Predatorprey systems can be modeled with simple math

1
Predator-prey systems can be modeled with simple
math

• R is pRey popn P is Predator popn

dR/dt rR - cRP
2
Predator functional response
Loss to predator population cRP
3
3 possible forms of the Predator Functional
Response
Type I linear increase with increasing
prey assumed by Lotka-Volterra Uncommon in
nature Type II predator consumption
saturates Limited by handling time and
digestion Type III accelerating phase at low
densities saturation at high densities Prey
switching/hiding places at low densities
satiation at high densities
4
Prey switching
5
Numerical response

• Change in predator population size in response to
  prey population
• Immigration/aggregation
• Highly mobile predators (faster response)
• Reproduciton/population growth
• Lags behind changes in prey abundance (slower
  response)

6
Factors that stabilize predator-prey systemswhy
dont most predator-prey populations cycle?

• Predator inefficiency
• Density-dependence of predators or prey
• Alternative food sources for predator
• Refuges for prey
• Reduced time delays in predator response to prey
  dynamics

7
Competition is the use/defense of a resource by
one individual that reduces its availability to
other individuals

• Interspecific competition
• (between species)
• Intraspecific competition
• (within species, e.g., logistic growth)

8
Competition is the use/defense of a resource by
one individual that reduces its availability to
other individuals

• Can also classify the type of competition by the
  nature of the interaction
• Resource competition
• When organisms use common resources that are in
  short supply
• Interference competition
• Organisms seeking a resource harm one another in
  the process

9
Resource versus Interference competition
Resource
Interference
10
Eucalyptus promotes hot fires

• -oil promotes hot fires
• Kills seedlings and young trees of potential
  competitors
• Leaves eucalyptus relatively unharmed

11
Sage exudes toxins - allelopathy
How could you demonstrate this experimentally?
12
Competition between two species of plants
(Tansley 1917)
Popular experimental design common garden
13
Soil treatments
neutral pH low pH
Species treatments
Species A Species B Species A B
14
Categories of resources
Nonrenewable e.g., space once it is
occupied, it is not replenished until the
organism leaves
Renewable e.g, nutrients, food,
etc continuously replenished (but at
varying rates!)
15
Competition for space in barnacles
Upper intertidal
Lower intertidal
16
Three types of renewable resources

• Externally supplied (light, rainfall)
• with weak or no feedbacks

2) Regenerated directly within the ecosystem
and affected by consumer (e.g., most
predator-prey, plant-herbivore)
3) Regenerated indirectly within ecosystem (e.g.,
nutrient recycling by herbivores)
17
Indirect regeneration
Direct regeneration
18
The competitive exclusion principle derived from
Gauses (1932) now famous experiments with
protozoans
Species 1
Species 2
19
Gauses (1932) As a result of competition two
similar species scarcely ever occupy similar
niches, but displace each other in such a manner
that each takes possession of certain peculiar
kinds of food and modes of life in which it has
an advantage over its competitor.
20
Niche concepts
Fundamental niche - a species role in the
community -overlap of all the tolerable
conditions for that species
21
Niche concepts
Fundamental niche -impossible to
measure -infinite number of possible
variables -would need to measure species in
the absence of competition/predation/etc.
22
Niche concepts
Realized niche - the observed resource use of
a species in the presence of competition
(predation, parasites, etc.) - can be a tiny
fraction of the fundamental niche
23
Competitive exclusion in nature
Fig. 12.9 12.10
24
Intraspecific competition via the logistic model
per capita population growth rate
25
Interspecific competition via the logistic model
26
Logistic population growth
dN/dt
Intraspecific
Population growth rate
Population size (N)
27
What is the difference between a resource and a
limiting resource?
Could you design an experiment to determine the
limiting resource?
28
Resources may interact to affect growth
29
Resources may interact to affect
growth (co-limitation)
30
Do other animals compete?
Asymmetric competition?
31
How would you design an experiment to
determine 1) whether two species were competing
with each other?, and 2) What the strength of the
competitive effects are?
32
Diet composition of two ant species
Do they compete?