Mean
time to
extinction for discrete-time
population
dynamics
(
離散時間的な個体群動態における平均絶滅
時間
)
Shizuoka
University,
Kazunori Sato (
静岡大学
,
佐藤一憲
)
Wc propose thc $1/\backslash$ . to $01_{J}t_{\dot{c}}\iota i_{I1}$ tbc discretc-tinic Markov proccsscs
cor-responding to thc discrete-time ($\iota_{(}\backslash .t_{1CI1}ni_{I1}istit^{\backslash }’$population dynainics models. The
motivation of our stucly come,$s$ from the present stata that the only few papers
deal with it while the continuous-tiine Markov
processes
correspondingto
thecontinuous-tiine dete]$ministi_{CO11\backslash }\cdot i\prime s$ have been well studied in various literatures $f\dot{\iota}\cdot t;mf\iota\iota ndalnt^{B}I11t\iota 1s$ to $c\backslash Pl$)$licatioltS[1]$. Our idea is based
on
the so-called “firstprinciples ofpopulation dynamic$\backslash ,$ which $\dot{c}an$ derive population dynamics
mod-el: in terrns of the spatial distribution and the reproduction for each individual
[2]. We obtain the result for the $discrete- t$}$ime$ Markov process corresponding to
$Ri_{1}.k_{C^{\backslash }}r$ rnodcl $t1_{1att1_{1C^{\tau}N1(}\grave{\prime}\dot{c}tI1}$ cxtii.tction tiinc is not always $1_{0I1}gc^{t}\iota$
.
for 1 とに gcr initialpopulation size.
References
[1] Allen, L. .I. S.
&Allen,
E. J. (2003). A comparison ofthreedifferent stochasticpopulatioll models with regard to persistence time. Theoret. Popul. Biol. 64:
439-449.
$\lfloor 2]$ Br\"annstr\"om,
A.
&Sumpter, D. J. T. (2005). The role of competition andctlustering in population dynaInics. Proc. R. Soc. $B_{4_{-}}’72:2065-2072$
