Diverging fluctuations in a spatial five-species cyclic dominance game

A five-species predator-prey model is studied on a square lattice where each species has two prey and two predators on the analogy to the Rock-Paper-Scissors-Lizard-Spock game. The evolution of the spatial distribution of species is governed by site exchange and invasion between the neighboring predator-prey pairs, where the cyclic symmetry can be characterized by two different invasion rates. The mean-field analysis has indicated periodic oscillations in the species densities with a frequency becoming zero for a specific ratio of invasion rates. When varying the ratio of invasion rates, the appearance of this zero-eigenvalue mode is accompanied by neutrality between the species associations. Monte Carlo simulations of the spatial system reveal diverging fluctuations at a specific invasion rate, which can be related to the vanishing dominance between all pairs of species associations.Comment: accepted for publication in Physical Review

From pairwise to group interactions in games of cyclic dominance

We study the rock-paper-scissors game in structured populations, where the invasion rates determine individual payoffs that govern the process of strategy change. The traditional version of the game is recovered if the payoffs for each potential invasion stem from a single pairwise interaction. However, the transformation of invasion rates to payoffs also allows the usage of larger interaction ranges. In addition to the traditional pairwise interaction, we therefore consider simultaneous interactions with all nearest neighbors, as well as with all nearest and next-nearest neighbors, thus effectively going from single pair to group interactions in games of cyclic dominance. We show that differences in the interaction range affect not only the stationary fractions of strategies, but also their relations of dominance. The transition from pairwise to group interactions can thus decelerate and even revert the direction of the invasion between the competing strategies. Like in evolutionary social dilemmas, in games of cyclic dominance too the indirect multipoint interactions that are due to group interactions hence play a pivotal role. Our results indicate that, in addition to the invasion rates, the interaction range is at least as important for the maintenance of biodiversity among cyclically competing strategies.Comment: 7 two-column pages, 6 figures; accepted for publication in Physical Review

DEVELOPING A SITE SPECIFIC UNDERSTANDING OF THE TOXICITY OF RARE EARTH ELEMENTS, CERIUM AND DYSPROSIUM, TO DAPHNIA PULEX AND HYALELLA AZTECA

Rare earth elements (REEs) are a group of similarly reactive metals that are divided into two groups; the light (LREEs) and heavy (HREEs) rare earths. These metals are used in a variety of industries and are critical to the function of modern society. The demand for REEs is expected to increase and as a result new mining projects are being developed with a potential for future mining in Canada. The toxicological understanding of these metals in the aquatic environment is very limited. The objective of this research is to compare the toxicological effect of REEs to the freshwater invertebrates Daphnia pulex and Hyalella azteca and in the more sensitive Hyalella to understand the toxicity modifying influence of cationic competition (Ca2+, Mg2+, Na+, H+) and dissolved organic matter (DOM) complexation. In this study cerium (Ce; a light REE) and dysprosium (Dy; a heavy REE) were chosen as representative of the two REE groups. Standard methods (Environment Canada) were followed for testing and culture; acute Ce tests were performed at low hardness (12.5 mg CaCO3 mg/L, pH 7.0, Ca 0.18, Na 0.14, Mg 0.14 (mM) for D. pulex and 32 mg CaCO3/L, pH 7.2, Ca 0.1, Na 0.101, Mg 0.03 (mM) for Hyalella at 21oC) while Dy tests were completed at intermediate hardness (62.5 mg CaCO3 mg/L) adjusted to pH 7.8 with Ca at 0.5, Na 0.5, Mg 0.125 (mM) and 23oC for both organisms. Acute toxicity tests were performed using \u3c24 h old neonates for 48 h in the case of Daphnia and with 2-9 d old offspring for 96 h tests with Hyalella. Dissolved concentrations (0.45 µm filtered) for Ce and Dy were lower than total (unfiltered) which demonstrated precipitation over the course of the exposures. As a result, the LC50s based on end concentrations provided the most conservative estimates of toxicity. Daphnia was identified as the more resilient organism to REE exposures and thus further testing with toxicity modifying factors was performed using Hyalella. The protective effect of cationic competition was tested with Ca (0.1 to 2.0 mM), Na (0.1 to 2.0 mM) and Mg (0.03 to 0.5 mM) and it was determined that Ca and Na (in the case of Dy exposures) were protective of acute REE toxicity while Mg had no effect. Moreover, tests where pH (6.5 - 8.0) was altered showed a protective effect of increased H+ on acute Dy toxicity. The ability of dissolved organic matter (DOM) to complex Ce and Dy were tested with DOM additions (4 to 15 mg C/L) and showed a dose dependent decrease in LC50s. Biotic ligand based parameters (Log K values) were calculated based on free ion relationships using geochemical equilibrium software (WHAM ver. 7.02). The Log K values derived from Ce3+ and Dy3+ LC50 to Hyalella were calculated as 7.3 and 7.75, respectively. The protective influence of Ca2+ was determined for Ce3+ (Log K = 3.9) and Dy3+ (Log K = 3.95) and in the case of Na+ and Dy3+ (Log K = 4.10). This study contributes data to the development of site specific water quality guidelines and criteria for Ce and Dy in freshwater

Accurate reactions open up the way for more cooperative societies

We consider a prisoner's dilemma model where the interaction neighborhood is defined by a square lattice. Players are equipped with basic cognitive abilities such as being able to distinguish their partners, remember their actions, and react to their strategy. By means of their short-term memory, they can remember not only the last action of their partner but the way they reacted to it themselves. This additional accuracy in the memory enables the handling of different interaction patterns in a more appropriate way and this results in a cooperative community with a strikingly high cooperation level for any temptation value. However, the more developed cognitive abilities can only be effective if the copying process of the strategies is accurate enough. The excessive extent of faulty decisions can deal a fatal blow to the possibility of stable cooperative relations

The Polumir granite: Addititional data on its origin

The Polumir granite is exposed on several localities due to erosion, and its chemical and mineral composition is presented in this paper. It is built of K-feldspar, plagioclase, myrmekite, metasomatic albite, biotite, muscovite and quartz, while apatite, magnetite, monazite, allanite and zircon are present as accessory minerals. According to its chemical and mineral composition and rock chemistry (trace and REE elements) the Polumir granite is leucocratic, sin-collisional, with S-type characteristics. It crystallized at temperature of about 650°C and under pressure of 2-4 kbar. Results of isotope analyses (K-Ar method on biotites) indicate that the Polumir granite was formed during the Miocene (14-19 Ma) and it has undergone subsequent weak remobilization afterwards