Attractors and Spatial Patterns in Hypercycles with Negative Interactions

This study reports on the effect of adding negative interaction terms to the hypercycle equation. It is shown that there is a simple parameter condition at which the behaviour of the hypercycle switches from dominant catalysis to dominant suppression. In the suppression!dominated hypercycles the main attractor turns out to be different for cycles consisting of an even or odd number of species. In "odd" cycles there is typically a limit cycle attractor, whereas in "even" cycles there are two alternative stable attractors each containing half of the species. In a spatial domain, odd cycles create spiral waves. Even cycles create a "voting pattern", i.e. initial fluctuations are quickly frozen into patches of the alternative attractors and subsequently, very slowly, small patches will disappear and only one of the two attractors remains. In large cycles (both even and odd) there are additional limit cycle attractors[ In a spatial domain these limit cycles fail to form stable spiral waves, but they can form stable rotating waves around an obstacle. However, these waves are outcompeted by the dominant spatial pattern of the system[ In competition between even and odd cycles, the patches of even cycles are generally stronger than the spiral waves of odd cycles. If the growth parameters of the species vary a little, a patch will no longer contain only half of the species but will instead attract "predator" species from the other patch type. In such a system one of the patch types will slowly disappear and the final dynamics resembles that of a predator-prey system with multiple trophic levels. The conclusion is that adding negative interactions to a hypercycle tends to cause the cycle to break and thereafter the system attains an ecosystem type of dynamics

Equal Pay for all Prisoners / The Logic of Contrition

This report deals with two questions concerning the emergence of cooperative strategies in repeated games. The first part is concerned with the Perfect Folk Theorem and presents a vast class of equilibrium solutions based on Markovian strategies. Simple strategies, called equalizers, are introduced and discussed: if players adopt such strategies, the same payoff results for every opponent. The second part analyzes strategies implemented by finite automata. Such strategies are relevant in an evolutionary context; an important instance is called Contrite Tit For Tat. In populations of players adopting such strategies, Contrite Tit For Tat survives very well -- at least as long as errors are restricted to mistakes in implementation ("the trembling hand"). However, this cooperative strategy cannot persist if mistakes in perception are included as well

Revisiting the nonequilibrium phase transition of the triplet-creation model

The nonequilibrium phase transition in the triplet-creation model is investigated using critical spreading and the conservative diffusive contact process. The results support the claim that at high enough diffusion the phase transition becomes discontinuous. As the diffusion probability increases the critical exponents change continuously from the ordinary directed percolation (DP) class to the compact directed percolation (CDP). The fractal dimension of the critical cluster, however, switches abruptly between those two universality classes. Strong crossover effects in both methods make it difficult, if not impossible, to establish the exact location of the tricritical point.Comment: 7 pages, 12 figure

Improving estimations of life history parameters of small animals in mesocosm experiments: a case study on mosquitoes

Mesocosm experiments enable researchers to study animal dynamics, but determining accurate estimates of survival and development rates of different life stages can be difficult, especially as the subjects may be hard to sample and mortality rates can be high. We propose a new methodology for estimating such parameters.We used an experimental set-up with 48 aquatic mesocosms, each with 20 first instar mosquito larvae and under 1 of 12 treatments with varying temperatures and nutrient concentrations. We took daily subsamples of the aquatic life stages as well as counting the emerging adults. We developed a method to estimate the survival and development probabilities at each life stage, based on optimising a matrix population model. We used two different approaches, one assuming the difference between predictions and observations was normally distributed, and the other using a combination of a normal and a multinomial distribution. For each approach, the resulting optimisation problem had around 100 parameters, making conventional gradient descent ineffective with our limited number of data points. We solved this by computing the formal derivatives of our matrix model.Both approaches proved effective in predicting mosquito populations over time, also when compared against a separate validation dataset, and the two approaches produced similar results. They also both predicted similar trends in the survival and development probabilities for each life stage, although there were some differences in the actual values. The approach which only used the normal distribution was considerably more computationally efficient than the mixed distribution approach.This is an effective approach for determining the survival and development rates of small animals in mesocosm experiments. We have not found any other reliable methodology for estimating these parameters, especially not from incomplete data or when there are many different experimental treatments. This methodology enables researchers to gain a much more detailed understanding of the life cycles of small animals, potentially leading to advances in a wide range of areas, for example in mosquito-borne disease risk or in considering the effects of biodiversity loss or climate change on different species.NWONWA.1160.1S.210Number theory, Algebra and Geometr

Recursiveness, Switching, and Fluctuations in a Replicating Catalytic Network

A protocell model consisting of mutually catalyzing molecules is studied in order to investigate how chemical compositions are transferred recursively through cell divisions under replication errors. Depending on the path rate, the numbers of molecules and species, three phases are found: fast switching state without recursive production, recursive production, and itinerancy between the above two states. The number distributions of the molecules in the recursive states are shown to be log-normal except for those species that form a core hypercycle, and are explained with the help of a heuristic argument.Comment: 4 pages (with 7 figures (6 color)), submitted to PR