TY - JOUR
T1 - Mum, why do you keep on growing? Impacts of environmental variability on optimal growth and reproduction allocation strategies of annual plants
AU - De Lara, Michel
PY - 2006/1/1
Y1 - 2006/1/1
N2 - In their 1990 paper Optimal reproductive efforts and the timing of reproduction of annual plants in randomly varying environments, Amir and Cohen considered stochastic environments consisting of i.i.d. sequences in an optimal allocation discrete-time model. We suppose here that the sequence of environmental factors is more generally described by a Markov chain. Moreover, we discuss the connection between the time interval of the discrete-time dynamic model and the ability of the plant to rebuild completely its vegetative body (from reserves). We formulate a stochastic optimization problem covering the so-called linear and logarithmic fitness (corresponding to variation within and between years), which yields optimal strategies. For "linear maximizers", we analyse how optimal strategies depend upon the environmental variability type: constant, random stationary, random i.i.d., random monotonous. We provide general patterns in terms of targets and thresholds, including both determinate and indeterminate growth. We also provide a partial result on the comparison between "linear maximizers" and "log maximizers". Numerical simulations are provided, allowing to give a hint at the effect of different mathematical assumptions.
AB - In their 1990 paper Optimal reproductive efforts and the timing of reproduction of annual plants in randomly varying environments, Amir and Cohen considered stochastic environments consisting of i.i.d. sequences in an optimal allocation discrete-time model. We suppose here that the sequence of environmental factors is more generally described by a Markov chain. Moreover, we discuss the connection between the time interval of the discrete-time dynamic model and the ability of the plant to rebuild completely its vegetative body (from reserves). We formulate a stochastic optimization problem covering the so-called linear and logarithmic fitness (corresponding to variation within and between years), which yields optimal strategies. For "linear maximizers", we analyse how optimal strategies depend upon the environmental variability type: constant, random stationary, random i.i.d., random monotonous. We provide general patterns in terms of targets and thresholds, including both determinate and indeterminate growth. We also provide a partial result on the comparison between "linear maximizers" and "log maximizers". Numerical simulations are provided, allowing to give a hint at the effect of different mathematical assumptions.
KW - Environmental variability
KW - Optimal allocation of resource
KW - Stochastic dynamic programming
UR - https://www.scopus.com/pages/publications/33645960971
U2 - 10.1007/s00285-005-0366-y
DO - 10.1007/s00285-005-0366-y
M3 - Article
C2 - 16463186
AN - SCOPUS:33645960971
SN - 0303-6812
VL - 52
SP - 633
EP - 666
JO - Journal of Mathematical Biology
JF - Journal of Mathematical Biology
IS - 5
ER -