Numerical Computation of Finite Size Scaling Functions: An Alternative Approach to Finite Size Scaling

Using single cluster flip Monte Carlo simulations we accurately determine new finite size scaling functions which are expressed only in terms the variable $x = \xi_L / L$, where $\xi_L$ is the correlation length in a finite system of size $L$. Data for the d=2 and d=3 Ising models, taken at different temperatures and for different size lattices, show excellent data collapse over the entire range of scaling variable for susceptibility and correlation length. From these finite size scaling functions we can estimate critical temperatures and exponents with rather high accuracy even though data are not obtained extremely close to the critical point. The bulk values of the renormalized four-point coupling constant are accurately measured and show strong evidence for hyperscaling.Comment: RevTex. 19 page

Complex Transition to Cooperative Behavior in a Structured Population Model

Cooperation plays an important role in the evolution of species and human societies. The understanding of the emergence and persistence of cooperation in those systems is a fascinating and fundamental question. Many mechanisms were extensively studied and proposed as supporting cooperation. The current work addresses the role of migration for the maintenance of cooperation in structured populations. This problem is investigated in an evolutionary perspective through the prisoner's dilemma game paradigm. It is found that migration and structure play an essential role in the evolution of the cooperative behavior. The possible outcomes of the model are extinction of the entire population, dominance of the cooperative strategy and coexistence between cooperators and defectors. The coexistence phase is obtained in the range of large migration rates. It is also verified the existence of a critical level of structuring beyond that cooperation is always likely. In resume, we conclude that the increase in the number of demes as well as in the migration rate favor the fixation of the cooperative behavior

Genetic protein variation in red mullet (Mullus barbatus) and striped red mullet (M-surmuletus) populations from the Mediterranean Sea

Starch-gel electrophoresis of allozymes was used to differentiate the two red mullet species (Mullus barbatus L. and ill. surmuletus L.) in the Mediterranean Sea and, further, to investigate the genetic stock structure of M. barbatus in the eastern Mediterranean area. Twenty putative enzyme-coding loci were examined in eight M. barbatus samples caught in the Aegean and Ionian Seas (Greece) and in the Gulf of Lion (France), and two M. surmuletus samples caught in the Aegean and Gulf of Lion. A high degree of genetic polymorphism was found in both species. Species-specific electrophoretic patterns were found in PGI* and PGM*. Estimates of variance of allele frequencies among samples (F-ST) and chi(2) analyses both revealed significant differences (P < 0.05) among the hi. barbatus samples. Mast of the genetic variation was among samples regardless of region. The mean value of Nei's genetic distance between the two species was 0.329. Genetic distance among M. barbatus samples was low (maximum Nei's D = 0.012), with the sample from Platania differing most from other M. barbatus samples. This is probably be due to founder effects existing at this area. These results suggest that allozyme analysis may provide important information on the genetic structure of the red mullet to ensure sustainable management of this species

Cooperation level conditioned on the persistence of the cooperative behavior.

<p>Frequency of cooperators as a function of migration . The parameter values are the same as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0039188#pone-0039188-g002" target="_blank">Figure 2</a>. The data points are averages over independent runs.</p

Description of the model.

<p>Left panel: The payoff matrix which describes the payoff value after one round of the prisoner's dilemma game between two players (blue and orange) according to their strategies. Middle panel: An illustration of the structured population model. In this instance the population comprises demes each one with carrying capacity . At this moment one of the demes is empty but recolonization is possible through migration from the two neighbor demes. Just to point out, after migration the number of individuals can exceed or be under the carrying capacity . Right panel: The links represent possible paths where migrants can go through.</p

Evolution of the cooperative behavior with migration.

<p>Panel(a) Persistence of the cooperative behavior. The likelihood of fixation of cooperators as a function of the migration rate . (b) Probability of coexistence between cooperators and defectors versus migration rate . The parameter values are maximum population size , number of subpopulations , elimination threshold and payoff matrix elements , , . The data points are averages over independent runs.</p

Effect of population size and number of demes on the outcomes of the model.

<p>Upper left panel: Probability of fixation of the cooperative strategy (triangles) and probability of coexistence between cooperators and defectors (circles) against migration rate for distinct values of population size. Upper right panel: frequency of cooperators as a function of migration rate and different values of the population size and representation follows the one used in the left panel. In the upper panels the parameter values are , , , , . Lower left panel: Probability of fixation of the cooperative strategy (triangles) and probability of coexistence between cooperators and defectors (circles) against migration rate for fixed population size and different number of demes. Lower right panel: frequency of cooperators as a function of migration rate and different values of deme size and representation follows the one used in the left panel. The parameter values are , , , , . The data points are averages over independent runs.</p

Dependence on the topology of the migration network.

<p>Left panel: Probability of fixation of the cooperative strategy (circles) and probability of coexistence between cooperators and defectors (squares) versus migration rate . Right panel: Frequency of cooperators as a function of the migration rate . In both panels, the topologies of the migratory networks are: random graph (black symbol), scale-free networks (red symbols), and island model (green symbols). The parameter values are , , , , , .</p