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I am generally interested in population- and community-level implications (including
ecological, evolutionary and epidemiological) of processes operating at individual level,
and in disclosure of mechanisms responsible for emerging patterns. The principal tools I
use to address these issues include mathematical models of any sort, ranging from deterministic
models defined by ordinary differential or difference equations up to stochastic and highly
flexible individual-based simulations.
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| Allee effects |
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Noone is perhaps surprised that the larger is a plant or animal population the stronger is
competition of its members for shared resources and the less each of them gains. However,
in small or sparse populations where competition is weak just the opposite phenomenon can
take a lead - organisms may profit (increase their fitness) from presence of conspecifics.
The reasons for this include the need to find mates, to avoid predators or to modify unfavorable
(e.g. toxic) environment. This phenomenon has been termed Allee effect, after the U.S. ecologist
W. C. Allee. If the Allee effect, or the need for conspecifics, is strong enough, it can give rise
to a critical population size necessary for survival of the entire population: if its size falls
below that value, the population will most likely die out. Actually, much of what we know about
these implications comes from mathematical models, and I am currently very much interested in
modelling dynamics of populations members of which face an Allee effect.
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| Two-sex population dynamics |
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Population models, even though often used to describe and understand sexually reproducing populations,
have not standardly discerned between males and females. This modelling paradigm is hunky once females
dominate population dynamics (i.e. there are always enough males to fertilize all receptive females) or
males and females share equal life histories. This is not often the case, however, and it has been shown
several times that asexual and equivalent two-sex population models differ in their predictions. Indeed,
there are many plausible situations in which any of these assumptions fails and where two-sex models become
inevitable. For example, sexes may differ in mortality rates, means of searching for mates, vulnerability
to predation or parasitism, or propensity to disperse from their natal patch, not to mention complexities
linked to sexual selection (male-male competition for females and female choice of males). Unfortunately,
methodology of modelling two-sex populations is far from established and sufficiently flexible to cover
many plausible scenarios, including varieties in mate searching strategies or mating systems. Some "standard"
phenomenological models do appear to exist, but these are only crude caricatures of what is actually going
on between males and females. I am generally interested in modelling and studying various ecological
interactions from the two-sex perspective.
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| Modelling infectious diseases |
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Emerging new and re-emerging known yet altered infectious diseases call for sophisticated methods to understand
their operation and spread. Mathematical models have already proven to be very useful in these respects.
Pathogens can also be efficient agents as regards pest population control - for example, a method commonly referred
to as virus-vectored immunocontraception has recently been promoted that consists of inoculating a population with
a virus able to sterilize either males or females and thus reduce its reproductive potential and hopefully also its
size. Also here, mathematical models are very helpful and commonly used to compare relative efficiency of various
control measures suggested to cope with pests, prior to their costly preparation and costly and potentially
hazardous and inefficient practical testing. I am primarily interested in how infectious diseases may affect
two-sex populations (or how predictions of asexual and two-sex population models may differ) potentially
exposed to Allee effects, thus combining the previous two topics with an applied issue.
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| Modelling (insect) population dynamics |
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Although much of my work concerns "strategic" population models that aim to help understand general
ecological processes and interactions spanning a wide diversity of plants or animals, from time to time
I happen to develop more "tactic" models that rather attempt to help understand specific behaviour or life
history trait of a species. Accomplished or ongoing studies conducted to model populations of insects or
other arthropods include a marine worm Bonellia viridis, Australian redback spider Latrodectus
hasselti, woodland butterfly Parnassius mnemosyne, German cockroach Blattella germanica
or several species of mosquitoes.
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