Open AccessA REACTION–DIFFUSION EQUATION MODELING THE INVASION OF THE ARGENTINE ANT POPULATION, LINEPITHEMA HUMILE , AT JASPER RIDGE BIOLOGICAL PRESERVE
Author(s) -
SHRYOCK KACEE A.,
BROWN SHARON L.,
SANDERS NATHAN J.,
BURROUGHS ELIZABETH
Publication year - 2008
Publication title -
natural resource modeling
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.28
H-Index - 32
eISSN - 1939-7445
pISSN - 0890-8575
DOI - 10.1111/j.1939-7445.2008.00014.x
Subject(s) - linepithema , argentine ant , population , biological dispersal , ridge , traveling wave , population model , diffusion , logistic function , mathematics , ecology , statistics , geology , biology , physics , mathematical analysis , demography , ant , paleontology , sociology , thermodynamics
A continuous reaction–diffusion model is developed for the invasive Argentine ant population within a preserve in northern California. The model is a second‐order partial differential equation incorporating a logistic growth term. The dispersal distance traveled during the reproductive process of budding is used to estimate the diffusion coefficient. The model has two homogeneous steady states, one occurring at the propagation front where the Argentine ant population does not yet exist and one occurring where the population has reached carrying capacity. The traveling wave solutions of the model depict the population density for a given time and location. Using current research, parameter values for the model are estimated and a traveling wave solution for the average parameter values is numerically demonstrated.