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Korveh, E. (2016) *Simple stochastic populations in habitats with bounded and varying carrying capacities*. Göteborg : Chalmers University of Technology

** BibTeX **

@misc{

Korveh2016,

author={Korveh, Edward},

title={Simple stochastic populations in habitats with bounded and varying carrying capacities},

abstract={A population consisting of one single type of individuals where reproduction is seasonal,
and by means of asexual binary-splitting with a probability, which depends
on the carrying capacity of the habitat, K and the present population is considered.
Current models for such binary-splitting populations do not explicitly capture the
concepts of early and late extinctions. A new parameter v, called the ‘scaling parameter’
is introduced to scale down the splitting probabilities in the first season,
and also in subsequent generations in order to properly observe and record early and
late extinctions. The modified model is used to estimate the probabilities of early
and late extinctions, and the expected time to extinction in two main cases. The
first case is for fixed and large K, where a new and more general upper bound for
the expected time to extinction is proposed to be evK. The risk of such populations
going extinct is found to be of the order O
_
p 1
(2v−1)K
_
. The second case considers
a scenario where the carrying capacity of the habitat varies in each season between
two values L (for low) and H (for high), randomly chosen with equal probabilities
to represent either a good or a bad season respectively. Both cases yielded similar
results with the probability of early extinction tending to zero as v increases, and
the probability of late extinction tending to one as v increases.
Keywords: habitat; carrying capacity; branching processes; supercritical; subcritical;
extinction time; binary-splitting.
v
},

publisher={Institutionen för matematiska vetenskaper, Chalmers tekniska högskola,},

place={Göteborg},

year={2016},

}

** RefWorks **

RT Generic

SR Electronic

ID 238122

A1 Korveh, Edward

T1 Simple stochastic populations in habitats with bounded and varying carrying capacities

YR 2016

AB A population consisting of one single type of individuals where reproduction is seasonal,
and by means of asexual binary-splitting with a probability, which depends
on the carrying capacity of the habitat, K and the present population is considered.
Current models for such binary-splitting populations do not explicitly capture the
concepts of early and late extinctions. A new parameter v, called the ‘scaling parameter’
is introduced to scale down the splitting probabilities in the first season,
and also in subsequent generations in order to properly observe and record early and
late extinctions. The modified model is used to estimate the probabilities of early
and late extinctions, and the expected time to extinction in two main cases. The
first case is for fixed and large K, where a new and more general upper bound for
the expected time to extinction is proposed to be evK. The risk of such populations
going extinct is found to be of the order O
_
p 1
(2v−1)K
_
. The second case considers
a scenario where the carrying capacity of the habitat varies in each season between
two values L (for low) and H (for high), randomly chosen with equal probabilities
to represent either a good or a bad season respectively. Both cases yielded similar
results with the probability of early extinction tending to zero as v increases, and
the probability of late extinction tending to one as v increases.
Keywords: habitat; carrying capacity; branching processes; supercritical; subcritical;
extinction time; binary-splitting.
v

PB Institutionen för matematiska vetenskaper, Chalmers tekniska högskola,

LA eng

LK http://publications.lib.chalmers.se/records/fulltext/238122/238122.pdf

OL 30