenotype to be determined by more than one gene each.

(vii) Environment cycle. This module updates the values of light and temperature according to a user selected scheme. It also updates the decaying mass array by adding the top entry to the available mass, moving the lower entries up one place and putting the recovered mass, from death and self- repair, into the bot tom of the decaying mass a r ray .

(viii) Data collection. Data collection is done once each cycle. The tables and graphs that are used in this report are compiled in this module.

3. Experimental results

3.1. Initial experiments

Initial experiments were useful in testing the assumptions of the model. In early gene cycle implementations mutat ions which took the gene out of functional bounds were repeated until a functional gene was obtained. This caused the probability of any gene mutating to a boundary value to be greater than that of mutating to an in-between value. Consequently the gene values were weighted toward the boundaries (see Fig. 2).

The same was true of the way amenability

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Fig. 2. Typical distribution of genes with an absorb- ing boundary.

mutat ions occurred and of the distribution of the amenabilities. Since this algorithm artifi- cially enhances the number of organisms at the boundaries a new algorithm was adopted. This is outlined in the gene cycle description. We mention this feature because this new algorithm led to bimodal distributions despite the fact that all boundary effects were elimin- ated.

Discovering the effect of the different values of the psxameters was another early task. The parameters are base cost, amena- bility cost and decay rate. The formula for mass required to :reproduce is:

MASS REQUIRED = BASE COST + AMENABILITY COST + (10 X AGING NUMBER)

If the ratio base cost /maximum aging number is high, then the trade off be tween high survivabilit:~ {high aging number) and fast reproduction (low aging number) is heavily weighted toward survivability. Ignor- ing amenability cost for the moment , if base cost is 300 and aging number is 9 we have an organism that needs to collect 390 mass units to reproduce and has a 90% chance of surviving each cycle if it collects its survival mass (a likely occurrence). If the aging number is 2 the mass required to reproduce is 320 bu t this organism only has a 20% chance to survive a cycle if it collects its survival mass. With this base cost the organ- isms with aging number 9 almost total ly dominate the populat ion as the low aging number organisms die before reproducing. When base cost was lowered to 2 the organ- isms {respectively) need 92 and 22 mass units to reproduce. In this case the populat ion has a more varied distribution of aging numbers in the organism.,;. This example of parameter adjustment illu.c.trates that the model can support a variety of radically different evolu- t ionary regimes.

Curiously the decay rate has little effect on the system. If the decay rate is high the mass available decreases as the populat ion increases

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until the average size of the populat ion stabilizes, i.e. until the number of births and deaths come into equilibrium. If the decay rate is low some oscillation of the usable mass occurs bu t this oscillation decreases with time. Decaying mass is simulated with a bucket brigade array. A low decay rate means a long brigade. It takes many cycles for a long array to stabilize, hence the oscillation of the available mass. These oscillations were in the range of + 10% of the available mass and the system exhibited no different behavior in any other respect due to different decay rates.

Changing the amenability cost has very subtle effects on the system. If the cost is drastically increased, the average amenabilities predictably fall as it is advantageous for organisms to need less food to reproduce. At cost levels in the lower ranges no simple effect of changing amenability cost has been discovered.

The populat ion reaches an equilibrium after about 80 generations. All data reported in this paper were taken from populations at either the 100th or 150th generation.

3.2. Constant environments

Under constant environments the tempera- ture and light genes of the organisms converge toward the environment. The data in Fig. 3. come from an experiment with a constant light of 6 and temperature of 6. After 150 cycles the genes of the population are pre- dominately genes that match these values. This occurs with any initial organism and with different sequences of " random" numbers used in the.probabilistic algorithms.

Two species develop under constant environments. These species are differentiated by reproduction and aging strategies. In Fig. 3c while aging gene 9 occurs most often, aging gene 5 also is favored. Organisms with aging gene 9 have a 90% chance of surviving if they have self-repair mass but they do not reproduce much. Organisms with aging gene 5 have only a 50% chance of surviving a cycle

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Fig. 3. Distribution of genes in a constant environment. (a) Temperature genes. (b) Light genes. (c) Aging genes. The amenability was zero in each case.

but they reproduce almost every cycle. This effect of two functionally distinct species occurs under many different environments. This is the first t ime such a speciation effect has been observed in a computer ecosystem experiment. We note that as the amenability charge increases the fast reproducing species disappears. This is due to the fact that this strategy then becomes more expensive relative to the repair strategy. The bimodal distribu- t ion disappears when the amenability charge is increased beyond two.

