My Library

University LibraryCatalogue

     
Limit search to items available for borrowing or consultation
Result Page: Previous Next
Can't find that book? Try BONUS+
 
Look for full text

Search Discovery

Search CARM Centre Catalogue

Search Trove

Add record to RefWorks

Cover Art
PRINTED BOOKS
Author Renshaw, Eric (Professor)

Title Modelling biological populations in space and time / Eric Renshaw.

Published Cambridge ; New York : Cambridge University Press, 1991.

Copies

Location Call No. Status
 UniM BioMed  574.5248072 RENS    AVAILABLE
Physical description xvii, 403 pages : illustrations, map ; 24 cm.
Series Cambridge studies in mathematical biology ; 11.
Cambridge studies in mathematical biology ; 11.
Bibliography Includes bibliographical references (pages [385]-393) and indexes.
Contents 1.1 Deterministic or stochastic models? 1 -- 1.2 Single-species populations 5 -- 1.3 Two-species populations 7 -- 1.4 Spatial effect 9 -- 1.5 Related topics 11 -- 2 Simple birth-death processes 15 -- 2.1 Pure birth process 16 -- 2.2 Pure death process 27 -- 2.3 Simple linear birth and death process 33 -- 2.4 Simple immigration-birth-death process 41 -- 3 General birth--death processes 46 -- 3.1 General population growth 46 -- 3.2 Logistic population growth 50 -- 3.3 Quasi-equilibrium probabilities 58 -- 3.4 Simulation of the general population process 59 -- 3.5 Normal approximation to the quasi-equilibrium probabilities 64 -- 3.6 Probability of ultimate extinction 65 -- 3.7 Mean time to extinction 66 -- 3.8 Probability of extinction by time t 68 -- 3.9 Comparison of approximate quasi-equilibrium probability distributions 70 -- 3.10 Diffusion approximation 78 -- 3.11 Application to the yeast and sheep data 81 -- 4 Time-lag models of population growth 87 -- 4.2 Reaction time-lag--deterministic analysis 90 -- 4.3 Reaction time-lag--stochastic analysis 94 -- 4.4 More general deterministic models 96 -- 4.5 Periodic and chaotic solutions 100 -- 4.6 Analysis of field and laboratory data 114 -- 4.7 Nicholson's blowflies 116 -- 4.8 Simulation of the two blowfly models 122 -- 5 Competition processes 128 -- 5.2 Experimental background 131 -- 5.3 Stability 137 -- 5.4 Stochastic behaviour 146 -- 5.5 Probability equations 154 -- 5.6 Extinction 156 -- 5.7 Quasi-equilibrium probabilities 161 -- 6 Predator-prey processes 166 -- 6.1 Lotka-Volterra model 167 -- 6.2 Volterra model 176 -- 6.3 Leslie and Gower model 191 -- 6.4 Holling--Tanner model 192 -- 6.5 A model for prey-cover 199 -- 7 Spatial predator--prey systems 205 -- 7.1 Huffaker's experiments 205 -- 7.2 Simulation of the spatial Lotka--Volterra model 208 -- 7.3 Matrix representation 214 -- 8 Fluctuating environments 223 -- 8.1 Deterministic variability 223 -- 8.2 Jillson's flour beetle experiment 233 -- 8.3 Stochastic behaviour with deterministic variability 236 -- 8.4 Random environments 241 -- 8.5 Canadian lynx data 253 -- 9 Spatial population dynamics 258 -- 9.1 Simple random walk 259 -- 9.2 Brownian motion 264 -- 9.3 Application of diffusion processes 266 -- 9.4 Stepping-stone models (1) 272 -- 9.5 Two-colony model 275 -- 9.6 Stepping-stone models (2) 284 -- 9.7 An application to the spread of Tribolium confusum 289 -- 9.8 Simulation of the diffusion and stepping-stone processes 295 -- 9.9 Spatial predator--prey processes revisited 299 -- 9.10 Turing's model for morphogenesis 310 -- 10 Epidemic processes 324 -- 10.2 Simple epidemics 325 -- 10.3 General epidemics 330 -- 10.4 Recurrent epidemics 336 -- 10.5 An extension to malaria 344 -- 10.6 Spatial models 350 -- 11 Linear and branching architectures 360 -- 11.1 Spatial distribution of Epilobium angustifolium in a recently thinned woodland 362 -- 11.2 Spatial branching models for canopy growth 368 -- 11.3 Spatial branching models for structural root systems 373 -- 11.4 Discussion of the role of simulation 380.
Summary This volume aims to develop a unifying approach to population studies which emphasises the interplay between modelling and experimentation. The aim throughout is to provide biologists and mathematicians with a framework within which population dynamics can be fully explored and understood.
Deterministic and stochastic models are considered together; spatial effects are investigated by developing models which highlight the consequences that geographical restriction and species mobility may have on population development. Model-based simulations of processes are used to explore hitherto unforeseen features and thereby suggest further profitable lines of both experimentation and theoretical study. Most aspects of population dynamics are covered, including birth -- death and logistic processes, competition and predator -- prey relationships, chaos, reaction time-delays, fluctuating environments, spatial systems, velocities of spread, epidemics, and spatial branching structures. All of these topics are accessible to students and researchers in biology and mathematics alike. While the more theoretically orientated sections will appeal principally to mathematical biologists, the material is presented in such a way that readers with virtually no mathematical expertise can bypass these without losing the main flow of the text.
The volume is suitable for postgraduates and advanced undergraduates of biology (population dynamics) and mathematics (modelling and applied stochastic processes), and all research scientists with a professional interest in mathematical modelling of population dynamics.
Subject Population biology -- Statistical methods.
Spatial analysis (Statistics)
ISBN 0521303885 (hardback)
0521448557 (paperback)