The MPDE annual conference (recently at Osnabruck, Turin , Niteroi and Marseille) is a vibrant meeting point for theory and experimentation in ecology. Ecology encompasses many scales, and models of populations provide a strongly integrating perspective on processes at the individual as well as at the landscape and ecosystem levels. This makes the MPDE a perfect interdisciplinary opportunity for biologists to see their work from a theoretical perspective and for mathematical modelers to discover relevant, exciting and important problems to work on in the ecological field.

This year in Cape Town, hosted by the universities of Cape Town and Stellenbosch, and taking place at the Waterfront, which apart from being a haven for tourists is a hub of innovation as well as part of a working harbour.

The focus is on Global Change, and the contribution of models and data at the population level to understanding of, mitigation of and adapting to what will remain humankind's most profound challenge for many decades.

- Renewable resources
- Invasion dynamics
- Monitoring & data management
- Ecological networks
- Epidemiology & disease ecology
- Land use change

- Mats Gyllenberg (University of Helsinki)
- Evolution and optimisation
It is a wide spread misconception that evolution optimizes some quantity like “fitness” or reproductive success. In this talk I give a brief introduction to adaptive dynamics, which is a mathematical theory that explicitly takes into account the interaction between population dynamics (ecology) and evolution by natural selection. Using the well-known rock-scissors-paper-game as a metaphor, I give necessary and sufficient conditions for when there is a function which is optimized by natural selection. It turns out that evolutionary optimization is extremely rare and hardly can happen in nature.

- Evolution and optimisation
- Robert Holt (University of Florida)
- On the interplay of demographic stochasticity, fitness, and the niche concept
The concepts of "fitness" and "niche": are arguably among the most central concepts of evolutionary biology and ecology. Both are often related to population measures such as intrinsic growth rates (e.g., Ronald Fishers' Malthusian parameter). My presentation will review the ways these two concepts are related, and explore some consequences of demographic and environmental stochasticity, and spatial dynamics. My talk will end with discussion of niche conservatism and evolution, pertinent to the issue of evolutionary rescue in our rapidly changing world.

- On the interplay of demographic stochasticity, fitness, and the niche concept
- Cang Hui (University of Stellenbosch)
- Trait evolution within bipartite ecological networks
Bipartite ecological networks are formed by interactions between species which exploit each other for survival and are crucial components to sustain ecosystem function and services, foster biodiversity and affect community stability. Despite their diversity, bipartitle ecological interactions exhibit surprisingly well-organised structures. In particular, they are often found to be within a certain range of connectance, nestedness and modularity, as well as a right skewed degree distribution. Evidently, these multiple features of bipartite ecological networks are not independent of each other, suggesting that an integrated model is required to better capture the intrinsic dynamic features of species interactions. Here, we review a list of eco-evolutionary models for investigating the pattern emergence in bipartite ecological networks with trait-mediated interactions phylogenetic modelling, adaptive interaction switching and adaptive dynamics. First, using knowledge of the phylogenies of the interacting species, our model yielded a significantly better fit to a quarter of a set of mutualistic networks. This highlights the importance, in a substantial minority of cases, of inheritance of interaction patterns without excluding the potential role of ecological novelties in forming the current network architecture. Second, the model allowing interaction switches between partner species produced predictions which fit remarkably well with observations, and thus the interaction switch is likely a key ecological process that results in observed structures of real- world networks. Finally, trait-based adaptive dynamics models highlight the importance of assortative interactions and the balance of costs incurred by coevolving species as factors determining the eventual phenotypic outcome of co- evolutionary interactions. The interplay of ecological and evolutionary processes through trait-mediated interactions can explain these widely observed architectures in bipartite networks. Coevolutionary networks provide an ideal model for modelling complex adaptive systems, which can help to address challenges from global changes facing many complex social-ecological systems.

- Trait evolution within bipartite ecological networks
- Horst Malchow (University of Osnabrück)
- Noise-mediated coexistence of competitors
Stochastic reaction-diffusion equations are a popular modelling approach for studying interacting populations in a heterogeneous environment under the influence of environmental fluctuations. Although the theoretical basis of alternative models such as Fokker-Planck diffusion is not less convincing, movement of populations is most commonly modelled using the diffusion law due to Fick. An interesting feature of Fokker-Planck diffusion is the fact that for spatially varying diffusion coefficients the stationary solution is not a homogeneous distribution - in contrast to Fick's law of diffusion. Instead, concentration accumulates in regions of low diffusivity and tends to lower levels for areas of high diffusivity. Thus, the stationary distribution of the Fokker-Planck diffusion can be interpreted as a reflection of different levels of habitat quality. Moreover, the most common model for environmental fluctuations, linear multiplicative noise, is based on the assumption that individuals respond independently to stochastic environmental fluctuations. For large population densities the assumption of independence is debatable and the model further implies that noise intensities can increase to arbitrarily high levels. Therefore, instead of the commonly used linear multiplicative noise model, the environmental variability is implemented by an alternative nonlinear noise term which never exceeds a certain maximum noise intensity. With Fokker-Planck diffusion and the nonlinear noise model replacing the classical approaches a simple invasive system is investigated based on the Lotka-Volterra competition model. It is found that the heterogeneous stationary distribution generated by Fokker-Planck diffusion generally facilitates the formation of segregated habitats of resident and invader. However, this segregation can be broken by nonlinear noise leading to coexistence of resident and invader across the whole spatial domain, an effect that would not be possible in the non-spatial version of the competition model for the parameters considered here.

- Noise-mediated coexistence of competitors
- Bob Scholes (University of the Witwatersrand)
- The Global Carbon cycle and where it intersects with population processes

- Katriona Shea (Pennsylvania State University)
- Using multiple models to address uncertainty, value of information, and optimal control of disease outbreaks
Major disease outbreaks often generate multiple modeling efforts to assist with forecasting and management. Uncertainty about appropriate parameters, model structure and management intervention implementation can generate significant disagreements, which in turns hampers policy-making for animal and public health. Using examples from human and livestock diseases, I outline approaches to address uncertainty and learning to help improve epidemiological management.

- Using multiple models to address uncertainty, value of information, and optimal control of disease outbreaks
- Sheetal Silal (University of Cape Town)
- Supporting Malaria Elimination in the Asia-Pacific through Mathematical Modelling
Countries in the Asia-Pacific region have made significant progress in combatting malaria, reducing deaths from the disease by more than 25% since 2000 and several countries are now working towards elimination with a regional goal for a malaria-free Asia-Pacific by 2030 endorsed at the highest levels. A mathematical model was developed to project rates of decline to elimination by 2030 and determine the costs for elimination in the Asia-Pacific region. The mathematical model is characterized as a dynamic economic-epidemiological multi-species model that will estimate the impact of interventions against the transmission of Plasmodium falciparum and Plasmodium vivax malaria. This talk will highlight results of the modelling project through an open source application aimed at making mathematical models more accessible to policy-makers and other key stakeholders.

- Supporting Malaria Elimination in the Asia-Pacific through Mathematical Modelling