## Critical phenomena in evolutionary dynamics

##### Author(s)

Manapat, Michael L. (Michael Linn)
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##### Other Contributors

Massachusetts Institute of Technology. Dept. of Mathematics.

##### Advisor

Martin A. Nowak.

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This thesis consists of five essays on evolutionary dynamics. In Chapters 1 and 2, we study the evolution of trust from the perspective of game theory. In the trust game, two players have a chance to win a sum of money. The "investor" begins with one monetary unit. She gives a fraction of that unit to the "trustee." The amount she gives is multiplied by a factor greater than one. The trustee then returns a fraction of what he receives to the investor. In a non-repeated game, a rational trustee will return nothing. Hence, a rational investor will give nothing. In behavioral experiments, however, humans exhibit significant levels of trust and trustworthiness. Here we show that these predispositions may be the result of evolutionary adaptations. We find that when investors have information about trustees, investors become completely trusting and trustees assume the minimum level of trustworthiness that justifies that trust. "Reputation" leads to efficient outcomes as the two players split all the possible payoff from the game, but the trustee captures most of the gains: "seller" reputation helps "sellers" more than it helps "buyers." Investors can capture more of the surplus if they are collectively irrational: they can demand more from trustees than is rational, or their sensitivity to information about trustees can be dulled. Collective investor irrationality surprisingly leads to higher payoffs for investors, but each investor has an incentive to deviate from this behavior and act more rationally. Eventually investors evolve to be highly rational and lose the gains their collective behavior had earned them: irrationality is a public good in the trust game. Next, we describe two evolutionarily robust mechanisms for achieving efficient outcomes that favor the investor while still compensating trustees for the value of their agency. In the first mechanism, "comparison shopping," investors compare limited information about various trustees before committing to a transaction. Comparing just two trustees at the beginning of each interaction is enough to achieve a split desirable to the investor, even when information about trustees is only partially available. In the other mechanism, a second layer of information is added so that trustees sometimes know what rates of return investors desire. The trust game then becomes similar to an ultimatum game, and positive investor outcomes can be reached once this second type of information is sufficiently pervasive. In Chapter 3, we study the origin of evolution and replication. We propose "prelife" and "prevolution" as the logical precursors of life and evolution. Prelife generates sequences of variable length. Prelife is a generative chemistry that proliferates information and produces diversity without replication. The resulting "prevolutionary dynamics" have mutation and selection. We propose an equation that allows us to investigate the origin of evolution. In one limit, this "originator equation" gives the classical selection equation. In the other limit, we obtain "prelife." There is competition between life and prelife and there can be selection for or against replication. Simple prelife equations with uniform rate constants have the property that longer sequences are exponentially less frequent than shorter ones. But replication can reverse such an ordering. As the replication rate increases, some longer sequences can become more frequent than shorter ones. Thus, replication can lead to "reversals" in the equilibrium portraits. We study these reversals, which mark the transition from prelife to life in our model. If the replication potential exceeds a critical value, then life replicates into existence. We continue our study of replication in Chapter 4, taking a more concrete, chemistry-oriented approach. Template-directed polymerization of nucleotides is believed to be a pathway for the replication of genetic material in the earliest cells. Adding template-directed polymerization changes the equilibrium structure of prelife if the rate constants meet certain criteria. In particular, if the basic reproductive ratio of sequences of a certain length exceeds one, then those sequences can attain high abundance. Furthermore, if many sequences replicate, then the longest sequences can reach high abundance even if the basic reproductive ratios of all sequences are less than one. We call this phenomenon "subcritical life." Subcritical life suggests that sequences long enough to be ribozymes can become abundant even if replication is relatively inefficient. Our work on the evolution of replication has interesting parallels to infection dynamics. Life (replication) can be seen as an infection of prelife. Finally, in Chapter 5, we study the emergence of complexity in early biochemical systems. RNA biochemistry is characterized by large differences in synthetic yield, reactivity to polymerization, and degradation rate, and these properties are believed to result in pools of highly homogeneous, low complexity sequences. Using simulations of prebiotic chemical systems, we show that template-directed ligation and the mass-action effect of sequence concatenation increase the average complexity and population diversity in pools of RNA molecules. We verify these theoretical results with experiments showing that ligation does enhance complexity in real RNA systems. We also find a correlation between predicted RNA folding energy and complexity, demonstrating the functional importance of this measure. These results contrast with previous assumptions that fine-tuning of the system is the only way to achieve high complexity. Our work shows that the chemical mechanisms involved in nucleic acid polymerization and oligomerization predispose the RNA world towards a diverse pool of complex, energetically stable sequences, setting the stage for the appearance of catalytic activity prior to the onset of natural selection.

##### Description

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010. Cataloged from PDF version of thesis. Includes bibliographical references (p. 118-128).

##### Date issued

2010##### Department

Massachusetts Institute of Technology. Dept. of Mathematics.##### Publisher

Massachusetts Institute of Technology

##### Keywords

Mathematics.