2,119,773 research outputs found
Extinction rates of established spatial populations
This paper deals with extinction of an isolated population caused by
intrinsic noise. We model the population dynamics in a "refuge" as a Markov
process which involves births and deaths on discrete lattice sites and random
migrations between neighboring sites. In extinction scenario I the zero
population size is a repelling fixed point of the on-site deterministic
dynamics. In extinction scenario II the zero population size is an attracting
fixed point, corresponding to what is known in ecology as Allee effect.
Assuming a large population size, we develop WKB (Wentzel-Kramers-Brillouin)
approximation to the master equation. The resulting Hamilton's equations encode
the most probable path of the population toward extinction and the mean time to
extinction. In the fast-migration limit these equations coincide, up to a
canonical transformation, with those obtained, in a different way, by Elgart
and Kamenev (2004). We classify possible regimes of population extinction with
and without an Allee effect and for different types of refuge and solve several
examples analytically and numerically. For a very strong Allee effect the
extinction problem can be mapped into the over-damped limit of theory of
homogeneous nucleation due to Langer (1969). In this regime, and for very long
systems, we predict an optimal refuge size that maximizes the mean time to
extinction.Comment: 26 pages including 3 appendices, 16 figure
Myths and Legends of the Baldwin Effect
This position paper argues that the Baldwin effect is widely
misunderstood by the evolutionary computation community. The
misunderstandings appear to fall into two general categories.
Firstly, it is commonly believed that the Baldwin effect is
concerned with the synergy that results when there is an evolving
population of learning individuals. This is only half of the story.
The full story is more complicated and more interesting. The Baldwin
effect is concerned with the costs and benefits of lifetime
learning by individuals in an evolving population. Several
researchers have focussed exclusively on the benefits, but there
is much to be gained from attention to the costs. This paper explains
the two sides of the story and enumerates ten of the costs and
benefits of lifetime learning by individuals in an evolving population.
Secondly, there is a cluster of misunderstandings about the relationship
between the Baldwin effect and Lamarckian inheritance of acquired
characteristics. The Baldwin effect is not Lamarckian. A Lamarckian
algorithm is not better for most evolutionary computing problems than
a Baldwinian algorithm. Finally, Lamarckian inheritance is not a
better model of memetic (cultural) evolution than the Baldwin effect
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