TY - JOUR

T1 - Extinction risk of a meta-population

T2 - Aggregation approach

AU - Hakoyama, Hiroshi

AU - Iwasa, Yoh

N1 - Funding Information:
This work has been supported by Core Research for Evolutional Science and Technology (CREST) of Japan Science and Technology Corporation (JST) (Principal investigator is J. Nakanishi) and the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Encouragement of Young Scientists (B), 14760128, 2002. We thank the following people for their helpful comments: J. Halley, Y. Harada, P. Haccou, K. Johst, K. Frank, H. Matsuda, J. Nakanishi, A. Sasaki, N. Shigesada, M. Shimada, Y. Tanaka, T. Yahara, and C. Wissel.

PY - 2005/1/21

Y1 - 2005/1/21

N2 - Aggregation of variables of a complex mathematical model with realistic structure gives a simplified model which is more suitable than the original one when the amount of data for parameter estimation is limited. Here we explore use of a formula derived for a single unstructured population (canonical model) in predicting the extinction time for a population living in multiple habitats. In particular we focus multiple populations each following logistic growth with demographic and environmental stochasticities, and examine how the mean extinction time depends on the migration and environmental correlation. When migration rate and/or environmental correlation are very large or very small, we may express the mean extinction time exactly using the formula with properly modified parameters. When parameters are of intermediate magnitude, we generate a Monte Carlo time series of the population size for the realistic structured model, estimate the "effective parameters" by fitting the time series to the canonical model, and then calculate the mean extinction time using the formula for a single population. The mean extinction time predicted by the formula was close to those obtained from direct computer simulation of structured models. We conclude that the formula for an unstructured single-population model has good approximation capability and can be applicable in estimating the extinction risk of the structured meta-population model for a limited data set.

AB - Aggregation of variables of a complex mathematical model with realistic structure gives a simplified model which is more suitable than the original one when the amount of data for parameter estimation is limited. Here we explore use of a formula derived for a single unstructured population (canonical model) in predicting the extinction time for a population living in multiple habitats. In particular we focus multiple populations each following logistic growth with demographic and environmental stochasticities, and examine how the mean extinction time depends on the migration and environmental correlation. When migration rate and/or environmental correlation are very large or very small, we may express the mean extinction time exactly using the formula with properly modified parameters. When parameters are of intermediate magnitude, we generate a Monte Carlo time series of the population size for the realistic structured model, estimate the "effective parameters" by fitting the time series to the canonical model, and then calculate the mean extinction time using the formula for a single population. The mean extinction time predicted by the formula was close to those obtained from direct computer simulation of structured models. We conclude that the formula for an unstructured single-population model has good approximation capability and can be applicable in estimating the extinction risk of the structured meta-population model for a limited data set.

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U2 - 10.1016/j.jtbi.2004.08.008

DO - 10.1016/j.jtbi.2004.08.008

M3 - Article

C2 - 15530490

AN - SCOPUS:7644228403

SN - 0022-5193

VL - 232

SP - 203

EP - 216

JO - Journal of Theoretical Biology

JF - Journal of Theoretical Biology

IS - 2

ER -