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A Unified Theory of Biodiversity

Page history last edited by Alex Backer, Ph.D. 14 years, 3 months ago

A Unified Theory of Biodiversity

 

A Role for Differential Susceptibility to Disease in the Origin and Stabilization of Biodiversity: A Unification of Twin Problems in Ecology and Evolution

 

Alex Bäcker1,2 and Ulrik R. Beierholm2

 

1: Sandia National Laboratories, P.O. Box 5800, Albuquerque, NM 87185

2: California Institute of Technology, MC 139-74, Pasadena, CA 91125

 

Correspondence or request for materials should be addressed to alex at caltech.edu and beierh at caltech.edu .

 

July 16, 2005

 

Based on this unfunded grant proposal, The effect of shared vulnerabilities on the survival of complex systems.

 

For figures and formatting see original MS Word document.

 

This is work in progress.

One of the central goals of ecology is to identify mechanisms that maintain biodiversity (Kerr et al., 2002; Chesson, 2000). The stability of biodiversity over millions of years of evolution has been one of the most persistent puzzles of ecology and evolution {Hutchinson, 1961 #723}{Wilson, 1992 #722}. This problem has two separate incarnations that, albeit traditionally treated in different literatures, share fundamental features: species coexistence and genetic polymorphisms. We postulate that these two problems are instances of one general problem and present a model that can explain both puzzles.

 

Introduction

 

Why are there so many species? Why haven’t the fittest of them all out competed the rest to extinction? And, intimately related and yet not recognized as such in the vast majority of the literature, why are close to 30% of gene loci in most every species examined polymorphic? Why haven’t the fittest of all genes become fixated? Modern textbooks present these enigmatic facts with no accepted explanation for them (Futuyma, ; Strickberger). Furthermore, the biochemical causes that sustain differences in polymorphisms between genes are unknown (Strickberger, 2000).

 

Darwin’s theory of natural selection requires resources to be limited by the abundance of individuals in such a way that the gain of one genotype implies necessarily the loss of another; it is frequencies, or fractional abundances, that matter in Darwinian evolution. As Darwin himself pointed out in The Origin of Species, twenty species coexist in a lawn which is mowed regularly, while only eleven persist in one given free rein. At the time, Darwin was attempting to explain the disappearance of nine species after mowing was interrupted. One hundred and fifty years later, with Darwinian evolution ingrained into our intuition, what is puzzling is quite the opposite: the fact that eleven species survived.

 

Darwinian theory sustains that, eventually, only the fittest among competitors will survive. Faced with the astounding diversity of genotypes both within species and across them, evolutionary biologists developed neutral theory, which argues that most mutations are neutral, and are thus not acted upon by natural selection. Darwin, they argued, was not wrong; his theory is simply excluded from playing a part in the fate of most mutations. Every study of human genetic diversity since Cavalli-Sforza and Edwards in 1964 has assumed that genetic polymorphisms are all neutral (Wells, 2002, p. 23).

 

And yet the evidence suggests that most accumulated mutations are not in random directions, as would be expected by the neutral theory (PNAS 2002?). Note that this does not imply that they are adaptive in any particular sense, but could derive from other constraints, such as a constant push away from a competing species. As Abrams put it (2001), “decades of experiments studying hundreds of species pairs have identified no conclusive cases of competitive equivalence”. Furthermore, contrary to the predictions of neutral theory, the most polymorphic genes, such as the HLA alleles, are at loci under great selective pressure due to their crucial role in resistance to disease.

Likewise across species, Darwinian theory states that a single resource should only create a niche large enough for a single species to prevail, yet several studies have in systems seemingly defined by small number of ressources found large number of species coexisting, a paradox that in the marine biological litterature is known as the “plankton paradox”.

