Through the recent results that we present , we wish to highlight the various time-scales on which the demographic dynamics and the natural selection can be retrieved from individual-based models. Although these results are by no means exhaustive, both on the mathematical and the biological level, they are very complementary . Indeed, they provide a viewpoint for the most classical time-scales of interest. They namely encompass the time-scale of the life of a single individual, the longer one on which a population can be characterized , the ecological one and at least four nested ones on which selection occurs. The limiting behavior is generally deterministic. Yet, since the selection acts on the alea in the history of individuals, the probabilities are shown to be a key element of understanding . Besides, the scarcity of mutations fixing in the poplation also induces some stochasticity .
This article is a presentation of specific recent results describing scaling limits of individual-based models. Thanks to them , we wish to relate the time-scales typical of demographic dynamics and natural selection to the parameters of the individual-based models. Although these results are by no means exhaustive, both on the mathematical and the biological level, they complement each other . Indeed, they provide a viewpoint for many classical time-scales . Namely, they encompass the timescale typical of the life-expectancy of a single individual, the longer one wherein a population can be characterized through its demographic dynamics, and at least four interconnected ones wherein selection occurs. The limiting behavior is generally deterministic. Yet, since there are selective effects on randomness in the history of lineages, probability theory is shown to be a key factor in understanding the results . Besides, randomness can be maintained in the limiting dynamics, for instance to model rare mutations fixing in the population .
R
Through the recent results that we present
This article is a presentation of specific recent results describing scaling limits of individual-based models. Thanks to them
R
highlight the various
relate the
R
on which the
typical of
R
the natural selection can be retrieved from
natural selection to the parameters of the
R
are very complementary
complement each other
R
the most
many
R
of interest. They namely encompass the time-scale of the life
. Namely, they encompass the timescale typical of the life-expectancy
R
on which
wherein
R
, the ecological one
through its demographic dynamics,
R
nested ones on which
interconnected ones wherein
R
the selection acts on the alea
there are selective effects on randomness
R
individuals, the probabilities are
lineages, probability theory is
R
element of understanding
factor in understanding the results
R
the scarcity of
randomness can be maintained in the limiting dynamics, for instance to model rare
R
poplation also induces some stochasticity
population