Modelling temperature-dependent larval development and\ud subsequent demographic Allee effects in adult populations of the alpine butterfly Parnassius smintheus

Climate change has been attributed as a driver of changes to ecological systems worldwide and understanding the effects of climate change at individual, population, community, and ecosystem levels has become a primary concern of ecology. One avenue toward understanding the impacts of climate change on an ecosystem is through the study of environmentally sensitive species. Butterflies are sensitive to climatic changes due to their reliance on environmental cues such as temperature and photoperiod, which regulate the completion of life history stages. As such, the population dynamics of butterflies may offer insight into the impacts of climate change on the health of an ecosystem. In this paper we study the effects of rearing temperature on the alpine butterfly Parnassius smintheus (Rocky Mountain Apollo), both directly through individual phenological changes and indirectly through adult reproductive success at the population level. Our approach is to formulate a mathematical model of individual development parameterized by experimental data and link larval development to adult reproductive success. A Bernoulli process model describes temperature-dependent larval phenology, and a system of ordinary differential equations is used to study impacts on reproductive success. The phenological model takes field temperature data as its input and predicts a temporal distribution of adult emergence, which in turn controls the dynamics of the reproductive success model. We find that warmer spring and summer temperatures increase reproductive success, while cooler temperatures exacerbate a demographic Allee effect, suggesting that observed yearly fluctuations in P. smintheus population size may be driven by inter-annual temperature variability. Model predictions are validated against mark-recapture field data from 2001 and 2003 − 2009

Modelling rainforests

In this dissertation, we develop a competition-colonisation model to describe the dynamics of interactions between tropical rainforest tree species.\ud \ud There is a great deal of interest in modelling rainforest diversity. Understanding the natural processes that maintain diversity is essential so that sustainable management systems can attempt to replicate important processes.\ud \ud We find, through numerical investigation and analysis, that with constant colonisation rates, $c_i$, we cannot predict multiple species coexistence. The inclusion of decaying colonisation rates, describing the seedling population decay over time, and random mass fruiting events allows coexistence of species, but using unrealistic parameter values. Finally we investigate a mathematical model without any competition between species and find that, using realistic parameter values, our results qualitatively mimic observations of rainforest dynamics. The results of the no competition model support Hubbell's null\ud hypothesis [17]

Achieving coexistence - Comment on "Modelling rain forest diversity:The role of competition by Bampfylde et al. (2005)

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Explaining rain forest diversity

This group, which is concerned with the applications of mathematics to agricultural science, was formed in 1970 and has since met at approximately yearly intervals in London for one-day meetings. The thirty-third meeting of the group, chaired by Professor P. K. Maini of the Mathematical Institute, University of Oxford, was held in the Kohn Centre at the Royal Society, 6 Carlton House Terrace, London on Friday, 6 April 2001 when the following papers were read

Mathematical modelling of rain forest regeneration dynamics : a case study in Sabah, Malaysia

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