Theorists have proposed explanations for coexistence by resorting to temporal or spatial inhomogeneities (e.g., Stewart and Levin 1973, Kondoh 2003) or nonequilibrium coexistence (e.g., Koch 1974; Armstrong and McGehee 1976a, b; Huisman and Weissing, 1999), or, for the special case of two coexisting species, by differential fitness ranks in juveniles and adults (McCann, 1998).

 

Regulation of populations by density-dependent mechanisms is one of the basic tenets of theory in population biology. Yet, most density-dependent mechanisms affect all species in a given niche, and thus do not solve the coexistence conundrum. We show here that the critical requirement for coexistence is differential vulnerabilities to density-dependent mechanisms and we argue that contagious disease is likely to be a major contributor to such differential density-dependent mechanisms

In this article we present a unifying framework to explain biodiversity at various levels, from the unexplained pervasiveness of polymorphisms to the coexistence of species in an ecological niche. Second, we show that coexistence of any number of species can result in stable equilibrium without the need for spatial or temporal inhomogeneities. Third, we show that this mechanism is robust to fluctuations in resource availability. Fourth, we show that shared vulnerabilities shared between species or genotypes lead to competitive exclusion, while a unique vulnerability in each species leads to coexistence.

 

Results

 

The probability that multiple species will de novo have identical fitness is very low. For a stable equilibrium to exist with multiple coexisting genotypes, what is needed is a restorative force that reduces the ratio of mortality to birth rates when a population’s size fluctuates downward, and vice-versa. More precisely, what we seek is that the effect of each species on its own growth-rate be more inhibiting than that of it on all other species (Cheeson, 2000). What , we ask, is this species-specific population-size-dependent force likely to be?

 

Any mechanism that increases fitness (fast enough) as population size decreases will work. Predators that specialize increasingly in a prey as its frequency increases decrease its fitness by the same mechanism of differentiating the vulnerabilities, but this is a slow effect if a change in behavior has to evolve. If the predators are shared, with equal vulnerabilities, the mechanism will not produce coexistence. Indeed, both field studies and theoretical studies show differences in predation selectivity for different prey species, if they exist at all, often cannot account for coexistence (Harding, 1997; GAEDKE and EBENHOH, 1991, Spiller and Schoener, 1998; but see Martínez et al., 1993; Sundell et al., 2003). In addition, the incidence of predation as a mortality cause has probably been overestimated because sick animals are more likely to be predated on, and signs of predation are more easily detected than those of infection. Moreover, differential susceptibility to predation is unlikely to account for the massive coexistence of polymorphisms within species.

 

Disease, in contrast: 1.Has an instantaneous effect on fitness as a function of density changes; 2. Evolves very fast, because disease-bearing agents are usually small parasites with short generation times.

 

How common is predation vs. disease as agent of death throughout the different forms of life? Although more experimental studies on the matter are called for, there is strong experimental evidence for density-dependent infection and for disease mediating much of the strong density dependence observed in an aquatic insect (Kohler and Hoiland, 2001).

 

The idea that an arms race versus parasites drives evolution of sex-related genes has recently received support (Haag et al, 2002). An often ignored consequence of the Red Queen hypothesis for the origin of sex, a theory which has received considerable empirical support in the last few years, is that, if correct, more than half of all deaths (or losses of fertility) in all sexual species (or their ancestors) must be caused by parasites. This suggests parasites as a natural candidate for the force determining population sizes at equilibrium.

A fundamental requirement of stability in the theory is that parasites not spread across the two coexisting populations (or that the interspecific effect be less than the intraspecific), for if they do, the effective population size determining the likelihood of an individual becoming infected will be the combined total across both populations, and thus a reduction in numbers of one of the two will not lead to a corresponding replenishment, leading to an eventual extinction of the population with lower fitness. This leads to a fundamental prediction of the theory: species which share all their vulnerabilities will not coexist in the long-term.

 

Indeed, the role of endemic infection in host population dynamics is a major open problem (Begon et al., 1998).

