The Evolution of Conditional Dispersal Strategies inSpatially Heterogeneous HabitatsHambrock, R.; Lou, Y.
doi: 10.1007/s11538-009-9425-7pmid: 19475455
To understand the evolution of dispersal, we study a Lotka–Volterra reaction–diffusion–advection model for two competing species in a heterogeneous environment. The two species are assumed to be identical except for their dispersal strategies: both species disperse by random diffusion and advection along environmental gradients, but with slightly different random dispersal or advection rates. Two new phenomena are found for one-dimensional habitats and monotone intrinsic growth rates: (i) If both species disperse only by random diffusion, i.e., no advection, it was well known that the slower diffuser always wins. We show that if both species have the same advection rate which is suitably large, the faster dispersal will evolve; (ii) If both species have the same random dispersal rate, it was known that the species with a little advection along the resource gradient always wins, provided that the other species is a pure random disperser and the habitat is convex. We show that if both species have the same random dispersal rate and both also have suitably large advection rates, the species with a little smaller advection rate always wins. Implications of these results for the habitat choices of species will be discussed. Some future directions and open problems will be addressed.
A Theoretical Analysis of Temporal Difference Learning intheIterated Prisoner’s Dilemma GameMasuda, Naoki; Ohtsuki, Hisashi
doi: 10.1007/s11538-009-9424-8pmid: 19479310
Direct reciprocity is a chief mechanism of mutual cooperation in social dilemma. Agents cooperate if future interactions with the same opponents are highly likely. Direct reciprocity has been explored mostly by evolutionary game theory based on natural selection. Our daily experience tells, however, that real social agents including humans learn to cooperate based on experience. In this paper, we analyze a reinforcement learning model called temporal difference learning and study its performance in the iterated Prisoner’s Dilemma game. Temporal difference learning is unique among a variety of learning models in that it inherently aims at increasing future payoffs, not immediate ones. It also has a neural basis. We analytically and numerically show that learners with only two internal states properly learn to cooperate with retaliatory players and to defect against unconditional cooperators and defectors. Four-state learners are more capable of achieving a high payoff against various opponents. Moreover, we numerically show that four-state learners can learn to establish mutual cooperation for sufficiently small learning rates.
Sequential Activation of Metabolic Pathways: a Dynamic Optimization ApproachOyarzún, Diego; Ingalls, Brian; Middleton, Richard; Kalamatianos, Dimitrios
doi: 10.1007/s11538-009-9427-5pmid: 19412635
The regulation of cellular metabolism facilitates robust cellular operation in the face of changing external conditions. The cellular response to this varying environment may include the activation or inactivation of appropriate metabolic pathways. Experimental and numerical observations of sequential timing in pathway activation have been reported in the literature. It has been argued that such patterns can be rationalized by means of an underlying optimal metabolic design. In this paper we pose a dynamic optimization problem that accounts for time-resource minimization in pathway activation under constrained total enzyme abundance. The optimized variables are time-dependent enzyme concentrations that drive the pathway to a steady state characterized by a prescribed metabolic flux. The problem formulation addresses unbranched pathways with irreversible kinetics. Neither specific reaction kinetics nor fixed pathway length are assumed.
The Mutation Process in Colored Coalescent TheoryTian, Jianjun; Lin, Xiao-Song
doi: 10.1007/s11538-009-9428-4pmid: 19462210
The mutation process is introduced into the colored coalescent theory. The mutation process can be viewed as an independent Poisson process running on the colored genealogical random tree generated by the colored coalescent process, with the edge lengths of the random tree serving as the time scale for the mutation process. Moving backward along the colored genealogical tree, the color of vertices may change in two ways, when two vertices coalesce, or when a mutation happens. The rule that governs the coalescent change of color involves a parameter x; the rule that governs the mutation involves a parameter μ. Explicit computations of the expectation of the coalescent time (the first hitting time), and the coalescent probabilities (the first hitting probabilities) are carried out. For example, our calculation shows that when x=1/2, for a sample of n colored individuals, the expected time for the colored coalescent process with the mutation process superimposed to first reach a black MRCA or a white MRCA, respectively, is 3−2/n with probability 1/2 for any value of the parameter μ. On the other hand, the expected time for the colored coalescent process with mutation to first reach a MRCA, either black or white, is 2−2/n for any values of the parameters μ and x, which is the same as that for the standard Kingman coalescent process.
