Kin Selection in the RNA World

Abstract

Various steps in the RNA world required cooperation. Why did life's first inhabitants, from polymerases to synthetases, cooperate? We develop kin selection models of the RNA world to answer these questions. We develop a very simple model of RNA cooperation and then elaborate it to model three relevant issues in RNA biology: (1) whether cooperative RNAs receive the benefits of cooperation; (2) the scale of competition in RNA populations; and (3) explicit replicator diffusion and survival. We show: (1) that RNAs are likely to express partial cooperation; (2) that RNAs will need mechanisms for overcoming local competition; and (3) in a specific example of RNA cooperation, persistence after replication and offspring diffusion allow for cooperation to overcome competition. More generally, we show how kin selection can unify previously disparate answers to the question of RNA world cooperation.

Keywords: Hamilton’s rule; RNA cooperation; RNA world; kin selection; limited diffusion; modelling the origin of life; origin of the genome; scale of competition.

Figure 1

The problem of cooperation in the RNA world. A cooperator (black squiggle) provides a benefit to other individuals (grey squiggle), increasing their relative replicative success at a cost to their own relative success. Over time, all else being equal, individuals that do not incur this cost but receive the benefits have higher replicative success, or fitness, and become better represented in the population. How, then, does cooperation evolve?

Figure 2

Limited diffusion in the RNA world. Cooperative RNAs are depicted as black squiggles, and selfish ones as grey squiggles. High diffusion leads to a well mixed population (low relatedness), which favours the evolution of selfishness. Limited diffusion leads to high relatedness. Cooperators are more likely to encounter other cooperators, and selfish individuals are unlikely to encounter cooperative ones to exploit. Selection favours cooperation.

Figure 3

Visual representation of the evolutionarily stable strategy (ESS) approach. Taylor and Frank (1996) developed an approach for identifying ESSs. An equation for fitness (y-axis) as a function of phenotype (x-axis) is either derived or assumed. Natural selection will move populations towards fitness peaks. At a fitness optimum, small phenotypic variations in either direction will have lower fitness, and therefore the population will remain the same. The ESS is the phenotype ($x^{*}$) where this occurs, and for a continuously differential fitness function, this happens at $dw/dx=0$. We expect organisms to express ESSs as a result of natural selection over time.

Figure 4

An illustration of the different types of cooperation in the RNA world. (a) Nucleotide synthetases (light grey cuboids) make nucleotides which benefit themselves, other nucleotides, and polymerases (dark grey spheroids). $\beta$ is relatively high, because being a cooperator does not limit a synthetase’s ability to benefit from cooperation. Similarly, polymerases can copy nucleotides and other polymerases, and they receive benefits both by making more synthetases (which leads to more nucleotides) and by being copied by other polymerases. (b) A cooperative replicase can copy a template, but cannot be copied by other replicases. Thus, $\beta =0$, because being a cooperator prevents one from receiving any benefits from cooperation.

Figure 5

Do cooperators receive the benefits of cooperation? The y-axis shows the ESS level of cooperation ($x^{*}$), plotted against relatedness (R). The three lines represent three different values of $\beta$, which measures the degree to which cooperators receive benefits. When $\beta$ is high, cooperators are equally as likely to receive the benefits of cooperative acts as non-cooperators. When $\beta$ is low, acting as a cooperative RNA limits or prevents a molecule from receiving the benefits of cooperation. When $\beta$ is low, only partial ($x^{*}<<1$) cooperation can evolve. For all values of $\beta$, increasing relatedness (R) increases the ESS value of cooperation. For all lines $b=0.8$, $c=0.1$.

Figure 6

The scale of competition in the RNA world. The y-axis shows the ESS, $x^{*}$, derived from the model in the text for different parameter values. The x-axis is relatedness (R). The three lines represent three different values of a, the scale of competition. When a is low, competition is relatively global. When it is high, competition is relatively local. Increasing a reduces the ESS value of cooperation. For all values of a, increasing relatedness favours cooperation. For all lines $b=0.8$, $c=0.1$.