 

For drowning sailors at sea, survival is not a competition between sailors; it is a battle against the sea. Analogously, species in today’s populated Earth live in a sea of parasites. we suggest Darwinian competition is not the major factor in the evolution of diversity on Earth. Instead, successful defense from parasites is.

 

As a consequence, it seems plausible that in recent evolution, more of our genes have evolved to combat parasites than have evolved to adapt to our physical environment. This is consistent with the surprising results of a recent study of XXX species (Japanese group) found that only XXX genes are required for the function of XXX in an isolated environment, a point that was not emphasized by the authors (was it?). Indeed, Flor found 27 genes in the flax plant, Linum usitatissium, that confer resistance against a single fungal rust pathogen, while the pathogen had a similar number of genes allowing it to overcome resistance conferred by those host genes (Flor, 1956, cited in Strickberger, 2000, p. 575).

 

We hypothesize that a principal cause of sequence polymorphisms, not only in the MHC, but throughout genomes, are frequency-dependent mechanisms related to pathogen resistance. Unlike previous theories of frequency-dependent mechanisms for the MHC (Hedrick, 2002 and references therein), ours does not call for temporal variation in selection coefficients. There is indeed experimental evidence for frequency-dependent selection of alleles, although the mechanism behind this had remained a puzzle (Kojima and Yarbrough, 1967). I further suggest that loci not associated with disease resistance that share susceptibility to parasitic infection by parasites coexisting with the host will tend toward a single neutral cloud in sequence space, through the extinction of all other genotypes. In contrast, species dissimilar enough not to share vulnerabilities to parasites can coexist in a stable equilibrium.

 

There is indeed recent experimental evidence that predators exert frequency-dependent selection on prey (Bond and Kamil, 2002).

 

Species are traditionally defined by the existence of gene flow within species and not across them. This definition does not easily extend to clonally-reproducing “species”, and yet clonal organisms are found to cluster in genetic space just as sexually-reproducing species do. We suggest that parasites are responsible for such clustering. This suggests a new functional definition of species that applies to clonally-reproducing creatures, one based on common susceptibility to parasitic infection. If the diversity of populations is indeed limited by the exclusion of genotypes with common susceptibility to parasites, organisms with no parasites, such as viruses, should exhibit the greatest diversity of all living organisms. Indeed, viruses such as HIV and the influenza viruses confirm this prediction: the variability of individuals within a viral population is not limited to a few peaks within a fitness landscape (of course, some limitations in genotype composition allowed are given by the adaptive landscape: an HIV virus incapable of replicating, for example, will not propagate in any population).

 

Note that this does not necessarily lead to massive parasite-driven extinctions, in the sense of an entire lineage lost with no closely related genotypes surviving, because the very mechanisms described above ensure that the populations in ways of extinction have close relatives that are susceptible to the same parasites. In this way, parasites ensure their long-term survival. (But Van Valen 1973 extinction power law suggests that p(extinction) constant through time?)

Model

To illustrate these ideas we use a common logistic population model with a monod type growth rate (ref monod) and added the concept of disease to be simulated (see Methods). For simplicity the model assumes species feeding off abiotic resources as in models of plankton populations, but the model can easily be expanded to species feeding off biotic resources (predator/prey models) with qualitatively similar results (see supplemental material).

Two versions of this model was used, one to examine the importance of disease for the interaction between species, and a slightly more complex model examining the importance of disease for different genotypes within a single species.

A number of species (6 in experiment 1, 2 in experiment 2) is simulated feeding off a number of resources less than the number of species (3 in experiment 1, 1 in experiment 2). The rate of infection was a function of the density of infected, a typical assumption in similar models (ref.).

In experiment one, six species were injected into a system with a slow inflow of three resources. Figure 1a shows how the population density of each species varies over time for the case without any diseases. The most fit species out competes the rest within ~10 generations.

