Modelling European red mite populations using the inverse approach
LE3 .A278 2014
Master of Science
Mathematics and Statistics
Mathematics & Statistics
An inverse approach was used to estimate the parameter values from a noisy dataset using a two-delay di erential equation system. The DDE system was developed from ecological rst principles and observations from an historical European red mite dataset constructed in 1967. Analysis of the 1967 dataset indicates that both stage structure and density e ects are present in the data. The main purpose of tting this model is to determine the parameter values of egg hatching time ( 1), maturation time ( 2), fecundity ( ), density dependant e ect ( ) and stage speci c mortality ( 2;3;4; f). In addition to these parameters, values of the initial conditions (Egg 1 and Egg 2) as well as the timing of the seasonal change (Season) from summer egg production to winter egg production are also determined. The model was t to data taken from individual trees (n = 24), and to bootstrapped averages (n = 400). Parameters returned from the individual trees were highly variable while parameters returned from the bootstrapped data had much less variability. The more numerous parameter sets from the bootstrapped data, allowed for more further analysis. Parameter distributions along with R2 values were used to evaluate the , 2 and 3 parameters to determine if they should be included in the model. Bootstrapping the data also allowed the relationships among parameters to be explored and evidence of non-unique solutions were observed. A nal model with 9 parameters was chosen with an R2 value of 0.91. The parameters returned from the tting process are compared to literature values
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