This implements differential equation model for aquatic mosquito ecology. The equations have been modified slightly from a version published by Smith DL, et al. (2013).
Variables:
\(L\): the density of mosquito larvae in each habitat
Input Term:
\(\eta\) or
eta: egg deposition rate (from F_eggs)
Parameters:
\(\psi\) or
psi: maturation rate\(\xi\) or
xi: delayed maturation parameter in response to mean crowding\(\phi\) or
phi: density-independent death rate\(\theta\) or
theta: the slope of the mortality rate in response to mean crowding
Dynamical System:
$$dL/dt = \eta - (\psi\;e^{-\xi L} + \phi + \theta L)L$$
Output Term:
The function F_emerge computes the net emergence rate (\(\alpha\)):
$$\alpha = \psi e^{-\xi L} L $$
Regulation:
In this model, population is regulated in two ways. First, per-capita mortality increases with mean crowding; per-capita mortality is \(\phi + \theta L.\) Second, maturation is delayed in response to mean crowding \(\psi\;e^{-\xi L.}\) Depending on the values of \(\xi,\) productivity in some habitats might not be a monotonically increasing function of egg laying.
The model by Smith DL, et al. (2013) did not include delayed maturation; that model is recovered by setting \(\xi=0.\)
Usage
# S3 method for class 'basicL'
dLdt(t, y, xds_obj, s)Value
a numeric vector
References
Smith DL, Perkins TA, Tusting LS, Scott TW, Lindsay SW (2013). “Mosquito population regulation and larval source management in heterogeneous environments.” PLoS ONE, 8(8), e71247. doi:10.1371/journal.pone.0071247 .