Figure 1b shows an example of a simulation of a system with six species feeding of 3 resources with diseases incapable of spreading across species. Each species is therefore regulated by its own disease. After 20-30 days the system reaches equilibrium with all species surviving despite having fewer resources than number of species. The diseases regulate each species keeping each from growing to a density where it would out compete the other species.

Figure 1c shows a similar system for which the mortality rate for diseased is higher, leading to damped oscillations of the density distribution. As the diseases spreads through the population, the population density is lowered to a level lower than what can sustain the disease, until the disease has almost died out, allowing the species density to grow again and the cycle repeats.

To further examine the relationships in the model we ran 100 simulations for several combinations of the infection rate, alpha, and the mortality rate of the infected, beta. In figure 2a we plot the average number of species surviving in these systems, with black being 1 survivor and white being all 6 species surviving. .

For low values of beta, the disease permeates the species in the system but does not significantly influence their fitness, and the system therefore acts as a system without disease. As an analogy, the disease can be thought of as a simple cold, that may spread easily but which seldom has lethal consequences.

For intermediate values of beta the disease exists in equilibrium in the population and has a large enough effect on a species fitness, so as to lower it enough for other species to be able to compete with the infected species.

As beta increases, the disease gets so lethal that it tends to kill the carriers of the disease before they have a chance to spread the disease to uninfected. Notice that this cutoff is dependant on the rate of infection, alpha. When beta>alpha the disease will be so deadly that it will be automatically eradicated from the population (can be seen mathematically by solving the equations for equilibrium by requiring dI/dt=0 and dN/dt=0).

We can try examining the same question in a system with cross species infection (see methods). Each species can now be infected by any other species, eliminating the species specific frequency dependant regulation, which allowed the coexistence of more species than resources in the system. When numerically simulated we find no systems with coexistence for any alpha and beta combination (figure 2b).

These simple simulations show that diseases can function as a density dependent population regulator assuming the disease is specific enough to only target single species and can therefore promote coexistence of several species.

In order to study how diseases can promote genetic polymorphism we included sexual reproduction in the second experiment. To do this we expanded our model to simulate two diploid species, each having three genotypes aa, ab and bb available in the population. We assumed that the aa genotype was advantageous and gave a 15% higher growth rate, the ab gave 5% higher growth rate. Furthermore for this experiment we assumed that the available resources were biotic, and that the inflow to the system was therefore a function of the current amount of resources.*

Two species were introduced in the system, with species 1 in addition having a 15% higher growth rate than species 2. Without the influence of diseases we would expect the aa genotype of species 1 to out compete the other types, as is what we see in figure 3a.

The introduction of a non-specific disease (fig. 3b), able to spread across genotypes and species, causes a depression of the entire population, but does not stop species 1 from out competing everything else.

However, if the disease is specific enough to only spread within a species (fig. 3c), we see that species 1 is sufficiently affected by the disease to allow the genotype aa of species 2 to coexist. This is exactly the same as what we saw in the first experiment.

If we further more assume that each genotype renders immunity to different diseases, essentially leaving each genotype with its own disease, we find complete coexistence between all species and genotypes (fig. 3d).

More complicated intermediate systems are of course also possible, leading to either exclusion or coexistence dependent on the parameter values.

If a gene confers an immunity to a disease, that constitutes an advantage which can allow it to survive in a population despite giving a seemingly lower growth/reproduction rate. This shows that the same mechanism that allows coexistence of species can also explain why there is an advantage in having multiple versions of a gene in a population if it confers immunity towards a certain disease. Through the specificity of diseases, specific species as well as genotypes can be down regulated allowing for the survival of species and genotypes with a lower fitness. This also shows how experimenting on cultures in isolation can yield very different results than doing experiments under more ‘natural’ conditions.

