Patchy populations in stochastic environments: Critical number of patches for persistence

We introduce a model for the dynamics of a patchy population in a stochastic environment and derive a criterion for its persistence. This criterion is based on the geometric mean (GM) through time of the spatial-arithmetic mean of growth rates. For the population to persist, the GM has to be greater than or equal to1. The GM increases with the number of patches (because the sampling error is reduced) and decreases with both the variance and the spatial covariance of growth rates. We derive analytical expressions for the minimum number of patches (and the maximum harvesting rate) required for the persistence of the population. As the magnitude of environmental fluctuations increases, the number of patches required for persistence increases, and the fraction of individuals that can be harvested decreases. The novelty of our approach is that we focus on Malthusian local population dynamics with high dispersal and strong environmental variability from year to year. Unlike previous models of patchy populations that assume an infinite number of patches, we focus specifically on the effect that the number of patches has on population persistence. Our work is therefore directly relevant to patchily distributed organisms that are restricted to a small number of habitat patches

Pattern formation in a predator-prey system characterized by a spatial scale of interaction

We describe pattern formation in ecological systems using a version of the classical Lotka-Volterra model characterized by a spatial scale which controls the predator-prey interaction range. Analytical and simulational results show that patterns can emerge in some regions of the parameters space where the instability is driven by the range of the interaction. The individual-based implementation captures realistic ecological features. In fact, spatial structures emerge in an erratic oscillatory regime which can contemplate predators' extinction.Comment: 5 pages, 4 figure

Population Cycling in Space-Limited Organisms Subject to Density-Dependent Predation

We present a population model with density-dependent disturbance. The model is motivated by, and is illustrated with, data on the percentage of space covered by barnacles on quadrats of rock in the intertidal zone. The autocorrelation function observed indicates population cycling. This autocorrelation function is predicted qualitatively and quantitatively by the detailed model we present. The general version of the model suggests the following rules regarding cycling in space-limited communities subject to density-dependent disturbances. These rules may apply to any space-limited community where a density-dependent disturbance reduces population densities to very low levels, like fire or wind for plant communities. We propose that the period of the cycle will be approximately equal to the time it takes the community to reach a critical density plus the average time between disturbance events when the density is above that critical density. The cycling will only be clear from autocorrelation data if the growth process is relatively consistent, there is a critical density (which the sessile organism reaches and passes) above which the probability of disturbance increases rapidly, and the time to reach the critical density is at least twice the average time between disturbance events

What does Remote Sensing Do for Ecology?

The phrase “remote sensing” sounds like a theoretician’s delight—a way to get data while sitting in an armchair. Unfortunately, while some remote sensing activities can be done in a chair, substantial legwork is also needed to ensure accurate interpretation o f remotely sensed signals. Even for the work done from the armchair, remote sensing analysis is far from sim ple and straightforward

Simulated ecology-driven sympatric speciation

We introduce a multi-locus genetically acquired phenotype, submitted to mutations and with selective value, in an age-structured model for biological aging. This phenotype describes a single-trait effect of the environment on an individual, and we study the resulting distribution of this trait among the population. In particular, our simulations show that the appearance of a double phenotypic attractor in the ecology induces the emergence of a stable polymorphism, as observed in the Galapagos finches. In the presence of this polymorphism, the simulations generate short-term speciation, when mating preferences are also allowed to suffer mutations and acquire selective value.Comment: 11 pages, 5 figures, 1 table, uses package RevTe

The asymptotic price of anarchy for k-uniform congestion games

We consider the atomic version of congestion games with affine cost functions, and analyze the quality of worst case Nash equilibria when the strategy spaces of the players are the set of bases of a k-uniform matroid. In this setting, for some parameter k, each player is to choose k out of a finite set of resources, and the cost of a player for choosing a resource depends affine linearly on the number of players choosing the same resource. Earlier work shows that the price of anarchy for this class of games is larger than 1.34 but at most 2.15. We determine a tight bound on the asymptotic price of anarchy equal to ≈1.35188. Here, asymptotic refers to the fact that the bound holds for all instances with sufficiently many players. In particular, the asymptotic price of anarchy is bounded away from 4/3. Our analysis also yields an upper bound on the price of anarchy <1.4131, for all instances

Ecological model of extinctions

We present numerical results based on a simplified ecological system in evolution, showing features of extinction similar to that claimed for the biosystem on Earth. In the model each species consists of a population in interaction with the others, that reproduces and evolves in time. Each species is simultaneously a predator and a prey in a food chain. Mutations that change the interactions are supposed to occur randomly at a low rate. Extinctions of populations result naturally from the predator-prey dynamics. The model is not pinned in a fitness variable, and natural selection arises from the dynamics.Comment: 16 pages (LaTeX type, RevTeX style), including 6 figures in gif format. To be published in Phys. Rev. E (prob. Dic. 96

The Price of Anarchy in Transportation Networks: Efficiency and Optimality Control

Uncoordinated individuals in human society pursuing their personally optimal strategies do not always achieve the social optimum, the most beneficial state to the society as a whole. Instead, strategies form Nash equilibria which are often socially suboptimal. Society, therefore, has to pay a price of anarchy for the lack of coordination among its members. Here we assess this price of anarchy by analyzing the travel times in road networks of several major cities. Our simulation shows that uncoordinated drivers possibly waste a considerable amount of their travel time. Counterintuitively,simply blocking certain streets can partially improve the traffic conditions. We analyze various complex networks and discuss the possibility of similar paradoxes in physics.Comment: major revisions with multicommodity; Phys. Rev. Lett., accepte

Mechanisms that Govern how the Price of Anarchy varies with Travel Demand

Selfish routing, represented by the User-Equilibrium (UE) model, is known to be inefficient when compared to the System Optimum (SO) model. However, there is currently little understanding of how the magnitude of this inefficiency, which can be measured by the Price of Anarchy (PoA), varies across different structures of demand and supply. Such understanding would be useful for both transport policy and network design, as it could help to identify circumstances in which policy interventions that are designed to induce more efficient use of a traffic network, are worth their costs of implementation. This paper identifies four mechanisms that govern how the PoA varies with travel demand in traffic networks with separable and strictly increasing cost functions. For each OD movement, these are expansions and contractions in the sets of routes that are of minimum cost under UE and minimum marginal total cost under SO. The effects of these mechanisms on the PoA are established via a combination of theoretical proofs and conjectures supported by numerical evidence. In addition, for the special case of traffic networks with BPR-like cost functions having common power, it is proven that there is a systematic relationship between link flows under UE and SO, and hence between the levels of demand at which expansions and contractions occur. For this case, numerical evidence also suggests that the PoA has power law decay for large demand

Efficiency in Multi-objective Games

In a multi-objective game, each agent individually evaluates each overall action-profile on multiple objectives. I generalize the price of anarchy to multi-objective games and provide a polynomial-time algorithm to assess it. This work asserts that policies on tobacco promote a higher economic efficiency