Central Place Foraging in Nonpatchy Habitats

This paper deal with a model of optimal foraging in a habitat with arbitrary food distribution. It takes into account an arbitrary risk cost related to the distance to the animal's nest. Food acquisition and risk cost are accounted for in common units of fitness. The resulting problem is solved in the context of Calculus of Variations. The optimal duration of absence from the nest and the optimal spatial allocation of foraging time are obtained: the optimal strategy leads to separate the habitat into a region to exploit and a region to ignore. The definition of these two distinct regions depends on the relative importance of risk and food availability. With realistic risk costs, the resulting strategy indicates a highly selective behaviour when far from the nest, as observed in field studies. The model is also extended to take account of the need of returning to the nest to guard it or to feed the young.     

一个具暂时免疫且总人数可变的传染病动力学模型

建立了一个具常恢复率和接触率依赖于总人数的SIRS传染病动力学模型，讨论了系统平衡点的存在性和稳定性，对双线性传染率的特殊情形，给出了传染病平衡点的全局稳定性结论，推广和改进了已有的相应结果。     

The regulation of mortality and fecundity in Schistosoma mattheei following a single experimental infection in sheep.

The regulation of mortality and fecundity of Schistosoma mattheei in sheep was examined using a series of mathematical models applied to data culled from the literature. Parasite mortality (μ) was found to be an increasing linear function of the magnitude of the initial infection over the ranges of doses examined (200–91, 000 cercariae) where μ = 9.78 × 10⁻³ + 3.476 × 10^−7* infection dose. Parasite fecundity (λ) was found to be inversely related to the duration of the infection. The best fit model for parasite fecundity was one in which fecundity decreased exponentially with time since initial infection, λ = λ₀e^−δ1−r. There was no evidence for density-dependent regulation of fecundity.     

Modelling various sculptures in the Cretaceous bivalve Inoceramus hobetsensis

The geometry of the external shell sculpture in the Late Cretaceous inoceramid bivalve Inoceramus hobetsensis Nagao & Matsumoto, 1939 was studied both empirically and theoretically. A large sample, collected from the Upper Cretaceous of Hokkaido, Japan, shows remarkably high intraspecific variation in the shell sculptural pattern. Quasi-commarginal ribs, slightly oblique to the external growth increments, occur in some specimens. These sculptures are commonly irregular in strength and spacing, and their features are successfully modelled by computer simulations when the commarginal ribs are superposed with nearly concentric divaricate rib. Computer models indicate that the divergent sculpture element, often found in other inoceramids, was present throughout the evolution of I. hobetsensis and was developing in the evolutionary lineage from I. hobetsensis nonsulcatus to I. hobetsensis hobetsensis, although it was only weakly expressed. The results also suggest that some apparently distinct sculptural patterns of I. hobetsensis are the result of minor changes in the morphogenetic program.     

Environmental and human factors influencing rare plant local occurrence, extinction and persistence: a 115-year study in the Mediterranean region

Aim Assessing whether environmental and human factors influenced the spatial distribution and the dynamics of regionally rare plant species since the late nineteenth century, and whether these spatial and temporal patterns of rare species occurrences differ according to their chorology (level of endemism and biogeographic affinity). Location An area extending over 6250 km² in the French Mediterranean Region. Methods We used two botanical surveys achieved in 1886 and in 2001, and considered species rare if occurring in only one or two sites in the study area. Each rare species was assigned to a group of endemism level (restricted endemic, non‐endemic), and of biogeographic affinity (Mediterranean, South/Central European, Mountain, Eurosiberian). A 1 × 1 km grid was applied to the study zone. Generalized linear models were developed to study the spatial distribution and the fate of rare species occurrences (local extinction vs. local persistence between 1886 and 2001), as a function of environmental and human variables. Multivariate analyses were used to test whether the spatial distribution and the fate of rare species occurrences differed according to their chorology. Results In 2001, rare species as a whole tended to occur at higher altitude, in zones dominated by semi‐natural open habitats, and where cultivated area had decreased in the last 30 years. Between 1886 and 2001, rare species were the most prone to local extinction in zones where human population density, cultivated area and livestock density had increased the most. Between 1886 and 2001, rare species had a higher probability of local persistence in zones of high altitude and steep slope, on basic bedrocks and with low cultivated area. Rare species with Mountain and Eurosiberian affinities occurred in marginal habitats in the study region, i.e. on gneiss‐micaschist bedrocks and at high altitudes, whereas Mediterranean and South/Central European rare species occupied more varied environmental conditions. Between 1886 and 2001, Eurosiberian rare species showed high rates of local extinction whereas Mediterranean rare species had a significantly higher probability of local persistence. Restricted endemic species mostly occurred in zones of high slope, low human population density, and where cultivated area had decreased in the last 30 years. Occurrences of restricted endemics remained significantly stable between 1886 and 2001. Main conclusions Environmental and land‐use changes that occurred over the twentieth century in the Mediterranean Basin had significant impacts on the spatial distribution and on the long‐term dynamics of rare species occurrences. Urbanization and recent agriculture intensification, occurring mainly in coastal plains and littoral zones, caused most local extinctions of rare species from 1886 to 2001. Local populations of Eurosiberian species, which reach their range limits in marginal zones of the Mediterranean, also appear to be highly vulnerable. Conversely, most restricted endemic species occur in habitats with harsh topography and low human disturbance and have a higher potential of local persistence.     

Demography in stochastic environments. I. Exact distributions of age structure

The steady state distribution of age structure is studied for populations with two age classes and stochastic vital rates. For a serially uncorrelated dichotomic vital rate the distribution of age structure is found analytically to be a singular steplike function; outside a specific region of vital rate values the singular function crosses a threshold to a smooth function. For a vital rate following a correlated two state Markov process the joint distributions of age structure and environment are found analytically to be singular steplike functions; again a threshold marks a transition to a smooth function. For fecundities which are serially uncorrelated but continuously distributed the age structure distribution is obtained as a smooth analytic function for all parameter values. These explicit results have applications to studies of age structure and average growth rate.