 

Evidence

 

Available evidence suggests that introduced competitors can drastically reduce the abundance and distribution of native species, but rarely lead to complete extinction, at least in terrestrial continental habitats (Frankel and Soulé 1981, Soulé 1983 as cited in Diamond, 1984). The reason pointed out by Soulé is that the relative competitive ability of species generally varies over habitats, and that it is probably rare for a species to be superior to another in all of its habitats. An alternative explanation would be that species show a reduced vulnerability to contagious disease once their population has been decimated.

 

Indeed, many parasites have been found living on plankton (Fahmi and Hussain, 2003). For example, not one but several viruses that are pathogenic to the common marine prasinophyte Micromonas pusilla (a small flagellate) have been isolated from sea water in several locations (Fuhrman, 1999). The recent realization that viruses may be the most abundant organisms in natural waters, surpassing the number of bacteria by an order of magnitude, has inspired a resurgence of interest in viruses in the aquatic environment. New methods have yielded data showing that viral infection can have a significant impact on bacteria and unicellular algae populations and supporting the hypothesis that viruses play a significant role in microbial food webs. Novel applications of molecular genetic techniques have provided good evidence that viral infection can significantly influence the composition and diversity of aquatic microbial communities (Wommack and Colwell, 2000). Field cage studies have shown that nematode parasites can reduce competitive superiority of the dominant species in a Drosophila community (Jaenike, 1995; Gillis and Hardy, 1997), and trematodes can favor invasion by a competitor in mussel communities (Calvo-Ugarteburu and McQuaid, 1997). Consistent with the predictions of our theory, plankton parasites can be so unique so as to allow the identification of the host through the parasite (Noble, 1972).

 

The importance of viruses for plankton diversity were put in question by results of both field and mesocosm studies that suggest that only ca. 20% or less of bacterioplankton and phytoplankton mortality is attributable to viral infection (Wommack and Colwell, 2000). The present study shows that a modest parasite-induced mortality in equilibrium is consistent nevertheless with a role of parasites in maintaining biodiversity.

 

These findings may also explain a seemingly unrelated puzzle, that of why different species of the D. willistoni group, as well as E. coli clones from the intestinal tracts of animals as diverse as lizards and humans from different continents share a narrow distribution of allozymes (enzyme polymorphisms) (Strickberger, 2000). If equilibrium distributions of polymorphisms were determined by minute fitness differences between alleles given by their environment, as proposed by Kojima and Yarbrough (1965) in the explanation given in today’s evolution textbooks (Strickberger, 2000), it would be hard to account for these distributions being equal in environments as varied as those of lizard and human guts. The similarities may be easier to account for if, on the other hand, the distributions are given by the steady-state frequencies for viral parasites, which depend more on their host than on the environment, and as such are more likely to remain constant for the same host in diverse environments.

 

An intriguing example of this exists between the annual legume Chamaecrista fasciculata (Caesalpiniaceae) and the large, dominant perennial grass Andropogon gerardii (Poaceae), which coexist in the Kansas tallgrass prairies. Holah & Alexander (1999) found that both species grew more poorly in soil from the root zone of Chamaecrista than in Andropogon soil, and that the effect was associated with fungi found uniquely on Chamaecrista roots. Pathogenic fungi “cultured” on Chamaecrista roots shift the competitive outcome against the dominant perennial grass, facilitating coexistence of the two plant species.

Understanding the host ranges of pathogens within a local plant assemblage and the possible adaptation by plants to actively culture pathogens that increase their competitive ability is a largely unexplored, but potentially fruitful field (Gilbert, 2002).

 

Indeed, for plants, native herbivores ( Janzen 1970; Hulme 1996) and disease ( Augspurger 1988; Harper 1990; Alexander 1992) have been hypothesized to contribute to the maintenance of plant species diversity, for which the density of seeds and the probability that a seed will mature are a function of the distance from the parent tree. This mechanism has been regarded as “far from an easy solution” (Chesson, 2000). We show here that a simple model that applies for any living being, and not plants alone, can lead to coexistence of any number of species.

