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

Influence of biomass combustion emissions on the distribution of acidic trace gases over the southern Pacific basin during austral springtime

This paper describes the large-scale distributions of HNO3, HCOOH, and CH3COOH over the central and South Pacific basins during the Pacific Exploratory Mission-Tropics (PEM-Tropics) in austral springtime. Because of the remoteness of this region from continental areas, low part per trillion by volume (pptv) mixing ratios of acidic gases were anticipated to be pervasive over the South Pacific basin. However, at altitudes of 2–12 km over the South Pacific, air parcels were encountered frequently with significantly enhanced mixing ratios (up to 1200 pptv) of acidic gases. Most of these air parcels were centered in the 3–7 km altitude range and occurred within the 15°−65°S latitudinal band. The acidic gases exhibited an overall general correlation with CH3Cl, PAN, and O3, suggestive of photochemical and biomass burning sources. There was no correlation or trend of acidic gases with common industrial tracer compounds (e.g., C2Cl4 or CH3CCl3). The combustion emissions sampled over the South Pacific basin were relatively aged exhibiting C2H2/CO ratios in the range of 0.2–2.2 pptv/ppbv. The relationships between acidic gases and this ratio were similar to what was observed in aged air parcels (i.e., \u3e3–5 days since they were over a continental area) over the western North Pacific during the Pacific Exploratory Mission-West Phases A and B (PEM-West A and B). In the South Pacific marine boundary layer a median C2H2/CO ratio of 0.6 suggested that this region was generally not influenced by direct inputs of biomass combustion emissions. Here we observed the lowest mixing ratios of acidic gases, with median values of 14 pptv for HNO3, 19 pptv for HCOOH, and 18 pptv for CH3COOH. These values were coincident with low mixing ratios of NOx(\u3c10 pptv), CO (≈50 parts per billion by volume (ppbv)), O3 (\u3c 20 ppbv), and long-lived hydrocarbons (e.g., C2H6 \u3c300 pptv). Overall, the PEM-Tropics data suggest an important influence of aged biomass combustion emissions on the distributions of acidic gases over the South Pacific basin in austral springtime

Reactive nitrogen in Asian continental outflow over the western Pacific: Results from the NASA Transport and Chemical Evolution over the Pacific (TRACE-P) airborne mission

We present here results for reactive nitrogen species measured aboard the NASA DC-8 aircraft during the Transport and Chemical Evolution over the Pacific (TRACE-P) mission. The large-scale distributions total reactive nitrogen (NOy,sum = NO + NO2 + HNO3 + PAN + C1–C5alkyl nitrates) and O3 and CO were better defined in the boundary layer with significant degradation of the relationships as altitude increased. Typically, NOy,sum was enhanced over background levels of ∼260 pptv by 20-to-30-fold. The ratio C2H2/CO had values of 1–4 at altitudes up to 10 km and as far eastward as 150°E, implying significant vertical mixing of air parcels followed by rapid advection across the Pacific. Analysis air parcels originating from five principal Asian source regions showed that HNO3 and PAN dominated NOy,sum. Correlations of NOy,sum with C2Cl4 (urban tracer) were not well defined in any of the source regions, and they were only slightly better with CH3Cl (biomass tracer). Air parcels over the western Pacific contained a complex mixture of emission sources that are not easily resolvable as shown by analysis of the Shanghai mega-city plume. It contained an intricate mixture of pollution emissions and exhibited the highest mixing ratios of NOy,sum species observed during TRACE-P. Comparison of tropospheric chemistry between the earlier PEM-West B mission and the recent TRACE-P data showed that in the boundary layer significant increases in the mixing ratios of NOy,sum species have occurred, but the middle and upper troposphere seems to have been affected minimally by increasing emissions on the Asian continent over the last 7 years

Asian Influence Over the Western North Pacific during the Fall Season: Inferences from Lead 210, Soluble Ionic Species and Ozone

Aerosol samples collected over the western Pacific during the NASA/Global Tropospheric Experiment Pacific Exploratory Mission (PEM-West A) expedition (September - October 1991) revealed mean Pb-210 concentrations in the free troposphere in the 5-10 fCi m(exp -3) STP range. Most soluble ionic aerosol-associated species were near detection limits [much less than 40 parts per trillion by volume (pptv)] in these same samples. The altitude distribution of O3 near Asia closely resembled that of Pb-210, while no relationship was found between the concentrations of O3 and Be-7. Free tropospheric air over the western Pacific was depleted in soluble aerosol-associated species but enriched in Pb-210 and O3, indicative of deep wet convection over the Asian continent. The influence of Asian air on the composition of the free troposphere over the western Pacific was evident on most of the PEM-West A flights. However, evidence of continental influence was largely restricted to those species that are relatively insoluble (or have insoluble precursors), hence escape scavenging during vertical transport from the boundary layer into the free troposphere by wet convective activity

