Abstract
Many biological populations tend to aggregate in response to concentration gradients of a chemoattractant secreted by themselves. The present study is motivated by the aggregation observed in Blattella germanica. At properly high densities, B. germanica individuals grow faster than do isolated ones, and they aggregate so as to maintain such densities (Ishii [1969]). This prominent feature suggests that there is evidently a correlation between the growth rate and population density of individuals.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
S. Childress and J. K. Percus, Nonlinear aspects of Chemotaxis, Math. Biosci. 56 (1981), 217–237.
O. Diekmann, H. J. A. M. Heijmans and H. R. Thieme, On the stability of the cell size distribution, J. Math. Biology. 19 (1984), 227–248.
S.-I. Ei and M. Mimura, Transient and large time behaviors of solutions to heterogeneous reaction-diffusion equations, Hiroshima Math. J. 14 (1984), 649–678.
S.-I. Ei, M. Mimura and S. Takigawa, (in preparation).
M. Gyllenberg, Nonlinear age-dependent population dynamics in continuously propagated bacterial cultures, Math. Biosci. 62 (1982), 45–74.
S. Ishii, Biologically active substances produced by insects, Nankodo, Tokyo, 1969 (in Japanese).
E. F. Keller and L. A. Segel, Initiation of slime mold aggregation viewed as an instability, J. Theor. Bio. 26 (1970), 399–415.
M. Mimura and S. Takigawa, A size-distribution model with density-dependent growth rates, (in preparation).
R. Schaaf, Global branches of one dimensional stationary solutions to Chemotaxis systems and stability, Lecture Notes in Biomathematics, Springer-Verlag, Berlin, 55 (1984), 341–349.
G. F. Webb, Theory of nonlinear age-dependent population dynamics, Marcel Dekker, Inc., New York, 1985.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1987 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Mimura, M., Takigawa, S. (1987). A spatially aggregating population model involving size-distributed dynamics. In: Teramoto, E., Yumaguti, M. (eds) Mathematical Topics in Population Biology, Morphogenesis and Neurosciences. Lecture Notes in Biomathematics, vol 71. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-93360-8_13
Download citation
DOI: https://doi.org/10.1007/978-3-642-93360-8_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-17875-0
Online ISBN: 978-3-642-93360-8
eBook Packages: Springer Book Archive