 

Jerome and Ford (2002) recently provided evidence both for parasitic specialization for similar hosts, and found that the number of parasitic races in a natural environment was slightly greater than the number of host species.

 

Brunet and Mundt (2000) found frequency-dependent selection in wheat in the presence of disease, but not enough to maintain polymorphisms. They used only 3 races of a single pathogen, though, which our model predicts would be insufficient to maintain the 4 genotypes they used in their experiments. Furthermore, while the genotypes they use show different susceptibilities to the pathogens used, it is not clear whether they show differential contagion of the pathogens, an essential requirement for coexistence. Realistic natural ecological conditions would have many more pathogens, and our model suggests this is essential for the maintenance of polymorphisms; future experiments should take this into account.

 

Discussion

 

We have seen that parasites can promote diversification, as can predators. Given the apparent simplicity of the former compared to the latter, could the Cambrian Explosion be due then, not to the appearance of metazoans (multicellular animals) as theorized by Stanley exactly 30 years ago, but rather to the appearance of the first parasites? And if so, what was the critical evolutionary advance that made them possible? After all, viruses are simpler than bacteria in terms of the size of their genome. Could it be that, once again (after the shock of the small number of genes in the human genome), evolution suggests that size isn’t everything? We know, for example, that the genetic content of viruses (e.g. Giorgi et al., 1983) and mitochondria (e.g. Leblanc et al., 1995) –which have become the ultimate parasites-- is extremely optimized, to the point that, in addition to having highly compact genomes, they have both evolved overlapping genes (see Normark et al., 1983 for a review). Thus, small genomes may be an evolutionary endpoint that follows, rather than precedes, large genomes. And the reason why the metaphytes (plants) and metazoans (multicellular animals) mysteriously originated almost simultaneously (Schopf et al., 1973) may be not that the origin of metazoans brought about the diversification of the metaphytes, as proposed by Stanley (1973), but rather that the critical innovation necessary for both was that of parasites and endosymbiosis, which allowed the appearance of mitochondria and chloroplasts and, through the cropping principle (Paine, 1966), caused the diversification of life forms we know as the Cambrian explosion.

 

Methods

 

For all simulations in this paper we use a modified version of a Monod model (Monod, 1950), assuming that n number of species living on p number of resources are governed by a set of differential equations. The abundance of species i, Ni, is given as

 

where μi is the growth rate of species i and mi is the mortality rate of the non-infected subpopulation of species i.

The second term implies that we have introduced a subset of Ni, Ii, which have been infected by a disease which, assuming βi>mi, increases the mortality rate of the infected.

βi is the mortality rate of the infected subpopulation and the abundance of infected within species i is given by (see doc.

 

αi is the rate of infection per non-infected. The difference between the two equations for Ii determine whether diseases can spread across species or are confined within a species.

The growth rate, μi , for species i is given by a minimum function over all the available resources,

 

where Kij is the half-saturation constant for species i with regard to resource j and r is the maximal growth rate, in our simulations set to 1.

The abundance of resource j, Rj, in the system is described by (see doc.

 

D is the inflow rate, Sj is the maximal availability of resource j and cij is the uptake of resource j that the growth of species i causes.

Notice that if we set the infection rate to zero, αi=0, and the mortality rate of the infected sub-population equal to that of the non-infected, βi=mi, we retain the formulas for a traditional Monod model.

In all simulations, Kij and cij were chosen as random variables uniformly distributed between [0.2:1.2] and [0.02:0.12], r=1, D-1=mi-1=4 days, Sj=10. The infection rate, αi, varied between 0.002 and 1.024 pr non-infected, and the infected mortality rate, βi, was between 0.3 and 6.65. Both αi and βi are given in the relevant figures.

 

Sexually reproducing model:

Assume two species which each has two genotypes in diploid organisms. This allows for 3 possible combinations in each species: aa, ab and bb.

 

To introduce competition, we will assume that genotype aa has a 15% higher growth rate and ab 5% higher growth rate relative to bb.

