The Evolutionarily Dynamics of Aposematism: a Numerical Analysis of Co-Evolution in Finite Populations

The majority of species are under predatory risk in their natural habitat and targeted by predators as part of the food web. During the evolution of ecosystems, manifold mechanisms have emerged to avoid predation. So called secondary defences, which are used after a predator has initiated prey-catching behaviour, commonly involve the expression of toxins or deterrent substances which are not observable by the predator. Hence, the possession of such secondary defence in many prey species comes with a specific signal of that defence (aposematism). This paper builds on the ideas of existing models of such signalling behaviour, using a model of co-evolution and generalisation of aversive information and introduces a new methodology of numerical analysis for finite populations. This new methodology significantly improves the accessibility of previous models. In finite populations, investigating the co-evolution of defence and signalling requires an understanding of natural selection as well as an assessment of the effects of drift as an additional force acting on stability. The new methodology is able to reproduce the predicted solutions of preceding models and finds additional solutions involving negative correlation between signal strength and the extent of secondary defence. In addition, genetic drift extends the range of stable aposematic solutions through the introduction of a new pseudo-stability and gives new insights into the diversification of aposematic displays

The Stabilisation of Equilibria in Evolutionary Game Dynamics through Mutation: Mutation Limits in Evolutionary Games

The multi-population replicator dynamics is a dynamic approach to coevolving populations and multi-player games and is related to Cross learning. In general, not every equilibrium is a Nash equilibrium of the underlying game, and the convergence is not guaranteed. In particular, no interior equilibrium can be asymptotically stable in the multi-population replicator dynamics, e.g. resulting in cyclic orbits around a single interior Nash equilibrium. We introduce a new notion of equilibria of replicator dynamics, called mutation limits, based on a naturally arising, simple form of mutation, which is invariant under the specific choice of mutation parameters. We prove the existence of mutation limits for a large class of games, and consider a particularly interesting subclass called attracting mutation limits. Attracting mutation limits are approximated in every (mutation-)perturbed replicator dynamics, hence they offer an approximate dynamic solution to the underlying game even if the original dynamic is not convergent. Thus, mutation stabilizes the system in certain cases and makes attracting mutation limits near attainable. Hence, attracting mutation limits are relevant as a dynamic solution concept of games. We observe that they have some similarity to Q-learning in multi-agent reinforcement learning. Attracting mutation limits do not exist in all games, however, raising the question of their characterization

The application of temporal difference learning in optimal diet models

An experience-based aversive learning model of foraging behaviour in uncertain environments is presented. We use Q-learning as a model-free implementation of Temporal difference learning motivated by growing evidence for neural correlates in natural reinforcement settings. The predator has the choice of including an aposematic prey in its diet or to forage on alternative food sources. We show how the predator's foraging behaviour and energy intake depend on toxicity of the defended prey and the presence of Batesian mimics. We introduce the precondition of exploration of the action space for successful aversion formation and show how it predicts foraging behaviour in the presence of conflicting rewards which is conditionally suboptimal in a fixed environment but allows better adaptation in changing environments

The effect of fight cost structure on fighting behaviour involving simultaneous decisions and variable investment levels

In the “producer–scrounger” model, a producer discovers a resource and is in turn discovered by a second individual, the scrounger, who attempts to steal it. This resource can be food or a territory, and in some situations, potentially divisible. In a previous paper we considered a producer and scrounger competing for an indivisible resource, where each individual could choose the level of energy that they would invest in the contest. The higher the investment, the higher the probability of success, but also the higher the costs incurred in the contest. In that paper decisions were sequential with the scrounger choosing their strategy before the producer. In this paper we consider a version of the game where decisions are made simultaneously. For the same cost functions as before, we analyse this case in detail, and then make comparisons between the two cases. Finally we discuss some real examples with potentially variable and asymmetric energetic investments, including intraspecific contests amongst spiders and amongst parasitoid wasps. In the case of the spiders, detailed estimates of energetic expenditure are available which demonstrate the asymmetric values assumed in our models. For the wasps the value of the resource can affect the probabilities of success of the defender and attacker, and differential energetic investment can be inferred. In general for real populations energy usage varies markedly depending upon crucial parameters extrinsic to the individual such as resource value and intrinsic ones such as age, and is thus an important factor to consider when modelling