3.3 Varying environments

(i) Harsh environments. Environments in which it is sometimes difficult to acquire food are called harsh. In this model these are environments in which the light cyclically varies by more than +1 around a midpoint. In these environments the light genes of the organisms will usually match the lower bound of the light's variation. Competit ion for food is most intense when light is low because the available food is a function of

light intensity. The best survival strategy is to have genes that make an organism most efficient when food is most scarce (see Fig. 4a). It is most important to match the environment when light is low. Hence, the populat ion is skewed to light gene 2. The populat ion grows quickly when light is at the high value and contracts sharply when it goes to the low value.

If temperature is held constant in varying light environments the temperature genes of the populat ion do not match the environ- ment very well. We believe this is because such strong selection is occurring on the

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light genes that temperature matching is a small factor in an organism's survival.

It should be noted here that there is a difference in the way the light and tempera- ture genes respond to changes in the environ- ment. Light intensity determines food availability, temperature does not. Hence, there is no symmetry in the behavior of the light and temperature genes in experiments where light and temperature vary in the same way.

In harsh environments it is difficult to collect enough food to reproduce. Organisms with a survival rather than a reproduction

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Fig. 4. Distribution of genes in a harshly varying light environment. (a) Light genes. (b) Aging genes. Light varied between 2 and 8. The amenability charge was zero.

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strategy dominate the populat ion (see Fig. 4b). The organisms with the high value aging genes have greater probabil i ty of surviv- ing if they collect their survival mass, as is the case. The birth rate is low in harsh environments as it is difficult to collect enough mass to r ep roduce .

(ii) Easy environments. Easy environments will be defined as those in which there is a constant inflow of energy. In these environ- ments there will not be large scale expansion

Number of organisms

and contraction of the population. Since the food supply is largely dependent on the light level, easy environments are those in which light variability is either constant or low. If environmental variation occurs it is due to temperature. In these environments the organisms with low aging gene values may persist as they may reproduce before dying. Speciation on the age gene occurs in these environments as in constant environments (see Fig. 5). It is possible for two survival

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5 (1) 5 (2) 15 (4) 5 (0) 6 (1) 5 (0) 3 (0)

22 (7) 42 (12) 20 (3) 27 (3) 25 (5) 28 (6) 12 (5)

Fig. 5. Distr ibut ion of aging genes in an easy (constant light) envi ronment . Each ent ry in the amenabi l i ty tables shows the number o f organisms o f each gene value tha t have a part icular amenabi l i ty value and the number o f these that have given bir th during the cycle for which the data are taken. For example, the ent ry 8(2) in row 8 and co lumn 1 means that there are eight organisms of gene value 9 that have amenabi l i ty 1 and that two of these have reproduced in this cycle. The amenabi l i ty charge was zero, the light was constant , and the t empera tu re varied be tween 2 and 8, wi th variations of ±6 every third cycle. The data were taken at generat ion 150.

strategies to coexist here. Both the strategy of short life with high birth rate and the strategy of long life with low birth rate are successful.

In cyclically varying environments (whether easy or harsh) 1;here are two different re- sponses to variation of light or temperature. One response is for genes to match the value of the cycle that cause s the most stress for the population. This was shown in the harsh environments when the light gene matched the low point of the light cycle. The other response is to match the midpoint of the cycle (Fig. 6). In this experiment the tempera- ture had a period of 12 time units, with

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increments or decrements of 1 temperature unit each time unit. The mode of the temper- ature gene is 5 on each cycle even though temperature varies from 2 to 8. The average of the temperature gene varies slightly but its cycle lags behind that of the temperature cycle b y 3 or 4 t ime units.

When the variability of temperature is lower, in a range of 4--6, the amenability of the temperature gene is higher for the opt imum gene, gene 5, than for the other genes. In Fig. 7 the mode of amenability for gene 5 is amenability 7. The mode of amenability for gene 6 is amenability 5 and the mode of amenability for gene 3 is amenability 4. The

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Fig. 6. Distribution of temperature genes in an environment of large temperature variability.

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Fig. 7. D i s t r i bu t ion of t e m p e r a t u r e genes in an e n v i r o n m e n t of low t e m p e r a t u r e var iabi l i ty .

populat ion is being locked in to gene 5 or at least it is being locked in to not changing away from gene 5 very quickly.