Species 1 will also be assumed to have a 10% higher growth rate than species 2.

Abundance of each species i, and each species genotypes j, were calculated as above except that each genotype was tracked

 

The total species (Uninfected plus infected):

dNaa,i/dt=(Naa,i*(pNab,i/2+pNab,i)+Nab,i.*pNab,i).*μ.*1.15 - Naa,i*m–ΣdIaa,i,d(βaai-m)

dNbb,i/dt=(Nbb,i*(pNab,i/2+pNbb,i)+Nab,i*pNab,i).* μ *1.00 - Nbb,i*m- Σd Ibb,i,d(βbbi-m)

dNab,i/dt=Nab,i*(pNab,i/2+pNaa,i/2+pNbb,i/2)+Naa,i*pNbb,i)* μ*1.05- Nbb,i*m- Σd Iab,i,d( βabi-m)

βji is the mortality rate of species i, genotype j, assumed to be equal across diseases. m is the mortality rate of the uninfected, μ is the growth rate of species i.

pNab,i is the normalized abundance of species i, genotype ab, that is pNab,i = Nab,i /Σj Nji

 

Infected abundance:

dIji,d/dt=(Nji – Σd Ij,i,d )* Σf Σg (αijfgd*Nfgd ) - Ij,i,d* βji ;

where j is either aa, bb or ab and d is one of the diseases.

αijfgd represents the probability of species i, genotype j, of getting infected by species f, genotype g by disease d.

 

The equations for both models were solved numerically using a stochastic second-order Runge-Kutta algorithm, programmed in C++.

 

 

Acknowledgements:

This work was supported by an award to A.B. from the DOE Office of Science’s MICS Program at Sandia National Laboratories and by the Beckman Institute at Caltech. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy.

 

References:

1. Abrams, PA (2001). A world without competition. Nature 412, 858 – 859.

2. Alexander, H.M. (1992) Fungal pathogens and the structure of plant populations and communities. The Fungal Community, its Organization and Role in the Ecosystem (eds G.C. Carroll & D.T. Wicklow), pp. 481 497. Marcel Dekker Inc., New York, NY.

3. Augspurger, C.K. (1988) Impacts of pathogens on natural plant populations. Plant Population Ecology(eds A.J. Davy, M.J. Hutchings & A.R. Watkinson), pp. 413 434 Symposium 28 of the British Ecological Society, Blackwell Science, Oxford.

4. G. Calvo-Ugarteburu and C.D. McQuaid, Parasitism and introduced species: epidemiology of trematodes in the intertidal mussels Perna perna and Mytilus galloprovincialis. J. Exp. Mar. Biol. Ecol. 120 (1997), pp. 47–65.

5. Harper, J.L. (1990) Pests, pathogens, and plant communities: an introduction. Pests, Pathogens and Plant Communities (eds J.J. Burdon & S.R. Leather), pp. 3 14. Blackwell Scientific Publications, Oxford, UK.

6. Holah JC, and Alexander HM. 1999. Soil pathogenic fungi have the potential to affect the co-existence of two tallgrass prairie species. J. Ecol. 87:598-608

7. Janzen, D.H. (1970) Herbivores and the number of tree species in tropical forests. The American Naturalist, 104, 501 528.

8. Strickberger, MW (2000). Evolution. Jones and Bartlett, Sudbury, MA.

9. Wells, S (2002). The Journey of Man. A Genetic Odissey. Princeton University Press, Princeton, NJ.

10. Monod, J. La technique de culture continue, theorie et applications. Ann. Inst. Pasteur (Paris) 79:390-410, 1950

 

Figure Legends:

Figure 1

Population density as a function of time for six species living off 3 resources. a) A system with no within species or across species diseases.

b) System with an introduced disease with no infection between species and with diseases with low infected mortality rate beta = 0.65 or high mortality rate of infected, beta = 3.45 (c).

d) Same system as in c) but with across species contamination.

