LPA and Ricker Model Simulators

This website provides interactive simlations for the discrete-time Ricker and LPA population models. Use the links on menu to the left to navigate to the different models and data views. Below are descriptions of the equations for the Ricker and LPA models.

Ricker Model

The equation for the discrete-time Ricker population model can be written as $$N(t+1) = N(t)\exp\left(r\left({K-N(t)} \over K\right)\right),$$ where \(N(t)\) is the size of the population at time \(t\), \(r\) is the intrinsic rate of population growth, and \(K\) is the population carrying capacity.

LPA Model

The LPA model describes the population dynamics of flour beetles. The model given by the following three equations: \begin{align} L(t+1) & = b L(t) \exp\bigl(-c_{el} L(t) - c_{ea} A(t)\bigr), \\ P(t+1) & = L(t) \bigl(1-\mu_l\bigr), \\ A(t+1) & = P(t) \exp\bigl(-c_{pa} A(t)\bigr) + A(t) \bigl(1-\mu_a\bigr). \end{align} The first equation is for the number of feeding larvae (referred to as the L-stage), the second is for the number of large larvae, non-feeding larvae, pupae and callow adults (called the P-stage), and the third is for the number of sexually mature adults (A-stage animals). The unit of time is two weeks and is, approximately, the average amount of time spent in the feeding larval stage under experimental conditions. The time unit is also approximately the average duration of the P-stage. The quantity \(b > 0\) is the number of larval recruits per adult per unit of time in the absence of cannibalism. The fractions \(\mu_l\) and \(\mu_a\) are the larval and adult rates of mortality in one time unit. The exponential functions account for the cannibalism of eggs by both larvae and adults and the cannibalism of pupae by adults. The fractions \(\exp\bigl(-c_{el} L(t)\bigr)\) and \(\exp\bigl(-c_{ea} A(t)\bigr)\) are the probabilities that an egg is not eaten in the presence of \(L(t)\) larvae and \(A(t)\) adults in one time unit. The fraction \(\exp\bigl(-c_{pa} A(t)\bigr)\) is the survival probability of a pupa in the presence of \(A(t)\) adults in one time unit.

For more information, see the pdf manual. A link is provided on the left column of this page.