A Unified Theory of Biodiversity

A Role for Differential Susceptibility to Disease in theOrigin 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 and .

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-dependentmechanisms 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[1]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 becaused 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 plausiblethat 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).

Wehypothesize 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 commonlogisticpopulation 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 1ashows 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 outcompete 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 growthrate 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).