Statistics for Spatial Data.

1. What are Allee effects? 2. Mechanisms for Allee effects 3. Population dynamics: modelling demographic Allee effects 4. Genetics and evolution 5. Conservation and management 6. Conclusions and perspectives

Allee Effects in Ecology and Conservation

Diffusion and ecological problems : mathematical models

http://www.oomvanlieshout.net/sander/work/docs/Birch2007EcolModel206_347.pdf

Rectangular and hexagonal grids used for observation, experiment and simulation in ecology

In this paper, we review mate-finding Allee effects from ecological and evolutionary points of view. We define ‘mate-finding’ as mate searching in mobile animals, and also as the meeting of gametes for sessile animals and plants (pollination). We consider related issues such as mate quality and choice, sperm limitation and physiological stimulation of reproduction by conspecifics, as well as discussing the role of demographic stochasticity in generating mate-finding Allee effects. We consider the role of component Allee effects due to mate-finding in generating demographic Allee effects (at the population level). Compelling evidence for demographic Allee effects due to mate-finding (as well as via other mechanisms) is still limited, due to difficulties in censusing rare populations or a failure to identify underlying mechanisms, but also because of fitness trade-offs, population spatial structure and metapopulation dynamics, and because the strength of component Allee effects may vary in time and space. Mate-finding Allee effects act on individual fitness and are thus susceptible to change via natural selection. We believe it is useful to distinguish two routes by which evolution can act to mitigate mate-finding Allee effects. The first is evolution of characteristics such as calls, pheromones, hermaphroditism, etc. which make mate-finding more efficient at low density, thus eliminating the Allee effect. Such adaptations are very abundant in the natural world, and may have arisen to avoid Allee effects, although other hypotheses are also possible. The second route is to avoid low density via adaptations such as permanent or periodic aggregation. In this case, the Allee effect is still present, but its effects are avoided. These two strategies may have different consequences in a world where many populations are being artificially reduced to low density: in the first case, population growth rate can be maintained, while in the second case, the mechanism to avoid Allee effects has been destroyed. It is therefore in these latter populations that we predict the greatest evidence for mate-finding Allee effects and associated demographic consequences. This idea is supported by the existing empirical evidence for demographic Allee effects. Given a strong effect that mate-finding appears to have on individual fitness, we support the continuing quest to find connections between component mate-finding Allee effects (individual reproductive fitness) and the demographic consequences. There are many reasons why such studies are difficult, but it is important, particularly given the increasing number of populations and species of conservation concern, that the ecological community understands more about how widespread demographic Allee effects really are, and why.

http://max2.ese.u-psud.fr/epc/conservation/PDFs/MateFinding.pdf

Dangerously few liaisons: a review of mate-finding Allee effects

http://www.tau.ac.il/~bennya/nordgis/Berec_Techniques%20of%20spatially%20explicit%20individual-based%20models.pdf

Techniques of spatially explicit individual-based models: construction, simulation, and mean-field analysis

In this paper we examine how the process of mate search, degree of mate choice and degree of mate fidelity may interact to affect long-term population dynamics of sexually reproducing species. In particular, we address the following questions: are degree of mate choice and degree of mate fidelity correlated? How does mate search shape this relationship? How does longevity affect mating behaviour? To resolve these questions, we develop a spatially explicit, individual-based model of a sexually reproducing population with single (i.e. unpaired) males, single females, and pairs as focal individuals. Both this model and its non-spatial approximation give rise to the Allee effect due to lack of mating possibilities, and sufficiently small/sparse populations always go extinct. We quantify combinations of mate choice and divorce rate under which populations persist or go extinct even from high sizes. We thus show that there exist ecological constraints for possible (co)evolution of mate choice and pair maintenance behaviour. Our models also suggest that colonial species with active mate search strategy survive at higher divorce rates than less colonial animals that search for their mates randomly, and that long-lived species sustain at higher degrees of mate choice and lower degrees of mate fidelity compared to the short-lived ones. Connection of these findings to other theoretical results and some empirical observations is discussed.

Lude ÿk Berec

Papers

Techniques of spatially explicit individual-based models: construction, simulation, and mean-field analysis

Implications of mate search, mate choice and divorce rate for population dynamics of sexually reproducing species