| Details: |
In this talk we will see three different population models
as well as a general framework in which we can place many population
models, in order to get a more general understanding of what can
happen in a specific model. The first model relates to migrating
species, where a species visits a breeding or non-breeding region
during different times of the year, and how a shift in the timing of
seasons due to climate change can disturb the size of a population.
The second model is a variant of the first model but with but with a
predator added to the breeding region. Here we analyse how the type of
predator, specialist or generalist, will affect the long-term
population sizes. We will also perform bifurcation analysis in order
to highlight typical behaviors in predator-prey models. In the third
model we analyse a predator-prey model in which the adults can have
different levels of protective behaviour towards the newborns. We show
how the level of successful attacks by the predators can affect the
long-term prey population sizes. Many population models have the
possibility of a behavior known as an Allee effect, where a small
population size lead to extinction but large initial population sizes
lead to non-zero steady-state population sizes. In the final part of
this talk we will see how general techniques from dynamical systems
analysis can help us in understanding when the Allee effects can occur
in specific models. |