Individual based simulations of population dynamics require the availability of growth models with adequate complexity. For this purpose a simple-to-use model (non-linear multiple regression approach) is presented describing somatic growth and reproduction of Daphnia as a function of time, temperature and food quantity. The model showed a good agreement with published observations of somatic growth (r2 = 0.954, n = 88) and egg production (r2 = 0.898, n = 35). Temperature is the main determinant of initial somatic growth and food concentration is the main determinant of maximal body length and clutch size. An individual based simulation was used to demonstrate the simultaneous effects of food and temperature on the population level. Evidently, both temperature and food supply affected the population growth rate but at food concentrations above approximately 0.4 mg Cl−1Scenedesmus acutus temperature appeared as the main determinant of population growth.
Four simulation examples are given to show the wide applicability of the model: (1) analysis of the correlation between population birth rate and somatic growth rate, (2) contribution of egg development time and delayed somatic growth to temperature-effects on population growth, (3) comparison of population birth rate in simulations with constant vs. decreasing size at maturity with declining food concentrations and (4) costs of diel vertical migration. Due to its plausible behaviour over a broad range of temperature (2–20 °C) and food conditions (0.1–4 mg Cl−1) the model can be used as a module for more detailed simulations of Daphnia population dynamics under realistic environmental conditions. 相似文献
Zones of increased concentration formed by a solvent flowing from a source are considered. A matehmatical model for forming such zones is proposed. It takes into account that such a zone is composed of a set of independent particles. Hence the distribution of a substance around the source can be explained by movement of an individual particle. In the model this movement is a continuous semi-Markov process with terminal stopping at some random point in space. Parameters of the process depend on the velocity field of the flow. Forward and backward partial differential equations for the distribution density of a random stopping point of the process are derived. The forward equation is investigated for the centrally symmetric case. Solutions of the equation demonstrate either a maximum or a local minimum at the source location. In the latter case a concentric ring around the source is formed. If different substances vary in their absorption rates, they can form separable concentration zones as a family of concentric rings. 相似文献