This document outlines a lab on predator-prey interactions using the Lotka-Volterra equations. The objectives are to understand predator-prey dynamics and how populations of each affect the other over time. The Lotka-Volterra equations model this relationship between changing predator and prey populations. Several simplifying assumptions are made, including predators relying solely on one prey species and prey having unlimited resources other than the predator. Students will use an online model to simulate predator-prey cycles over time.

1. Lab#5: Predator Prey Interaction
Asian University For Women
BIOL/ENVS 3003: ECOLOGY (Lab)
Fall 2022
Syed Mohammad Lokman
Instructor
Asian University for Women

2. BIOL/ENVS 3003: ECOLOGY (Lab) Syed Mohammad Lokman (syed.lokman@auw.edu.bd)
Objectives:
● To understand the basic concept of Prey-Predator dynamics using the
established Mathematical model of Lotka-Volterra Equations, i.e., how
predators affect prey populations, and vice-versa.

3. BIOL/ENVS 3003: ECOLOGY (Lab) Syed Mohammad Lokman (syed.lokman@auw.edu.bd)
Predator-Prey Relationship
● The predator-prey relationship is substantial in maintaining the equilibrium
between various animal species.
● Without predators, certain species of prey would force other species to
extinction as a result of competition.
● Without prey, there would be no predators! The key feature of predation
thus is the predator's direct impact on the prey population.

4. BIOL/ENVS 3003: ECOLOGY (Lab) Syed Mohammad Lokman (syed.lokman@auw.edu.bd)
Predator-Prey Relationship
● Many studies on the population ecology of predators have demonstrated
that predator numbers rise-and-fall cyclically with those of their
preferred prey - albeit that there is a synchronicity between the populations.
● This scenario -- where the predator populations crash shortly after their
prey populations experience a crash; this is known as predator-prey
cycle.

5. BIOL/ENVS 3003: ECOLOGY (Lab) Syed Mohammad Lokman (syed.lokman@auw.edu.bd)
Predator-Prey Relationship

6. BIOL/ENVS 3003: ECOLOGY (Lab) Syed Mohammad Lokman (syed.lokman@auw.edu.bd)
Predator-Prey Relationship

7. BIOL/ENVS 3003: ECOLOGY (Lab) Syed Mohammad Lokman (syed.lokman@auw.edu.bd)
Lotka−Volterra Equations
● In order to simulate these dynamics, Mathematical models need to be
incorporated.
● The population dynamics of predator-prey interactions can be modeled
using the Lotka−Volterra equations, which is based on differential
equations.

8. BIOL/ENVS 3003: ECOLOGY (Lab) Syed Mohammad Lokman (syed.lokman@auw.edu.bd)
The Lotka-Volterra Prey-Predator model involves two equations:
● one which describes how the prey population changes and
● the second which describes how the predator population changes.
Lotka−Volterra Equations
Change of Prey (R) Population =>
Change of Predator (S) Population =>

9. BIOL/ENVS 3003: ECOLOGY (Lab) Syed Mohammad Lokman (syed.lokman@auw.edu.bd)
Lotka−Volterra Equations
Change of Prey (R) Population =>
Change of Predator (S) Population =>
Where,
a is natural growth rate of R in absence of S,
c is natural death rate of S in the absence of food R,
b is the death rate per encounter of R due to predation,
e is the efficiency of turning predated R into S.

10. BIOL/ENVS 3003: ECOLOGY (Lab) Syed Mohammad Lokman (syed.lokman@auw.edu.bd)
Lotka−Volterra Equations
Change of Prey (R) Population =>
Change of Predator (S) Population =>
Where,
a = natural growth rate of R in absence of S,
c = natural death rate of S in the absence of R,
b = death rate per encounter of R due to predation,
e = efficiency of turning predated R into S.
● Also can be expressed as:
Where,
● x is the number of prey;
● y is the number of predator;
● t represents time;
● α, β, γ, δ are positive real parameters describing the
interaction of the two species.

11. BIOL/ENVS 3003: ECOLOGY (Lab) Syed Mohammad Lokman (syed.lokman@auw.edu.bd)
To simplify the complexity of the Dynamic models being studied,
we make some (unrealistic) assumptions:
● The predator species is totally dependent on a single prey
species as its only food supply,
● The prey species has an unlimited food supply and
● There is no threat to the prey other than the specific predator.
Lotka−Volterra Equations

12. BIOL/ENVS 3003: ECOLOGY (Lab) Syed Mohammad Lokman (syed.lokman@auw.edu.bd)
https://exchange.iseesystems.com/
public/jondarkow/lotka-volterra-pred
ator-prey-model/index.html#page2

13. BIOL/ENVS 3003: ECOLOGY (Lab) Syed Mohammad Lokman (syed.lokman@auw.edu.bd)

14. BIOL/ENVS 3003: ECOLOGY (Lab) Syed Mohammad Lokman (syed.lokman@auw.edu.bd)
Exercise
Lab#5: Predator Prey Interaction