Ecology 8310
Population (and Community)
Ecology
• Patch selection (e.g., Marginal Value Theorem)
• Prey selection (optimal diet theory)
• Moving beyond feeding (energy intake): predation risk (u/g)
Patch selection:
• Consider a forager moving among many patches
during a foraging bout (rodent among seed caches,
pollinator among flowers, etc.)
• Which patches does it feed in?
• For how long? (when does it leave?)
• How are these decisions altered by patch density?
• Or the quality of other patches?
Patch selection:
Patch selection:
GOAL: Maximize rate of net energy gain (intake – losses / time)
Cumulative energy intake
Patch selection:
Patch selection:
Marginal Value Theorem:
Leave when: dg/dT = En*
Marginal Value Theorem:
Another way to look at this
(when there is only 1 patch type)
Slope = Energy gain/Time
Point of
diminishing
Which strategy
yields the
greatest E/T?returns
Time to leave!
Travel Time
Search Time in Patch
Time
Marginal Value Theorem:
What if patches are denser (travel time is less)?
Dense
Sparse
Leave earlier when
travel time is
shorter.
Travel Time
Search Time in Patch
Time
Patch selection:
Predictions of MVT:
1.
2.
3.
4.
Leave at a fixed MV (indep. of patch quality
Stay in higher quality patches longer
Skip patches in which dg/dt|t=0 < En*
As the density of patches increase…
a. Reduce residency time
b. Drop low quality patches from diet
5. Variants:
a. Giving up density (uniform among patches)
b. Giving up time (time since last prey taken)
Prey selection:
Prey selection:
• Consider a forager moving WITHIN a patch
• Which prey does it attack?
• How are these decisions altered by prey density?
• …or the types of prey available?
• Assume: energy maximization
Prey selection:
Assume a forager has Ts units of search time
available.
How can we express the rate of net energy gain to
that forager during the foraging bout?
Two main components:
Net energy gained (intake – losses)
Time expended (searching and handling)
En/T = Net energy gained / Time expended
Prey selection:
k
En /T =
Ts å ai ei Ni Pi
i=1
k
Ts +Ts å ai Ni Pi hi
i=1
k
=
åa e N P
i i
i=1
k
i i
1+ å ai Ni Pi hi
i=1
Prey selection:
The solution and insights:
• Rank prey by ei/hi (=profitability)
• Predator can only decide on Pi's (attack, don't attack,
sometimes attack).
• Optimal Pi is either 0 or 1 (attack or don't attack)
• RULE: Attack if ei/hi>E*/T; else ignore. [As in MVT]
• Inclusion of a prey type in the diet is only a function of
density of MORE valuable prey.
• Examine graphically….
A test:
From Richardson and Verbeek (1986)
Laboratory test: Bluegill sunfish
Based upon Werner and Hall (1974)
Prey selection: Field (lake)
From Mittelbach (1981)
Can we use the diet model to predict field patterns
(growth and habitat use)?
Habitat selection: "Field" (Ponds)
Open water
Vegetation
From Werner et al (1983
Problems?
Early models were very simple
Ignored complexities (e.g., capture probability, search
images, nutrients, etc.)
Other species ….
Lakes:
Open water often the most
profitable.
Used by large bluegill.
BUT small bluegill use the
vegetated habitat.
Why?
Can we incorporate predation risk into our predictive framework?
Old rule: maximize "g" (growth)
New rule: minimize  /g (risk to growth)
Other implications of this work (stage-structure in bluegill)?
Small Bluegill
Littoral
Invertebrates
Large Bluegill
Zooplankton
Small Bluegill
Littoral
Invertebrates
Large Bluegill
Zooplankton