 

Figure 2

Plot of average number of survivors given infection rate alpha and mortality rate beta. 1000 random systems were generated, each with 6 species living off 3 resources. The color coding shows the average number of surviving species after 10,000 days(?).

In a) there is cross contamination between species (gamma=0.1?), in b) there is no cross contamination (gamma =0).

 

Figure 3

Population density of two diploid species, with two different alleles for which one homozygote has a higher fitness ie. higher growth rate, than the other and the heterozygote has an intermediate value. A disease is included in the system. In a) the disease can spread across species and across genetic variation. In b) the disease is only able to spread within a species creating survival of both species. In c) the disease is confined to spread within the same species and only to species with the same alleles.

 

 

Notes:

 

In the presence of multiple resources, stable equilibria with more than one species, namely one per resource, exists. [ refs?] However when several species forage off one common resource, traditional population biology states that the more fit of the two should out compete the less fortunate one.

A persistent puzzle in evolution, one which has come to be known as the “paradox of the plankton”, is the empirical fact that multiple species can coexist per resource, contrary to the predictions of Darwinian doctrine. (ref?)

 

The idea that addition of a trophic level to a given food web tends to promote increased diversity at the next lower trophic level was first put forth by Paine (1966, cited in Stanley, 1973). In fact, this principle has been invoked to explain the suddenness of the Cambrian explosion by Stanley (1973), who hypothesized that the appearance of heterotrophic multicellular organisms gave rise to the diversity of life that ensued during the early Cambrian. Previous attention on the influence of predators and disease on coexistence has centered mostly on shared predators (e.g. Abrams, 1999) and diseases (Holt and Pickering, 1985; Anderson and May, 1986; Begon et al., 1992; Dobson and Crawley, 1994; Abrams and Kawecki, 1999), and thus on their negative effect on biodiversity. Indeed, shared susceptibilities lead to competitive exclusion in our model. A model for the role of disease has been presented for the limited case of two species and a single intra-species disease (Venturino, 2001). In contrast, little work has been focused on the effect of multiple infectious diseases on the coexistence of multiple host species. Recent work suggests that multiple pathogens must be studied in combination to understand ecological processes (Rohani et al., 2003). A recent review on solutions to the paradox of the plankton (Scheffer et al., 2003) made the implicit assumption that non-equilibrium is needed to solve the paradox.

 

As the differential vulnerability to virus and worm attacks of different operating system attests to, our findings have implications for the design of computer systems robust to attacks. They also suggest a method to engineer stable biological (e.g. microbial) communities through the introduction of one parasite per competitor.

 

Indeed, susceptibility of different species to predation varies significantly among related species, and predicts population declines (Jackson and Green, 2000).

 

Figure 1 shows that as long as the rate of infection is large enough, so that the cost of dense populations is large enough to halt population growth, coexistence will ensue, if the mortality rate of those infected is high enough to halt population growth but low enough to allow effective transmission of the disease. The minimum mortality rate for coexistence is constant across infection rates, and relates to the birth rate: the mortality rate of infected individuals has to be at least as large as the birth rate if a population is to achieve a stable population size. In contrast, the maximum mortality rate for coexistence shows a trade-off with contagion rates: the higher the rate of infection, the more deadly a disease can be while still allowing coexistence, because faster transmission allows contagion even if time to death is shorter, and conversely, the higher the mortality rate, the higher the minimum contagion rates necessary to ensure spreading of the disease.

 

At low transmission rates, oscillations in species abundance and infected fractions are seen due to the lag between changes in population density and the changes in infected fractions that follow. At high transmission rates, these effects happen much faster, and the oscillations disappear.

 

 

KEYWORDS: pathogens – parasites – contagious disease – coexistence – maintenance of polymorphisms – evolution – ecology – frequency-dependent selection – density-dependent mechanisms – ecological niche

 

 

 

 

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