Fixation, transient landscape and diffusion's dilemma in stochastic evolutionary game dynamics

Agent-based stochastic models for finite populations have recently received much attention in the game theory of evolutionary dynamics. Both the ultimate fixation and the pre-fixation transient behavior are important to a full understanding of the dynamics. In this paper, we study the transient dynamics of the well-mixed Moran process through constructing a landscape function. It is shown that the landscape playing a central theoretical "device" that integrates several lines of inquiries: the stable behavior of the replicator dynamics, the long-time fixation, and continuous diffusion approximation associated with asymptotically large population. Several issues relating to the transient dynamics are discussed: (i) multiple time scales phenomenon associated with intra- and inter-attractoral dynamics; (ii) discontinuous transition in stochastically stationary process akin to Maxwell construction in equilibrium statistical physics; and (iii) the dilemma diffusion approximation facing as a continuous approximation of the discrete evolutionary dynamics. It is found that rare events with exponentially small probabilities, corresponding to the uphill movements and barrier crossing in the landscape with multiple wells that are made possible by strong nonlinear dynamics, plays an important role in understanding the origin of the complexity in evolutionary, nonlinear biological systems.Comment: 34 pages, 4 figure

Assessment of ozone photochemistry in the western North Pacific as inferred from PEM-West A observations during the fall 1991

This study examines the influence of photochemical processes on ozone distributions in the western North Pacific. The analysis is based on data generated during NASA's western Pacific Exploratory Mission (PEM-West A) during the fall of 1991. Ozone trends were best described in terms of two geographical domains: the western North Pacific rim (WNPR) and the western tropical North Pacific (WTNP). For both geographical regions, ozone photochemical destruction, D(O3), decreased more rapidly with altitude than did photochemical formation, F(O3). Thus the ozone tendency, P(O3), was typically found to be negative for z <6 km and positive for z > 6-8 km. For nearly all altitudes and latitudes, observed nonmethane hydrocarbon (NMHC) levels were shown to be of minor importance as ozone precursor species. Air parcel types producing the largest positive values of P(O3) included fresh continental boundary layer (BL) air and high-altitude (z > 7 km) parcels influenced by deep convection/lightning. Significant negative P(O3) values were found when encountering clean marine BL air or relatively clean lower free-tropospheric air. Photochemical destruction and formation fluxes for the Pacific rim region were found to exceed average values cited for marine dry deposition and stratospheric injection in the northern hemisphere by nearly a factor of 6. This region was also found to be in near balance with respect to column-integrated O3 photochemical production and destruction. By contrast, for the tropical regime column-integrated O3 showed photochemical destruction exceeding production by nearly 80%. Both transport of O3 rich midlatitude air into the tropics as well as very high-altitude (10-17 km) photochemical O3 production were proposed as possible additional sources that might explain this estimated deficit. Results from this study further suggest that during the fall time period, deep convection over Asia and Malaysia/Indonesia provided a significant source of high-altitude NOx to the western Pacific. Given that the high-altitude NOx lifetime is estimated at between 3 and 9 days, one would predict that this source added significantly to high altitude photochemical O3 formation over large areas of the western Pacific. When viewed in terms of strong seasonal westerly flow, its influence would potentially span a large part of the Pacific. Copyright 1996 by the American Geophysical Union

Le Chatelier principle in replicator dynamics

The Le Chatelier principle states that physical equilibria are not only stable, but they also resist external perturbations via short-time negative-feedback mechanisms: a perturbation induces processes tending to diminish its results. The principle has deep roots, e.g., in thermodynamics it is closely related to the second law and the positivity of the entropy production. Here we study the applicability of the Le Chatelier principle to evolutionary game theory, i.e., to perturbations of a Nash equilibrium within the replicator dynamics. We show that the principle can be reformulated as a majorization relation. This defines a stability notion that generalizes the concept of evolutionary stability. We determine criteria for a Nash equilibrium to satisfy the Le Chatelier principle and relate them to mutualistic interactions (game-theoretical anticoordination) showing in which sense mutualistic replicators can be more stable than (say) competing ones. There are globally stable Nash equilibria, where the Le Chatelier principle is violated even locally: in contrast to the thermodynamic equilibrium a Nash equilibrium can amplify small perturbations, though both this type of equilibria satisfy the detailed balance condition.Comment: 12 pages, 3 figure