Behavioral Ecology P2

Foundations of Foraging Decisions and Optimality Theory

Core Foraging Questions:
- Any foraging organism, such as a pika, must continuously solve fundamental operational decisions:
- How far should it travel to gather food?
- How long should it remain foraging inside a specific patch?
- Which specific prey or plant species should it harvest?
Evolutionary Framework:
- Natural selection favors individuals whose foraging behaviors maximize net rate of energy gain or overall evolutionary fitness, all else being equal.
- Optimality Theory posits that behavioral strategies have evolved to maximize benefits relative to costs.
Role of Optimality Models:
- Optimality models formulate clear, mathematically testable predictions specifying how an optimally foraging individual should behave under explicit environmental conditions.
- Hypotheses are tested by directly comparing quantitative model predictions against empirical observations of animal or human behavior.

Pika grazing alpine avens (Geum rossii) on the Beartooth Plateau

Variation in Food Sources and Prey Profitability

Resource Heterogeneity:
- Food options in a foraging patch differ in handling ease, nutritional value, and energetic content.
- An optimal forager must evaluate whether to consume an encountered lower-quality item or bypass it to continue searching for a superior item.
Key Parameters of Prey Value:
- Energy Content ( $E$ ): The total caloric energy provided by consuming a single prey item, measured in calories ( $\text{cal}$ ) or kilocalories ( $\text{kcal}$ ).
- Handling Time ( $h$ ): The time required to process a single prey item. This includes capture/collection time, cleaning, shelling, or mechanical manipulation, and actual swallowing/consumption time, measured in seconds ( $\text{s}$ ) or minutes ( $\text{min}$ ).
- Crucial Constraint: A forager cannot search for additional prey items while actively handling a previously captured item.
Prey Profitability Formula:
- Profitability represents the net energetic gain per unit of handling time:

$\text{Profitability} = \frac{E}{h}$

Comparative Example (Pika Flower Harvesting):
- Yellow Flowers (Prey 1):
- Energy content: $E_1 = 12 \text{ cal}$
- Handling time: $h_1 = 3 \text{ s}$
- Profitability: $\frac{E_1}{h_1} = \frac{12 \text{ cal}}{3 \text{ s}} = 4 \text{ cal/s}$
- Blue Flowers (Prey 2):
- Energy content: $E_2 = 15 \text{ cal}$
- Handling time: $h_2 = 5 \text{ s}$
- Profitability: $\frac{E_2}{h_2} = \frac{15 \text{ cal}}{5 \text{ s}} = 3 \text{ cal/s}$
- Conclusion: Although blue flowers contain higher total energy per item ( $15 \text{ cal} > 12 \text{ cal}$ ), yellow flowers are significantly more profitable ( $4 \text{ cal/s} > 3 \text{ cal/s}$ ) because energy is extracted at a more efficient rate.

The Optimal Diet Model and Critical Search Time

Search Time ( $S$ ):
- The time required to locate a prey item of a given type.
- Upon encountering a less profitable prey item (Prey 2), its search time is effectively zero ( $S_2 = 0 \text{ s}$ ) because it is already found.
- The search time for the preferred prey item ( $S_1$ ) depends strictly on its environmental density and abundance.
Decision Rule for Dietary Expansion:
- An optimal forager should expand its diet to include a secondary, less profitable item (Prey 2) whenever the energy rate obtained from stopping to handle Prey 2 exceeds the expected overall energy rate from ignoring Prey 2 and continuing to search for Prey 1:

$\frac{E_1}{h_1 + S_1} \frac{E_2}{h_2}$

Critical Search Time Derivation:
- Rearranging the inequality for $S_1$ yields the Critical Search Time ( $S_1^*$ ) threshold:

$S_1 > \frac{E_1 h_2}{E_2} - h_1$

Diet Classification Rules:
- Generalist Strategy (eat both Prey 1 and Prey 2): Adopted when $S_1 > S_1^*$ . Preferred prey is rare and difficult to locate; taking secondary prey yields higher energy intake overall.
- Specialist Strategy (eat Prey 1 exclusively): Adopted when $S_1 \frac{E_1 h_2}{E_2} - h_1$ .
Key Properties of the Optimal Diet Model:
- Independence from Secondary Item Abundance: The decision to consume or ignore Prey 2 depends solely on the abundance and search time of the primary prey ( $S_1$ ), completely independent of the abundance or search time of Prey 2 ( $S_2$ ).
- Abrupt Transition: The predicted transition between specialization and generalization occurs abruptly as a step function at the threshold $S_1 = S_1^*$ .

