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Project Progress

The huge diversity of life poses a major challenge to ecological theory and a major source of optimism for astrobiology. Ecological theory argues that a single environmental niche should be colonized by a single species of organism, or perhaps a small community, and so the diversity of life should be essentially a measure of the number of niches present. The dramatic failure of this idea has been formulated in what is sometimes known as “The Paradox of the Plankton” and is fundamentally unresolved at the present time. The huge diversity of life does suggest, however, that the ability of life to explore, colonize and especially create environmental niches has been drastically underestimated. Accordingly, the likelihood of extraterrestrial life arising is also underestimated, or at least inadequately estimated, by our present understanding of biological evolution. We have started to address this question theoretically, prompted initially by our ongoing work on the breakdown of the progenote state. We have succeeded in developing a theoretical approach for predicting biodiversity in multi-dimensional niche spaces, arising due to ecological drivers such as competitive exclusion.

The puzzle in ecology arises from the common observation that very closely related species often coexist in the same environment, apparently occupying very nearly the same (if not identical) ecological niches. An example is that of the various types of Anolis lizards found in tropical rainforests, which share a common prey — insects — but avoid competition by living in different parts of the rainforest. Various species of finches look similar to each other except for such traits as beak design, which have specialized the finches to different food needs.

Although it is clear that resource competition is an essential driver of ecological structure it is equally clear that this idea by itself cannot be the whole story. One the one hand, species live into a high-dimensional niche space and can minimize competition by moving onto different dimensions. On the other hand, similar species can coexist in one-dimensional niche space by forming lumps inside which the individual suppress shared competitors.

Due to their inherent computational complexity, methods have not been available for predicting the individual distribution in niche space under the assumption that the niche space itself can be multidimensional. This issue is addressed in this paper, where we develop and solve a framework for analyzing ecological models. By representing ecological niches as sequences of strings, we are able to describe multiple traits each with its own variability. A novel symmetry in the community matrix allows us to report analytical progress, and we accurately predict the behavior of an ensemble forecast for the ecosystem dynamics.

The novelty of our approach relies on the fact that ecological niches are described by sequences of strings, which allows us to describe multiple traits. Our work proposes a mathematical framework for analyzing pattern forming instabilities in these models, and shows surprisingly that the analytic linear theory predicts the asymptotically long time population distributions of niches in the model. We also proposed a test for identifying ecological drivers in biodiversity distributions, based on representing ecosystem data by means of a certain transform introduced in the theory. The theoretical work in this project models the formation of species or genetic clusters of organisms as occurring via a pattern forming instability in genotype or phenotype space. An initially uniform distribution of organisms or genomes spontaneously self-organizes into clusters that one can think of as species or operational taxonomic units. We believe that the mathematical techniques developed here also underpin the breakdown of a progenote state, stabilized by massive horizontal gene transfer, into a state where genetic clusters form corresponding to the domains of life. Our work shows that this can happen, in principle, and in the coming grant period will be used to attack the question of how the domains of life arise from the most unstable modes of the progenote state.