The effect of fight cost structure on fighting behaviour

A common feature of animal populations is the stealing by animals of resources such as food from other animals. This has previously been the subject of a range of modelling approaches, one of which is the so called "producer-scrounger" model. In this model a producer finds a resource that takes some time to be consumed, and some time later a (generally) conspecific scrounger discovers the producer with its resource and potentially attempts to steal it. In this paper we consider a variant of this scenario where each individual can choose to invest an amount of energy into this contest, and the level of investment of each individual determines the probability of it winning the contest, but also the additional cost it has to bear. We analyse the model for a specific set of cost functions and maximum investment levels and show how the evolutionarily stable behaviour depends upon them. In particular we see that for high levels of maximum investment, the producer keeps the resource without a fight for concave cost functions, but for convex functions the scrounger obtains the resource (albeit at some cost)

Evolutionary Dynamics on Small-Order Graphs

Abstract. We study the stochastic birth-death model for structured finite populations popularized by Lieberman et al. [Lieberman, E., Hauert, C., Nowak, M.A., 2005. Evolutionary dynamics on graphs. Nature 433, 312-316]. We consider all possible connected undirected graphs of orders three through eight. For each graph, using the Monte Carlo Markov Chain simulations, we determine the fixation probability of a mutant introduced at every possible vertex. We show that the fixation probability depends on the vertex and on the graph. A randomly placed mutant has the highest chances of fixation in a star graph, closely followed by star-like graphs. The fixation probability was lowest for regular and almost regular graphs. We also find that within a fixed graph, the fixation probability of a mutant has a negative correlation with the degree of the starting vertex. 1

The health care utilization and out-of-pocket expenditure associated with asthma amongst a sample of Australian women aged over 45 years: analysis from the '45 and up' study.

Objective: This study aims to describe the prevalence of health care utilization (including conventional medicine, self-care and complementary medicine treatments) for the management of asthma by women aged 45 years and over and their associated out-of-pocket expenditure.Methods: A self-reported mail survey of 375 Australian women, a cohort of the national 45 and Up Study, reporting a clinical diagnosis of asthma. The women were asked about their use of health care resources including conventional medicine, complementary medicine, and self-prescribed treatments for asthma and their associated out-of-pocket spending. Spearman's correlation coefficient, student's t-test and chi-square test were used as appropriate. Population level costs were created by extrapolating the costs reported by participants by available national prevalence data.Results: Survey respondents (N = 375; response rate, 46.9%) were, on average, 67.0 years old (min 53, max 91). The majority (69.1%; n = 259) consulted at least one health care practitioner in the previous 12 months for their asthma. Most of the participants (n = 247; 65.9%) reported using at least one prescription medication for asthma in the previous 12 months. The total out-of-pocket expenditure on asthma treatment for Australian women aged 50 years and over is estimated to be AU$159 million per annum.Conclusions: The breadth of conventional and complementary medicine health care services reported in this study, as well as the range of treatments that patients self-prescribe, highlights the challenges of coordinating care for individuals living with asthma

Approximating Fixation Probabilities in the Generalized Moran Process

We consider the Moran process, as generalized by Lieberman, Hauert and Nowak (Nature, 433:312--316, 2005). A population resides on the vertices of a finite, connected, undirected graph and, at each time step, an individual is chosen at random with probability proportional to its assigned 'fitness' value. It reproduces, placing a copy of itself on a neighbouring vertex chosen uniformly at random, replacing the individual that was there. The initial population consists of a single mutant of fitness $r>0$ placed uniformly at random, with every other vertex occupied by an individual of fitness 1. The main quantities of interest are the probabilities that the descendants of the initial mutant come to occupy the whole graph (fixation) and that they die out (extinction); almost surely, these are the only possibilities. In general, exact computation of these quantities by standard Markov chain techniques requires solving a system of linear equations of size exponential in the order of the graph so is not feasible. We show that, with high probability, the number of steps needed to reach fixation or extinction is bounded by a polynomial in the number of vertices in the graph. This bound allows us to construct fully polynomial randomized approximation schemes (FPRAS) for the probability of fixation (when $r\geq 1$) and of extinction (for all $r>0$).Comment: updated to the final version, which appeared in Algorithmic

