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Project Progress

Task 1: When are two heads better than one?

Ecosystems as wholes do not undergo “Darwinian” competition per se, since they are not individuals, but the combined Darwinian competitions and interaction-dynamics of the members determine which ecological configurations can displace others and can themselves resist invasion by alternatively-composed or alternatively-structured communities. The difficulties of performing ecosystem functions under the control of multiple autonomously evolving genomes — involving coordination and the stabilization of cooperative interactions — have been a subject of extensive study and formal modeling since the introduction of evolutionary game theory by Maynard Smith and Price (1973). Many of these difficulties are ameliorated when the same functions can be carried out under the control of a single genome (e.g., if a collection of heterotrophs is replaced by an autotroph), yet empirically we find that most natural environments are dominated not by multi-functional autotrophs, but by consortia of complementary specialists.

Our question is when metabolic, physiological, or evolutionary criteria favor the splitting of control across autonomous genomes sufficiently to pay the extra costs of coordination that result from the split. The role of complementarity is a central theme in the study by Co-I McCutcheon of bacterial symbionts of insects, which occupy an evolutionary borderline between autonomous peers in an ecosystem, and fully-entrained organelles of cells, and falls under Astrobiology Roadmap Objective 5.2: Co-evolution of microbial communities. The larger problem of understanding the role of ecosystems as mediating the growth of complexity through more genomic autonomy falls under Objective 4.2: Production of complex life.

Two study systems are currently in use in this work. The first is the example of spontaneous emergence of heterogeneity and coexistence in a population of E. coli grown on limiting glucose, first explained as a result of cross-feeding by PI Rosenzweig (1994) and subsequently developed by Co-I Kinnersley et al. (2014) including several members of this NAI team. PI Rosenzweig and Co-I Kinnersley, in collaboration with Ivana Gudelj of the University of Exeter, have made a draft model of the cross-feeding relations in this system. Co-I Smith is attempting to determine whether systems of this kind reflect inevitable evolutionary trade-offs, or only short-term partitions of components which had evolved in other contexts but did not represent evolutionary optima under long-term innovation. The second study system is detailed in the next task.

Task 1 References:

Maynard Smith, J. and G. R. Price. (1973) The logic of animal conflict. Nature 246:15—18 doi:10.1038/246015a0

Rosenzweig, R. F., R. R. Sharp, D. S. Treves, and J. Adams. (1994) Microbial evolution in a simple unstructured environment: Genetic differentiation in Escherichia coli. Genetics 137:903—917

Kinnersley, M., J. Wenger, E. Kroll, J. Adams, G. Sherlock, and F Rosenzweig. (2014) Ex Uno Plures: Clonal Reinforcement Drives Evolution of a Simple Microbial Community. PLoS Genetics 10:e1004430

Task 2: Co-evolutionary dynamics on stochiometrically-constrained spaces

The second study system is a constructed chemical (rather than organismal) model of ecological feedbacks, derived from the reaction-network theory of alternative implementations of the pentose-phosphate pathway. In actual ecosystems, coevolution is constrained by the reliance of organisms on metabolites (or their avoidance of toxic effects from wastes) that only they or other organisms in the ecosystem can produce or recycle. The fitnesses of all member species depend on the frequencies of all others, not directly as through predation, but mediated by environmental concentrations of metabolites that have their own dynamics. The coupled rates of production of metabolites and wastes within each organism lead to complex webs of constraint, and the determination of balanced flows — the only class of solutions that are eligible to be evolutionary steady states — is generally a computationally hard problem (Anderson, et al. 2012).

Abstract chemical models with a high degree of combinatorial complexity can automatically be generated, and their totally-balanced flows exhaustively enumerated, with recent graph-grammar methods (Anderson 2012, 2013, 2014), permitting the study of problems in model-ecosystem optimization that are more complex than those for which complete stoichiometric data are available for organism consortia. In this task Co-I Smith is seeking to use the E. coli cross-feeding model from Task 1 as a basis for biologically appropriate abstractions of the reason organisms adopt syntrophic lifestyles in which they are genomically autonomous but interdependent through resource flows mediated by the environment. The totally-balanced flows should be locally or globally stable fixed points of the stochastic evolutionary dynamics on these constrained networks.

The planned second stage in the task is to use generalizations of the Price equation introduced by Kerr and Godfrey-Smith (2008) to derive the correct evolutionary summary statistics for such ecologically coupled co-evolutionary dynamics. Because ecosystems do not “replicate”, and their alternate forms to not “compete” in a strict sense, they are instead constructed moment-by-moment from the bodies and by-products of their replicating and competing members. Generalizations of the Price equation are needed to express regression among such constructed relations through time, which Fisherian fitness provides (Frank, 1997) for their strictly-replicated components.

Both projects fall within the scope of our originally proposed work on Competition versus Cooperation in major transitions, specifically Case 4: Network constraints from metabolism. Both projects are in intermediate stages of completion, and are not yet submitted for publication.

References:

Andersen, J. L., C. Flamm, D. Merkle, and P. F. Stadler. (2012) Maximizing output and recognizing autocatalysis in chemical reaction networks is NP-complete. Journal of Systems Chemistry. 3:1 DOI:10.1186/1759-2208-3-1

Andersen, J. L. C. C. Flamm, D. Merkle, and P. F. Stadler. (2013) Inferring chemical reaction patterns using rule composition in graph grammars. Journal of Systems Chemistry. 4:1—14 doi:10.#1186/#1759-2208-4-4

Andersen, J. L. C. C. Flamm, D. Merkle, and P. F. Stadler. (2014) Generic strategies for chemical space exploration.International Journal of Computational Biology and Drug Design 7:225—258 (2014) DOI: http://dx.doi.org/10.1504/IJCBDD.2014.061649

Kerr, B. and P. Godfrey-Smith. (2008) Generalization of the Price Equation for evolutionary change. Evolution 63:531—536 DOI: 10.1111/j.1558-5646.2008.00570.x

Frank, S. A. (1997) The Price equation, Fisher’s fundamental theorem, kin selection, and causal analysis. Evolution 51:1712—1729 DOI: 10.2307/2410995