Stochastic differential equations for evolutionary dynamics with demographic noise and mutations

We present a general framework to describe the evolutionary dynamics of an arbitrary number of types in finite populations based on stochastic differential equations (SDE). For large, but finite populations this allows to include demographic noise without requiring explicit simulations. Instead, the population size only rescales the amplitude of the noise. Moreover, this framework admits the inclusion of mutations between different types, provided that mutation rates, $\mu$, are not too small compared to the inverse population size 1/N. This ensures that all types are almost always represented in the population and that the occasional extinction of one type does not result in an extended absence of that type. For $\mu N\ll1$ this limits the use of SDE's, but in this case there are well established alternative approximations based on time scale separation. We illustrate our approach by a Rock-Scissors-Paper game with mutations, where we demonstrate excellent agreement with simulation based results for sufficiently large populations. In the absence of mutations the excellent agreement extends to small population sizes.Comment: 8 pages, 2 figures, accepted for publication in Physical Review

Coevolutionary Dynamics: From Finite to Infinite Populations

Traditionally, frequency dependent evolutionary dynamics is described by deterministic replicator dynamics assuming implicitly infinite population sizes. Only recently have stochastic processes been introduced to study evolutionary dynamics in finite populations. However, the relationship between deterministic and stochastic approaches remained unclear. Here we solve this problem by explicitly considering large populations. In particular, we identify different microscopic stochastic processes that lead to the standard or the adjusted replicator dynamics. Moreover, differences on the individual level can lead to qualitatively different dynamics in asymmetric conflicts and, depending on the population size, can even invert the direction of the evolutionary process.Comment: 4 pages (2 figs included). Published in Phys. Rev. Lett., December 200

Phase transitions and volunteering in spatial public goods games

Cooperative behavior among unrelated individuals in human and animal societies represents a most intriguing puzzle to scientists in various disciplines. Here we present a simple yet effective mechanism promoting cooperation under full anonymity by allowing for voluntary participation in public goods games. This natural extension leads to rock--scissors--paper type cyclic dominance of the three strategies cooperate, defect and loner i.e. those unwilling to participate in the public enterprise. In spatial settings with players arranged on a regular lattice this results in interesting dynamical properties and intriguing spatio-temporal patterns. In particular, variations of the value of the public good leads to transitions between one-, two- and three-strategy states which are either in the class of directed percolation or show interesting analogies to Ising-type models. Although volunteering is incapable of stabilizing cooperation, it efficiently prevents successful spreading of selfish behavior and enables cooperators to persist at substantial levels.Comment: 4 pages, 5 figure

Coevolutionary dynamics in large, but finite populations

Coevolving and competing species or game-theoretic strategies exhibit rich and complex dynamics for which a general theoretical framework based on finite populations is still lacking. Recently, an explicit mean-field description in the form of a Fokker-Planck equation was derived for frequency-dependent selection with two strategies in finite populations based on microscopic processes [A. Traulsen, J. C. Claussen, and C. Hauert, Phys. Rev. Lett. 95, 238701 (2005)]. Here we generalize this approach in a twofold way: First, we extend the framework to an arbitrary number of strategies and second, we allow for mutations in the evolutionary process. The deterministic limit of infinite population size of the frequency-dependent Moran process yields the adjusted replicator-mutator equation, which describes the combined effect of selection and mutation. For finite populations, we provide an extension taking random drift into account. In the limit of neutral selection, i.e., whenever the process is determined by random drift and mutations, the stationary strategy distribution is derived. This distribution forms the background for the coevolutionary process. In particular, a critical mutation rate uc is obtained separating two scenarios: above uc the population predominantly consists of a mixture of strategies whereas below uc the population tends to be in homogeneous states. For one of the fundamental problems in evolutionary biology, the evolution of cooperation under Darwinian selection, we demonstrate that the analytical framework provides excellent approximations to individual based simulations even for rather small population sizes. This approach complements simulation results and provides a deeper, systematic understanding of coevolutionary dynamics

