Z404 Prey with two predator dynamic

Model name

Z404 Prey with two predator dynamic

Original author(s)

Hartmut Bossel

References and/or links for original model

Format of original model

Vensim

Converted by

Francesco Benvenuti

Date submitted

20/04/2012

Purpose

This model allows to explore population dynamics of Prey and of two predators.

Often a single prey population is the source of food for several competing predators (e.g. mice as prey of foxes and birds of prey). The Model provide a reliable intuitive assessment of long-term development of a prey population and that of two predator relying on it as a food source. The model assists in recognizing development trends inherent in the system structure even if in reality a variety of other factors determine the development and may cause it to proceed on a somewhat different path.

Description

In this system with a single prey population and two predator populations predator A and predator B there exist again two predator-prey linkages (prey encounters predator A, and prey encounters predator B). These linkages correspond to those in the normal predator-prey system. Predator A and predator B have specific energy consumption rate a and energy consumption rate b. The prey population has (relative) growth rate prey. The rates of increase of the predator populations (predator A gain, and predator B gain) are determined by (relative) prey gain predator a and prey gain predator b. The prey loss is a function of (relative) loss caused by predator a and loss caused by predator b.

However, a small disadvantage of predator A (insignificantly higher energy consumption rate a) suffices to cause this population to disappear after some time. Thereafter an undamped oscillation develops for prey and the remaining predator B (undamped because of unrestricted carrying capacity)

Model size indicators

Stocks and flows

Simile diagram

Simile equations

Predator A loss = Predator_A*Energy_consumption_rate_A

Predator B gain = Prey_gain_Predator_B*Prey_encounters_predator_B

Predator B loss = Predator_B*Energy_consumption__Rate_B

Predator A gain = prey_gain__predator_A*prey_encounters__predator_A

Prey gain = Growth_rate_prey*Prey

prey loss = loss_caused_by_predator_A*prey_encounters__predator_A + loss_caused_by_predator_B*Prey_encounters_predator_B

Prey encounters predator B = Predator_B*Prey

prey encounters predator A = Predator_A*Prey

Files

The model and associated files are listed at the bottom of this page. The model may be provided in more than one format (e.g. as Vensim .mld and Simile .sml files).

Notes on the conversion process

Extra information on original model

In the long run, the behavior of the system corresponds to that of the predator-prey system in model Z401(Predator and unlimited prey)