Organisation at Population Level 37
Trophic relations, and therefore predator-prey interactions, are frequently
successional in nature leading to the formation of the so-termed food
chains. Usually, food chains combine with one another, generating complex
trophic networks in which one population can be preyed upon by numerous
predators and/or, simultaneously predate upon numerous preys. Primary
producers and top predators are placed at the food chain boundaries.
3.4.3.1 Predator-Prey Interaction Models
Predation as a quantitative interaction of two populations is described by
the typical Lotka-Volterra equations:
dN dt r N
N N
dN dt
r N
N N
1
1 1
21 1 2
2
2 2
12 1 2
=
−
= −
+
α
α
which are based on the exponential model; they can be formulated for the
logistic model respectively:
dN dt r N
N N q N
dN dt
r N
N N q N
1
1 1
21 1 2
1 1
2
2
2 2
12 1 2
2
=
−
−
= −
+
−
α
α
2 2
2
where r 1 represents the prey increase rate when no predator is present and –r 2
is the predator decrease rate when no prey, i.e. no food, is present. The intensity of the populations’ interaction is regulated by coefficients α 21 and α 12 .
The presence of the N 1 N 2 product is explained as in the case of competition.
From these equations it becomes obvious that prey growth rate decreases
due to predator presence, whereas predator growth rate increases due to
prey presence. We observe that if N 2 = 0 (predator absence), prey population
N 1 increases. But if N 1 = 0 (prey absence), predator population N 2 decreases
since the predator presumably has no other food source but the prey. In the
case of an alternative food source existence, the second equation is rewritten
without the presence of the (–) sign in front of the r 2 N 2 term.
In the above equations the following assumptions have been made, which
allow for a simple approach with enough realism, that is, without excessively departing from reality:
• Prey numbers consumed by the predator are proportional (linear relationship) to the prey population size.
• Predator population variation is proportional (linear relationship) to
the number of preys consumed by it.
The substitution of the prey’s linear response in relation to the predator (–α 21 N 1 N 2 ) and of the predator’s linear response in relation to the prey
Trophic relations, and therefore predator-prey interactions, are frequently
successional in nature leading to the formation of the so-termed food
chains. Usually, food chains combine with one another, generating complex
trophic networks in which one population can be preyed upon by numerous
predators and/or, simultaneously predate upon numerous preys. Primary
producers and top predators are placed at the food chain boundaries.
3.4.3.1 Predator-Prey Interaction Models
Predation as a quantitative interaction of two populations is described by
the typical Lotka-Volterra equations:
dN dt r N
N N
dN dt
r N
N N
1
1 1
21 1 2
2
2 2
12 1 2
=
−
= −
+
α
α
which are based on the exponential model; they can be formulated for the
logistic model respectively:
dN dt r N
N N q N
dN dt
r N
N N q N
1
1 1
21 1 2
1 1
2
2
2 2
12 1 2
2
=
−
−
= −
+
−
α
α
2 2
2
where r 1 represents the prey increase rate when no predator is present and –r 2
is the predator decrease rate when no prey, i.e. no food, is present. The intensity of the populations’ interaction is regulated by coefficients α 21 and α 12 .
The presence of the N 1 N 2 product is explained as in the case of competition.
From these equations it becomes obvious that prey growth rate decreases
due to predator presence, whereas predator growth rate increases due to
prey presence. We observe that if N 2 = 0 (predator absence), prey population
N 1 increases. But if N 1 = 0 (prey absence), predator population N 2 decreases
since the predator presumably has no other food source but the prey. In the
case of an alternative food source existence, the second equation is rewritten
without the presence of the (–) sign in front of the r 2 N 2 term.
In the above equations the following assumptions have been made, which
allow for a simple approach with enough realism, that is, without excessively departing from reality:
• Prey numbers consumed by the predator are proportional (linear relationship) to the prey population size.
• Predator population variation is proportional (linear relationship) to
the number of preys consumed by it.
The substitution of the prey’s linear response in relation to the predator (–α 21 N 1 N 2 ) and of the predator’s linear response in relation to the prey