IL1B and DEFB1 Polymorphisms Increase Susceptibility to Invasive Mold Infection After Solid-Organ Transplantation

Background. Single-nucleotide polymorphisms (SNPs) in immune genes have been associated with susceptibility to invasive mold infection (IMI) among hematopoietic stem cell but not solid-organ transplant (SOT) recipients. Methods. Twenty-four SNPs from systematically selected genes were genotyped among 1101 SOT recipients (715 kidney transplant recipients, 190 liver transplant recipients, 102 lung transplant recipients, 79 heart transplant recipients, and 15 recipients of other transplants) from the Swiss Transplant Cohort Study. Association between SNPs and the end point were assessed by log-rank test and Cox regression models. Cytokine production upon Aspergillus stimulation was measured by enzyme-linked immunosorbent assay in peripheral blood mononuclear cells (PBMCs) from healthy volunteers and correlated with relevant genotypes. Results. Mold colonization (n = 45) and proven/probable IMI (n = 26) were associated with polymorphisms in the genes encoding interleukin 1β (IL1B; rs16944; recessive mode, P = .001 for colonization and P = .00005 for IMI, by the log-rank test), interleukin 1 receptor antagonist (IL1RN; rs419598; P = .01 and P = .02, respectively), and β-defensin 1 (DEFB1; rs1800972; P = .001 and P = .0002, respectively). The associations with IL1B and DEFB1 remained significant in a multivariate regression model (P = .002 for IL1B rs16944; P = .01 for DEFB1 rs1800972). The presence of 2 copies of the rare allele of rs16944 or rs419598 was associated with reduced Aspergillus-induced interleukin 1β and tumor necrosis factor α secretion by PBMCs. Conclusions. Functional polymorphisms in IL1B and DEFB1 influence susceptibility to mold infection in SOT recipients. This observation may contribute to individual risk stratificatio

Influence of IFNL3/4 polymorphisms on the incidence of cytomegalovirus infection after solid-organ transplantation

Background. Polymorphisms in the interferon-λ (IFNL) 3/4 region have been associated with reduced hepatitis C virus clearance. We explored the role of such polymorphisms on the incidence of CMV infection in solid-organ transplant (SOT) recipients. Methods. Caucasian patients participating in the Swiss Transplant Cohort Study in 2008-2011 were included. A novel functional TT/-G polymorphism (rs368234815) in the CpG region upstream of IFNL3 was investigated. Results. A total of 840 SOT recipients at risk for CMV were included, among whom 373 (44%) received antiviral prophylaxis. The 12-months cumulative incidence of CMV replication and disease were 0.44 and 0.08, respectively. Patient homozygous for the minor rs368234815 allele (-G/-G) tended to have a higher cumulative incidence of CMV replication (SHR=1.30 [95%CI 0.97-1.74], P=0.07) compared to other patients (TT/TT or TT/-G). The association was significant among patients followed by a preemptive approach (SHR=1.46 [1.01-2.12], P=0.047), especially in patients receiving an organ from a seropositive donor (D+, SHR=1.92 [95%CI 1.30-2.85], P=0.001), but not among those who received antiviral prophylaxis (SHR=1.13 [95%CI 0.70-1.83], P=0.6). These associations remained significant in multivariate competing risk regression models. Conclusions. Polymorphisms in the IFNL3/4 region influence susceptibility to CMV replication in SOT recipients, particularly in patients not receiving antiviral prophylaxi

PTX3 Polymorphisms and Invasive Mold Infections After Solid Organ Transplant

Donor PTX3 polymorphisms were shown to influence the risk of invasive aspergillosis among hematopoietic stem cell transplant recipients. Here, we show that PTX3 polymorphisms are independent risk factors for invasive mold infections among 1101 solid organ transplant recipients, thereby strengthening their role in mold infection pathogenesis and patients' risk stratificatio