Ecological niche similarities of Peponapis bees and non-domesticated Cucurbita species

Peponapis bees are considered specialized pollinators of Cucurbita flowers, a genus that presents several species of economic value (squashes and pumpkins). Both genera originated in the Americas, and their diversity dispersion center is in Mexico. Ten species of Peponapis and ten species of Cucurbita (only non-domesticated species) were analyzed considering the similarity of their ecological niche characteristics with respect to climatic conditions of their occurrence areas (abiotic variables) and interactions between species (biotic variables). The similarity of climatic conditions (temperature and precipitation) was estimated through cluster analyses. The areas of potential occurrence of the most similar species were obtained through ecological niche modeling and summed with geographic information system tools. Three main clusters were obtained: one with species that shared potential occurrence areas mainly in deserts (P. pruinosa, P. timberlakei, C. digitata, C. palmata, C. foetidissima), another in moist forests (P. limitaris, P. atrata, C. lundelliana, C. o. martinezii) and a third mainly in dry forests (C. a. sororia, C. radicans, C. pedatifolia, P. azteca, P. smithi, P. crassidentata, P. utahensis). Some species with similar ecological niche presented potential shared areas that are also similar to their geographical distribution, like those occurring predominantly on deserts. However, some clustered species presented larger geographical areas, such as P. pruinosa and C. foetidissima suggesting other drivers than climatic conditions to shape their distributions. The domestication of Cucurbita and also the natural history of both genera were considered also as important factors. (C) 2011 Elsevier B.V. All rights reserved.

STABILITY ANALYSIS WITH APPLICATIONS OF A TWO-DIMENSIONAL DYNAMICAL SYSTEM ARISING FROM A STOCHASTIC MODEL FOR AN ASSET MARKET

We analyze the stability properties of equilibrium solutions and periodicity of orbits in a two-dimensional dynamical system whose orbits mimic the evolution of the price of an asset and the excess demand for that asset. The construction of the system is grounded upon a heterogeneous interacting agent model for a single risky asset market. An advantage of this construction procedure is that the resulting dynamical system becomes a macroscopic market model which mirrors the market quantities and qualities that would typically be taken into account solely at the microscopic level of modeling. The system`s parameters correspond to: (a) the proportion of speculators in a market; (b) the traders` speculative trend; (c) the degree of heterogeneity of idiosyncratic evaluations of the market agents with respect to the asset`s fundamental value; and (d) the strength of the feedback of the population excess demand on the asset price update increment. This correspondence allows us to employ our results in order to infer plausible causes for the emergence of price and demand fluctuations in a real asset market. The employment of dynamical systems for studying evolution of stochastic models of socio-economic phenomena is quite usual in the area of heterogeneous interacting agent models. However, in the vast majority of the cases present in the literature, these dynamical systems are one-dimensional. Our work is among the few in the area that construct and study analytically a two-dimensional dynamical system and apply it for explanation of socio-economic phenomena.