Light was held constant at 5 or to +-1 around 5 in the easy environment experi- men t s . The most favQred light gene was 5, predictably (Fig. 8). High amenability is not strongly linked to the opt imum gene here as it was for the temperature gene.

(iii) Effect of amenability charge. Some effects of changing the amenability charge may be seen in Figs. 9--11. The average and mode of aging gene amenability decreased when the amenability cost was increased. When the amenability cost was zero the most

favored amenability for temperature was 6 (Fig. 10), bu t when the amenability cost was 10 the most favored amenability was 2 (Fig. 11). The amenability of the two other genes does not change in so drastic a fashion. Comparison of Figs. 10 and 11 shows that when the amenability cost was raised the temperature tracking strategy was abandoned in favor of a scattering strategy. This indicates that it is more important to budget mass to the light and aging gene amenability when the cost of amenability is high and that while tracking of temperature is important it is not an overriding priority.

Aging gene 9 completely dominates when

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Fig. 8. Dis t r ibut ion o f light genes in an env i ronment o f low tempera tu re variability. Tempera tu re varied be tween 3 and 7 and varied by -+ 1 every second cycle. Light was constant and amenabi l i ty charge was zero.

the cost of amenability is high (Fig. 9). This is because it becomes more favorable for organisms to use a self-repair strategy when it is necessary to collect more mass in order to reproduce. Paradoxically a low amenability of 2 is the most frequent amenability for this gene. This indic~tes that even though natural selectiorl favors a high value of the aging gene it also favors an aging gene which is more likely tomutate to a low gene value, therefore to a strategy of high reproduction rate. The

same conflicting features are present in Fig. 5 even though the cost of amenability is zero. Opposing selection pressures are evidently acting on this system, with one of the selec- tion pressures favoring individuals with a repair strategy and the other favoring lineages with a reproduction strategy. This effect becomes less marked as the amenability cost decreases and disappears when the cost exceeds 2 (since the bimodal distribution then disappears).

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9

Amenab i l i t y 1 2 3 4 5 6 7 8

0 (0) 0 {0) 0 (0) 0 (0) 0 (0) 0 (0) 0 (0) 0 (0)

0 (0) 0 (0) 0 (0) 0 (0) 0 (0) 0 (0) 0 (0) 0 (0)

0 (0) 0 (0) 0 (0) 0 (0) 0 (0) 0 (0) 0 (0) 0 (0)

0 (0) 0 (0) 0 (0) 0 (0) 0 (0) 0 (0) 0 (0) 0 (0)

1 (0) 0 (0) 0 (0) 1 (1) 0 (0) 0 (0) 0 (0) 0 (0)

0 (0) 0 (0) 0 (0) 0 (0) 0 (0) 0 (0) 0 (0) 0 (0)

0 (0) 0 (0) 0 (0) 0 (0) 0 (0) 0 (0) 0 (0) 0 (0)

1 (1) 0 (0) 1 (0) 0 (0) 0 (0) 1 (0) 0 (0) 0 (0)

0 (0) 1 (1) 1 (0) 3 (1) 2 (0) 1 (0) 1 (0) 2 (0)

27 (4) 40 (7) 30 (5) 31 (6) 39 (6) 13 (2) 15 (3) 6 (2)

Fig. 9. D i s t r i bu t ion o f aging genes w h e n cost o f a m e n a b i l i t y was high. A m e n a b i l i t y charge was 10. The var ia t ion of t h e e n v i r o n m e n t was t h e same as in Fig. 5. T he p o p u l a t i o n is s h o w n at gene ra t i on 150.

4. Conclusions

The major features exhibited by the Evolve II model may be summarized as follows:

(1) Different species develop which cope with the environment by different strategies. All organisms exist in the same environ- ment yet there are of ten two successful strategies for the persistence of a line of organisms.

(2) Strategies are adopted to slow mutat ion away from functional traits. The amena- bility of genes is of ten high. This is a conservative adaptation to a relatively certain, though varying, environment.

(3) Organisms evolve with genes that match the environment. The organisms have adaptive properties as one would expect in a model of an evolving ecosystem.

(4) If the environment is changing slowly the populat ion tracks the environment.

