Derivatives for basicL (L Component)

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:

• $\eta$ 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

• $\varphi$ or phi: density-independent death rate

• $\theta$ or theta: the slope of the mortality rate in response to mean crowding

Dynamics:

$$dL/dt=\eta -(\psi e^{-\xi L}+\varphi +\theta L)L$$

Output:

• 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 $\varphi +\theta L.$ 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 $\xi =0.$