Stochastic models in population biology and their deterministic analogs

In this paper we introduce a class of stochastic population models based on "patch dynamics". The size of the patch may be varied, and this allows one to quantify the departures of these stochastic models from various mean field theories, which are generally valid as the patch size becomes very large. These models may be used to formulate a broad range of biological processes in both spatial and non-spatial contexts. Here, we concentrate on two-species competition. We present both a mathematical analysis of the patch model, in which we derive the precise form of the competition mean field equations (and their first order corrections in the non-spatial case), and simulation results. These mean field equations differ, in some important ways, from those which are normally written down on phenomenological grounds. Our general conclusion is that mean field theory is more robust for spatial models than for a single isolated patch. This is due to the dilution of stochastic effects in a spatial setting resulting from repeated rescue events mediated by inter-patch diffusion. However, discrete effects due to modest patch sizes lead to striking deviations from mean field theory even in a spatial setting.Comment: 47 pages, 9 figure

'Mobile Only' Users Powered by Fixed-Mobile Substitution

In a context of partial fixed-mobile substitution, we analyze fixed-mobile bundling and mobile-to-fixed off-loading in a duopoly model in which consumers buy one or two products. A joint purchase discount mitigates fixed-mobile substitutability and consequently reduces mobile-only and fixed-only consumers. Practises like introducing a small discount, applied on a bundle of multiple service or mobile-to-fixed offloading by both operators are analysed. We find that such practises do not have negative impacts on the profits of whole market and lead to both consumers' surplus and welfare gains. The investment incentives in fixed network are positive and can be boosted by FM bundling without considering regulatory intervention and before taking into account of fixed costs. The investment incentives in mobile network are more likely a situation of prisoners' dilemma where operators should invest as long as there are mobile-only consumers

Unbundling in Current Broadband and Next-Generation Ultra-Broadband Access Networks

This article overviews the methods that are currently under investigation for implementing multi-operator open-access/shared-access techniques in next-generation access ultra-broadband architectures, starting from the traditional "unbundling-of-the-local-loop" techniques implemented in legacy twisted-pair digital subscriber line access networks. A straightforward replication of these copper-based unbundling-of-the-local-loop techniques is usually not feasible on next-generation access networks, including fiber-to-the-home point-to-multipoint passive optical networks. To investigate this issue, the article first gives a concise description of traditional copper-based unbundling-of-the-local-loop solutions, then focalizes on both next-generation access hybrid fiber-copper digital subscriber line fiber-to-the-cabinet scenarios and on fiber to the home by accounting for the mix of regulatory and technological reasons driving the next-generation access migration path, focusing mostly on the European situation. © 2014 Taylor and Francis Group, LLC

Does Sex-Selective Predation Stabilize or Destabilize Predator-Prey Dynamics?

Background: Little is known about the impact of prey sexual dimorphism on predator-prey dynamics and the impact of sexselective harvesting and trophy hunting on long-term stability of exploited populations. Methodology and Principal Findings: We review the quantitative evidence for sex-selective predation and study its longterm consequences using several simple predator-prey models. These models can be also interpreted in terms of feedback between harvesting effort and population size of the harvested species under open-access exploitation. Among the 81 predator-prey pairs found in the literature, male bias in predation is 2.3 times as common as female bias. We show that long-term effects of sex-selective predation depend on the interplay of predation bias and prey mating system. Predation on the ‘less limiting’ prey sex can yield a stable predator-prey equilibrium, while predation on the other sex usually destabilizes the dynamics and promotes population collapses. For prey mating systems that we consider, males are less limiting except for polyandry and polyandrogyny, and male-biased predation alone on such prey can stabilize otherwise unstable dynamics. On the contrary, our results suggest that female-biased predation on polygynous, polygynandrous or monogamous prey requires other stabilizing mechanisms to persist. Conclusions and Significance: Our modelling results suggest that the observed skew towards male-biased predation might reflect, in addition to sexual selection, the evolutionary history of predator-prey interactions. More focus on these phenomena can yield additional and interesting insights as to which mechanisms maintain the persistence of predator-prey pairs over ecological and evolutionary timescales. Our results can also have implications for long-term sustainability of harvesting and trophy hunting of sexually dimorphic species

Recruitment Constraints in Singapore's Fluted Giant Clam (Tridacna squamosa) Populations - A Dispersal Model Approach

10.1371/journal.pone.0058819PLoS ONE83

Checking Individual Agent Behaviours in Markov Population Models by Fluid Approximation

In this chapter, we will describe, in a tutorial style, recent work on the use of fluid approximation techniques in the context of stochastic model checking. We will discuss the theoretical background and the algorithms working out an example. This approach is designed for population models, in which a (large) number of individual agents interact, which give rise to continuous time Markov chain (CTMC) models with a very large state space. We then focus on properties of individual agents in the system, specified by Continuous Stochastic Logic (CSL) formulae, and use fluid approximation techniques (specifically, the so called fast simulation) to check those properties. We will show that verification of such CSL formulae reduces to the computation of reachability probabilities in a special kind of time-inhomogeneous CTMC with a small state space, in which both the rates and the structure of the CTMC can change (discontinuously) with time. In this tutorial, we will discuss only briefly the theoretical issues behind the approach, like the decidability of the method and the consistency of the approximation scheme