Understanding the limits to generalizability of experimental evolutionary models

Abstract

Given the difficulty of testing evolutionary and ecological theory in situ, in vitro model systems are attractive alternatives1; however, can we appraise whether an experimental result is particular to the in vitro model, and, if so, characterize the systems likely to behave differently and understand why? Here we examine these issues using the relationship between phenotypic diversity and resource input in the T7–Escherichia coli co-evolving system as a case history. We establish a mathematical model of this interaction, framed as one instance of a super-class of host–parasite co-evolutionary models, and show that it captures experimental results. By tuning this model, we then ask how diversity as a function of resource input could behave for alternative co-evolving partners (for example, E. coli with lambda bacteriophages). In contrast to populations lacking bacteriophages, variation in diversity with differences in resources is always found for co-evolving populations, supporting the geographic mosaic theory of co-evolution2. The form of this variation is not, however, universal. Details of infectivity are pivotal: in T7–E. coli with a modified gene-for-gene interaction, diversity is low at high resource input, whereas, for matching-allele interactions, maximal diversity is found at high resource input. A combination of in vitro systems and appropriately configured mathematical models is an effective means to isolate results particular to the in vitro system, to characterize systems likely to behave differently and to understand the biology underpinning those alternatives.

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Figure 1: Infection mechanisms between bacteria ( B ) and phages ( P).
Figure 2: Bacterial diversity at steady state as a function of resource input, as provided by the mathematical model for different infection mechanisms.
Figure 3: Experimentally derived bacterial diversity and phage abundance as a function of resource input.
Figure 4: Phage diversity at steady state as a function of resource input for different infection mechanisms.

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Acknowledgements

We thank A. Buckling, S. Nuismer, K. Rich, J. Hoeksema and C. Jessup for their comments on an earlier version of this manuscript. L.D.H. is a Royal Society Wolfson Research Merit Award Holder. I.G. is supported by a NERC Advanced Fellowship. S.S.A. is funded by an ORS award and a studentship for the Department of Mathematics at Imperial College London. S.E.F. and J.N.T. are supported by the National Science Foundation DEB 0515598.

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Correspondence to Laurence D. Hurst.

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Supplementary Information

This file contains Supplementary Discussion and Supplementary Figures 1-11. The file contains the following sections: 1. Introduction; 2. The mathematical model; 3. Measuring diversity generated by the model: a rationale; 4. Equilibrium structure of the model; 5. E.coli-T7 case study; 6. Alternative diversity curves; 7. Comments. The Supplementary Information defines the class of mathematical models of bacteria-page co-evolution and shows that there is at least one system that fits the mean experimental data. It then asks, within the entire class of models proposed, which features of E.coli-T7 interaction are universal to all models and which are system specific. (PDF 676 kb)

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Forde, S., Beardmore, R., Gudelj, I. et al. Understanding the limits to generalizability of experimental evolutionary models. Nature 455, 220–223 (2008). https://doi.org/10.1038/nature07152

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