(5} Variation of light has different effects than variation of temperature. We initially expected the light and temperature genes to respond to variations of the environ- ment in the same way. They did not. The linkage of light intensity to food supply produced asymmetrical results.

(6} In a large number of the experiments many of the high value aging genes had low

associated ~unenabflities. This occurred even when the charge for amenability was zero. This is evidence that organisms carry traits that are advantageous to the population even though they will lead to the production of offspring with traits disadvantageous to the individual. The advantage to the population (that is to the growth of the lineage) is that these high aging gene value organisms are more likely to produce offspring with lower aging numbers than if they had high amenabilities. This benefits the popula- t ion in the sense that these offspring can reproduce more than high aging gene value organisms. This is a graphic illustra- t ion of selec~ion acting at the individual level, giving a high aging number, versus selection acting, in effect, at the level of the population, giving a low amenability.

Result (1), that different species develop, is surprising. According to the competitive exclusion principle distinct species should not be able to survive indefinitely in the same niche. There is no possibility for resource partitioning in t]ais model. Yet two different

Number of organisms

100

90

80

?0

60

50

40

i)0

20

10

I

I i

I i 1 2 1 ) ~ 5 6 ~

Arnena~ lity value

Fig. 10. Distributi~on of temperature amenability when amenability cost was zero. Light was constant. Temperature varied from 2 to 8 by increments of + 1 every cycle.

257

Number of organisms

too

90

80

7o

60

5o

L~o

30

20

2 3 ~ , 5 Amenabiii ly value

Fig. 11. Distribution of temperature amenability when amenability cost was high. The amenability charge was 10. The light was constant and the temperature switched between 2 and 8 every third c y c l e .

typological species (species as defined by overall similarity) coexist. Another way of looking at this result is to picture the evolu- tion process as an existential game, in the sense defined by Slobodkin and Rapoport (1974). The payoff is remaining in the game. Existential games axe outside the usual frame- work of game theory and very few mathe- matical results exist. The experimental result reported here demonstrates that it is possible to construct an existential game in which more than one strategy is a winning strategy.

This result may explain some perplexing field observations. Rabinowitz (1978; Rabinowitz and Rapp, 1981) have shown that seven species of grass can coexist on the great plains, with no obvious environmental basis for their relative occurrence. The different species have different reproductive and survival strategies. Our results suggest that such coexistence may be due to the fact that alternative strategies can coexist in nature even in the same niche. Of course since the competitive exclusion principle was originally enunciated by Volterra (1931) and Gause (1934) modifications to the

258

principle have become a theme in biology. From the theoretical point of view exceptions can occur as a result of spatial structure and diffusion (Levin, 1978), temporal variation of the environment, or from cross-inhibition being stronger than self-inhibition (Slobodkin, 1961). The exception which appears to occur in our model does not result from any of these mechanisms. Rather it appears to be a possibility inherent in evolution by variation and selection when this process is embedded in constraints of the type which must be present in any ecosystem.

Result (6) also deserves comment. This bears on the controversial issue of individual versus species selection. Usually it is stated that a trait can only persist if it is evolution- arily stable (an ESS in the terminology of Maynard Smith and Price, 1973). Result (6) suggests that the concept of an evolutionary stable strategy must be applied rather care- fully. Mutation to a low aging gene is not an ESS, implying that the mutated organism has a disadvantage. But mutat ion to a gene structure that enhances the chance of mutat- ing to a low aging gene is an ESS in this system. Since it cannot be an advantage to the individual it must be an advantage to the lineage. Thus it cannot be concluded, as is frequently done, that ESS always favors the individual over the lineage.

Evolve II is more realistic in its representa- t ion of biological systems than purely analytic models, but it is clearly very simple in com- parison to nature. It is not intended to model any specific system, but to provide a theo- retical laboratory, just in the sense that the Lotka-Volterra equations provide a theoretical laboratory. It is evident that the conclusions from such models must be treated with care, just as they must be from models which a t tempt to incorporate large amounts of specific data. Results such as (2) and (6) should be interpreted in the following way. Even in very simple evolutionary systems alternate strategies can coexist and features beneficial to the lineage rather than the individual can develop. The conclusion is that the occurrence of such phenomena in

the much richer evolutionary systems in nature is theoretically plausible and at very least cannot be excluded on the basis of purely evolutionary arguments.

Acknowledgment

This work was supported in part by grant MCS-82-05423 from the National Science Foundation.

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