The Effect of Time Distribution Shape on a Complex Epidemic ModelCamitz, Martin; Svensson, Åke
doi: 10.1007/s11538-009-9430-xpmid: 19475454
In elaborating a model of the progress of an epidemic, it is necessary to make assumptions about the distributions of latency times and infectious times. In many models, the often implicit assumption is that these times are independent and exponentially distributed. We explore the effects of altering the distribution of latency and infectious times in a complex epidemic model with regional divisions connected by a travel intensity matrix. We show a delay in spread with more realistic latency times. More realistic infectiousness times lead to faster epidemics. The effects are similar but accentuated when compared to a purely homogeneous mixing model.
A Geometric Buildup Algorithm for the Solution oftheDistance Geometry Problem Using Least-Squares ApproximationSit, Atilla; Wu, Zhijun; Yuan, Yaxiang
doi: 10.1007/s11538-009-9431-9pmid: 19533250
We propose a new geometric buildup algorithm for the solution of the distance geometry problem in protein modeling, which can prevent the accumulation of the rounding errors in the buildup calculations successfully and also tolerate small errors in given distances. In this algorithm, we use all instead of a subset of available distances for the determination of each unknown atom and obtain the position of the atom by using a least-squares approximation instead of an exact solution to the system of distance equations. We show that the least-squares approximation can be obtained by using a special singular value decomposition method, which not only tolerates and minimizes small distance errors, but also prevents the rounding errors from propagation effectively, especially when the distance data is sparse. We describe the least-squares formulations and their solution methods, and present the test results from applying the new algorithm for the determination of a set of protein structures with varying degrees of availability and accuracy of the distances. We show that the new development of the algorithm increases the modeling ability, and improves stability and robustness of the geometric buildup approach significantly from both theoretical and practical points of view.
The Role of Spatial Refuges in Coupled Map Lattice Model for Host-Parasitoid SystemsMistro, Diomar; Rodrigues, Luiz; Varriale, Maria
doi: 10.1007/s11538-009-9432-8pmid: 19495886
A Coupled Map Lattice (CML) model, for host-parasitoid Nicholson–Bailey interactions, with an explicit spatial distribution of partial refuge areas, is presented by considering the parasitoid attack rate as a patch dependent parameter. The effect of habitat heterogeneity on the dynamics of both populations, that is, on their spatial distribution and temporal behavior is analyzed. Our results show that depending on many features such as position, size, and fragmentation of a refuge, as well as the dispersal parameters of hosts and parasitoids, together with the parasitoid attack rate, the inclusion of refuges may as well stabilize as destabilize the host-parasitoid dynamics. The results are analyzed for the local and the global scales. Spatial patterns resulting from such heterogeneous patchy environments are also obtained.
On the Final Size of Epidemics with SeasonalityBacaër, Nicolas; Gomes, M. Gabriela M.
doi: 10.1007/s11538-009-9433-7pmid: 19475453
We first study an SIR system of differential equations with periodic coefficients describing an epidemic in a seasonal environment. Unlike in a constant environment, the final epidemic size may not be an increasing function of the basic reproduction number ℛ0 or of the initial fraction of infected people. Moreover, large epidemics can happen even if ℛ0<1. But like in a constant environment, the final epidemic size tends to 0 when ℛ0<1 and the initial fraction of infected people tends to 0. When ℛ0>1, the final epidemic size is bigger than the fraction 1−1/ℛ0 of the initially nonimmune population. In summary, the basic reproduction number ℛ0 keeps its classical threshold property but many other properties are no longer true in a seasonal environment. These theoretical results should be kept in mind when analyzing data for emerging vector-borne diseases (West-Nile, dengue, chikungunya) or air-borne diseases (SARS, pandemic influenza); all these diseases being influenced by seasonality.