Exercise, or exercise and diet for the management of polycystic ovary syndrome:a systematic review and meta-analysis

Background: Typically, management of PCOS focuses on lifestyle changes (exercise and diet), aiming to alleviate symptoms, and lower the associated risk of type 2 diabetes and cardiovascular disease. Our objective was to analyse evidence on the effectiveness of exercise in the management of PCOS, when compared to (i) usual care, (ii) diet alone, and (iii) exercise combined with diet, and also exercise combined with diet, compared to (i) control or usual care and (ii) diet alone. Methods: Relevant databases were searched (June 2017) with no time limit for trial inclusion. Eligible trials employed a randomised or quasi-randomised design to measure the chronic effects of exercise, or exercise and diet in women with PCOS. Results: Searches returned 2390 articles; of those, 27 papers from 18 trials were included. Results are presented as mean difference (MD) and 95% confidence intervals (95% CI). Compared with control, exercise had a statistical effect on change from baseline fasting insulin (MD - 2.44 μIU/mL, 95% CIs - 4.24 to - 0.64; very low-quality evidence), HOMA-IR (- 0.57, - 0.99 to - 0.14; very low-quality evidence), total cholesterol (- 5.88 mg/dL, - 9.92 to - 1.83; low-quality evidence), LDL cholesterol (- 7.39 mg/dL, - 9.83 to - 4.95; low-quality evidence), and triglycerides (- 4.78 mg/dL, - 7.52 to - 2.05; low-quality evidence). Exercise also improved VO 2 max (3.84 ml/kg/min, 2.87 to 4.81), waist circumference (- 2.62 cm, - 4.13 to - 1.11), and body fat percentage (- 1.39%, - 2.61 to - 0.18) when compared with usual care. No effect was found for change value systolic/diastolic blood pressure, fasting glucose, HDL cholesterol (all low-quality evidence), or waist-to-hip ratio. Many favourable change score findings were supported by post-intervention value analyses: fasting insulin (- 2.11 μIU/mL, - 3.49 to - 0.73), total cholesterol (- 6.66 mg/dL, - 11.14 to - 2.17), LDL cholesterol (- 6.91 mg/dL, - 12.02 to - 1.80), and VO 2 max (5.01 ml/kg/min, 3.48 to 6.54). Statistically lower BMI (- 1.02 kg/m 2 , - 1.81 to - 0.23) and resting heart rate (- 3.26 beats/min - 4.93 to - 1.59) were also revealed in post-intervention analysis. Subgroup analyses revealed the greatest improvements in overweight/obese participants, and more outcomes improved when interventions were supervised, aerobic in nature, or of a shorter duration. Based on limited data, we found no differences for any outcome between the effects of exercise and diet combined, and diet alone. It was not possible to compare exercise vs diet or exercise and diet combined vs diet. Conclusion: Statistically beneficial effects of exercise were found for a range of metabolic, anthropometric, and cardiorespiratory fitness-related outcomes. However, caution should be adopted when interpreting these findings since many outcomes present modest effects and wide CIs, and statistical effects in many analyses are sensitive to the addition/removal of individual trials. Future work should focus on rigorously designed, well-reported trials that make comparisons involving both exercise and diet

Eco-rating System for Optimizing Pesticide Use at Farm Level Part 2, Evaluation, Examples and Piloting K A

Abstract The development of a decision support system aims to encourage farmers in the UK to adopt a more environmentally friendly approach to their daily activities. Part of the system concentrates on crop protection encouraging best practice and the principles of integrated pest management. The system compares actual practices on a field by field basis with what is perceived to be best practice and, using scoring techniques, derives numerical performance indices, known as eco-ratings, which lie on a defined scale. The conceptual framework of the system is designed such that by analysing past decisions it can help to identify strengths and weaknesses of current practices and so support future decisions and planning. This paper presents some of the evaluation work and provides examples and information on the scoring system used. The examples used illustrate the success of the system in providing the user with sufficient advice and information such that informed decisions regarding pesticide choice, application and general management can be made. An associated paper (Part 1) in this journal details the theory, design and development of the methodology