Optimal Foraging Theory Notes

Most common application of optimality theory is in studies on animal foraging decisions.
Makes predictions about how animals maximize fitness while foraging.
All foraging tactics come with costs and benefits in terms of energy.

Food provides energy intake benefits.
Finding food has costs:
- Search time: Time and energy spent locating food.
- Handling time: Time and energy spent accessing food.
Energy is the primary currency in most models.
Optimization focuses on energy gain per cost (time or energy).

Two models of prey value, measured by mass of prey consumed per unit time:
- Model A: Considers only time to attack and capture rate.
- Model B: Includes attack time, capture rate, and post-capture handling time.
- Which model is more realistic?

Crows feed on whelks.
Large whelks required fewer 5-meter drops to break.
The probability of a large whelk breaking was constant at approximately $1/4$ per drop, regardless of the number of previous drops.

Male foraging efficiency increases reproductive opportunities.
Experiment setup:
- Divided cage with males on both sides.
- One side had a branch with empty pinecones; the other had unaltered pinecones.
Female crossbills preferred males that secured many seeds.

Many factors, including the biology of the organism, can influence how well empirical data fit the predictions.
Eurasian oystercatchers tend to choose fairly large mussels, but not the very largest.

Model A: Profitability based on energy available in opened mussels of different sizes divided by the time required to open them.
Model B: Profitability considers that some very large mussels must be abandoned after being attacked because they are impossible to open.

Larger mussels are more likely to be covered by an impenetrable layer of barnacles.
Incorporating prey-opening time and the size range of realistically available prey into the model:
- Conclusion: Birds should focus on 30-45 mm mussels.

Dugongs alter their foraging tactics when dangerous sharks are likely to be present.
Time spent excavating sea grass from the ocean bottom declines in relation to the probability that tiger sharks will be in the area.

Life-dinner principle:
- The coevolutionary arms race between predator and prey is asymmetrical.
- Staying alive usually trumps eating.
- Forgoing one meal is less critical than dying (Dawkins and Krebs, 1979).
Trade-offs exist between finding food and avoiding predators.
Landscape of fear:
- Spatially explicit elicitation of fear in prey by the perceived risk of predation (Gallagher et al., 2017).

After wolves were reintroduced into the Yellowstone ecosystem:
- Elk spent more time hidden in woodlands rather than feeding in exposed meadows.
- This change reduced the production of calves and decreased the survival of the calves they did have.
- Trade-off between reproduction and survival.

The New Caledonian crow routinely modifies a wide variety of objects (e.g., palm leaves, sticks, grass stems) and uses them to extract grubs and other food items from their hiding places.
Elevation-related cognitive differences among mountain chickadees in the Sierra Nevada.

Croston et al. (2017) investigated how environmental harshness influences cognitive ability and caching behavior in mountain chickadees.
Used a spatial learning and memory reversal task on populations of birds from high and low elevations.
- Sites differed in the degree of winter climate severity.

Birds were trained to retrieve sunflower seeds from RFID “smart” feeders that only opened for individual birds tagged with a transponder coded for a specific feeder.
After a few weeks, learning was reversed by assigning each bird to a new “target” feeder.
Results:
- High-elevation birds visited feeders more often and made more location errors during the reversal period.
- Mountain chickadees are more reliant on food caches in harsher environments.
- They may be initially better at spatial learning but at the expense of reduced cognitive flexibility.

Evolutionary stable strategy (ESS):
- When a single strategy for a given population cannot be invaded by an alternative strategy that is initially rare.
ESS is a refinement of Nash equilibrium.
- Nash equilibrium is a solution (or optimal strategy) for how competing individuals, corporations, or governments should act to maximize their gains.

Hawk-Dove game:
- Contestants can adopt one of two behavioral strategies:
  - Hawk strategy: Individual first displays aggression and then escalates into a fight until it either wins or is injured (and loses the fight).
  - Dove strategy: Individual first displays aggression and then either retreats to safety if faced with an escalation or attempts to share the resources if not faced with an escalation.

Generally assumed that the value of the resource is less than the cost of a fight ( $C > V > 0$ ).
Questions:
- Are either of these strategies impervious to invasion by another?
- In a population of all hawks, could a dove strategy invade?
- Could either strategy be considered a “pure” ESS?

Example:
- Payoff values: $V = 6$ and $C = 18$ .
What if we violate the assumption that the value of the resource is less than the cost of a fight? ( $C > V > 0$ )
- Try reversing the values: $V = 18$ and $C = 6$ .
- What happens to the mixed ESS?

Frequency-dependent selection occurs when the fitness of one strategy is a function of its frequency relative to the other inherited behavioral trait.
Genotypic fitness can either increase (positive frequency-dependent selection) or decrease (negative frequency-dependent selection) as the frequency of the genotype increases.

Fruit fly larvae come in two forms:
- Active rovers.
- Sedentary sitters.
- With correspondingly divergent foraging behaviors.
Why are both types still reasonably common?

When resources are scarce, the fitness of sitters vs. rovers depends on which of the two types is rarer.
In this case, negative frequency-dependent selection led to an increase in the frequency of the rarer behavioral type.

African cichlid fish come in two forms:
- One with the jaw twisted to the right.
- The other with the jaw twisted to the left.
Adults with the jaw twisted to the right always attack the prey’s left flank, while those with the jaw twisted to the left hit the right side.

Both types occur because prey learn to expect an attack from the left if most attacks were directed at the left flank.
If the right-jawed form predominated, left-jawed fish would have an advantage because its prey would be less vigilant on the right flank.
Results in higher reproductive success for the rarer phenotype and an increase in its frequency until left-jawed fish make up half the population.
Note how the frequency of the left-jawed phenotype oscillates around the equilibrium point.