Eco-evolutionary dynamics, coding structure and the information threshold

Abstract

Background: The amount of information that can be maintained in an evolutionary system of replicators is limited by genome length, the number of errors during replication (mutation rate) and various external factors that influence the selection pressure. To date, this phenomenon, known as the information threshold, has been studied (both genotypically and phenotypically) in a constant environment and with respect to maintenance (as opposed to accumulation) of information. Here we take a broader perspective on this problem by studying the accumulation of information in an ecosystem, given an evolvable coding structure. Moreover, our setup allows for individual based as well as ecosystem based solutions. That is, all functions can be performed by individual replicators, or complementing functions can be performed by different replicators. In this setup, where both the ecosystem and the individual genomes can evolve their structure, we study how populations cope with high mutation rates and accordingly how the information threshold might be alleviated.

Results: We observe that the first response to increased mutation rates is a change in coding structure. At moderate mutation rates evolution leads to longer genomes with a higher diversity than at high mutation rates. Thus, counter-intuitively, at higher mutation rates diversity is reduced and the efficacy of the evolutionary process is decreased. Therefore, moderate mutation rates allow for more degrees of freedom in exploring genotype space during the evolutionary trajectory, facilitating the emergence of solutions. When an individual based solution cannot be attained due to high mutation rates, spatial structuring of the ecosystem can accommodate the evolution of ecosystem based solutions.

Conclusions: We conclude that the evolutionary freedom (eg. the number of genotypes that can be reached by evolution) is increasingly restricted by higher mutation rates. In the case of such severe mutation rates that an individual based solution cannot be evolved, the ecosystem can take over and still process the required information forming ecosystem based solutions. We provide a proof of principle for species fulfilling the different roles in an ecosystem when single replicators can no longer cope with all functions simultaneously. This could be a first step in crossing the information threshold.

Figure 1

Coding Structure. The genetic representation of predators and scavengers is a tree-like coding structure. This genotype defines the phenotypic reaction to a prey, based on the (x, y)-value of this prey. That is, how does one process prey consisting of a certain amount of nutrients, x and y. The functional representation of this replicator would be (+ ($ x x) (* (+ y 3) y)).

Figure 2

Fitness Evaluation. Schematic representation of fitness evaluation of predators, scavengers and prey. Dashed lines denote on basis of which value a response is. That is, predators produce a value based on the (x, y)-values of a prey (colored red and green respectively). This value, relative to the value which the prey produces (based on the evolutionary target), defines the fraction of prey which is eaten by the predator. A scavenger feeds on the remains of prey, based on the same (x, y)-values of prey. Fitness is based on the fraction of prey which is eaten. In this particular example, the fitness of this prey would then be 0.2 (1. - 0.8) and the predator and scavenger would get respectively 0.82 (e^-0.2) and 0.63 (e^-0.47) added to their fitness.

Figure 3

Evolved Solutions under Different Mutation Rates. Type of solutions (classified as described in the methods section) under different mutation rates (per base) for the evolutionary targets of table 1 with minimal coding length of (a) 13, (b) 15, (c) 15, (d) 19. Note that the exact nature of the target does also make a difference as shown by the difference in shift for both targets with a minimal coding length of 15. Blue and green represent simulations which evolve an individual solution, where blue has a transient state of ecosystem based solutions. Red and orange represent ecosystem based solutions, where in the orange cases this solution is lost again later in evolution. For each target the information threshold for maintaining the target is indicated with a star. Above this mutation rate the shortest solution for this target cannot be maintained as described in the last paragraph of the results section.

Figure 4

Initial and Final Coding Length for Different Mutation Rates. A decrease in initial coding length under higher mutation rates is observed. Restructuring of initial solutions after prolonged evolution also decreases length. For each mutation rate 25 simulations are run. The length distributions under different mutation rates are shown for (a) first evolved individual base solutions and (b) most compact individual based solution 250 generations later, for the target with minimal coding length 13; (c) first evolved individual based solutions and (d) most compact individual based solution 250 generations later, for the target with minimal coding length 19. Note that some first evolved solutions are lost from the population after prolonged evolution due to the information threshold (for example the solution found for the longest target with μ = 0.095 in (c) is lost in (d)).

Figure 5

Generations Needed to Evolve a Full Solution. For evolutionary targets with minimal coding length (a) 13, (b) 15, (c) 15 and (d) 19, the median number of generations needed for the evolution of a full solution is shown. Error bars depict the minimum and maximum number of generations. On the right (in red) the actual number of solutions out of 25 simulations per mutation rate is plotted. Among the solutions shown are some which cannot be maintained and are lost from the population. Leaving out these solutions even strengthens our conclusions. Prolonged experiments (maximum generations = 20000) with high mutation rates give comparable results. That is, results do not qualitatively depend on the amount of time provided for information accumulation.

Figure 6

Spatial Ecosystem Distribution. This figure shows the spatial structure of an ecosystem based solution under high mutation rates. The shade of green denotes the fitness of prey, or rather: how much of the prey is eaten. Prey depicted as yellow are fully eaten by an ecosystem based solution. Red denotes single prey which are fully eaten by a predator alone (not being an individual based solution). In this case the pattern is governed by the prey which are fully eaten by a predator-scavenger pair. Such a pattern, with comparable numbers of 'yellow' prey, can only be met when a correct ecosystem based solution is present in the population.

Figure 7

Passing the Information threshold. When seeding a population under mutation rates above the information threshold (μ = 0.13), with correct individual based solutions, these solutions are quickly lost from the population. This is shown by the declining number of prey which are eaten by correct individual based solutions(black line). The loss of these individual based solutions creates a niche for ecosystem based solutions, which indeed arise as can be observed by the increase of prey consumed by a correct ecosystem based solution (red line).