Case Studies and Quantitative Foraging Calculations

Pika Simulation Experiments:
- Experimental Parameters: Area = $2 \text{ m}^2$ , Duration = $120 \text{ s}$ , Prey 1 (Yellow) = $4 \text{ cal/s}$ , Prey 2 (Blue) = $3 \text{ cal/s}$ .
- Calculated Critical Search Time for Yellow Flowers:

$S_1^* = \frac{12 \times 5}{15} - 3 = 1 \text{ s}$

Experiment 1 Data (Varying Yellow Flower Density; Blue Density fixed at $25 \text{ flowers/m}^2$ ):
- Trial 1 ( $5 \text{ yellow/m}^2$ , $S_1 > 1 \text{ s}$ ): $5$ Yellow eaten, $20$ Blue eaten (Generalist diet).
- Trial 2 ( $25 \text{ yellow/m}^2$ , $S_1 > 1 \text{ s}$ ): $16$ Yellow eaten, $22$ Blue eaten (Generalist diet).
- Trial 3 ( $35 \text{ yellow/m}^2$ , $S_1 \frac{830 \times 8}{390} - 10 \frac{6640}{390} - 10 \frac{180 \text{ min}}{7.03 \text{ min}}$ ).

Empirical Testing, Limitations, and Deviations

Great Tit Laboratory Experiment:
- Conducted by John Krebs, Eric Charnov, and collaborators using great tits (Parus major) foraging on mealworms moving on a conveyor belt.
- Prey types: Large mealworms (higher energy, lower handling time) vs Small mealworms with attached plastic tape (lower energy, higher handling time).
- Search times were precisely manipulated by varying conveyor belt speed and item spacing.

Predicted and observed results for Parus major foraging on mealworms

Observed Deviations from Theory:
- Real animals (such as Parus major) and simulated pikas display partial preference rather than an instantaneous step-function shift.
- Birds switched to specialization more gradually than predicted and continually ingested small amounts of suboptimal prey even when preferred prey was abundant.
Reasons for Suboptimal Foraging Decisions:
- Imperfect Information and Sampling: Animals lack complete environmental knowledge and must sample options to evaluate patch quality.
- Predation Risk and Defense Strategies: Foraging choices are balanced against danger from predators or prey defensive mechanisms.
- Nutritional Demands: Energetic yield is not the sole currency; animals must obtain essential micronutrients, amino acids, or vitamins.
- Misidentification Errors: Animals may mistake one prey species for another, accidentally ingesting suboptimal items.

Central-Place Foraging and the Marginal Value Theorem

Central-Place Foraging Concept:
- Organisms (e.g., pikas accumulating haypiles, starlings feeding nestlings) travel from a central home base or nest to patches, collect food, and return.
Diminishing Returns inside Patches:
- As a forager harvests inside a patch, local prey density decreases and load capacity limits (e.g., mouth size) slow processing.
- Represented by a concave-down gain curve plotting load collected ( $L$ ) against in-patch foraging time ( $T_f$ ).
Marginal Value Theorem (MVT) Model:
- Formulated by evolutionary ecologist Eric Charnov to predict optimal in-patch foraging time ( $T_f^*$ ) and optimal load size ( $L^*$ ).
- Overall harvest rate ( $H$ ) over a complete foraging bout:

$H = \frac{L}{T_b} = \frac{L}{T_t + T_f}$

$T_t$ = Constant round-trip travel time to and from the patch.
$T_f$ = Foraging time inside the patch.

Graphical model of the marginal value theorem

Graphical Solution Method:
- Travel time ( $T_t$ ) is plotted on the horizontal axis to the left of the origin (as $-T_t$ ).
- Foraging time ( $T_f$ ) is plotted to the right of the origin.
- Construct a straight line originating from $-T_t$ tangent to the gain curve.
- The point of tangency defines the optimal foraging time ( $T_f^*$ ) and optimal load size ( $L^*$ ).
- The slope of this tangent line represents the maximum overall harvest rate ( $H^*$ ).
MVT Predictions Regarding Patch Distance:
- As travel time ( $T_t$ ) to distant patches increases:
- The optimal foraging time in the patch ( $T_f^*$ ) increases (forager stays longer).
- The optimal load collected ( $L^*$ ) increases (forager collects a larger load).

Empirical Validation and Human Behavioral Ecology

Starling Load Size Experiment:
- Alejandro Kacelnik tested MVT using European starlings (Sturnus vulgaris) harvesting leatherjackets (larvae of Tipula flies) for nestlings.
- Controlled gain curves using artificial feeders delivering mealworms at expanding time intervals.
- Varied feeder distance ( $8 \text{ m}$ to $600 \text{ m}$ ), categorizing round-trip flight times into Short ( $4\text{--}18 \text{ s}$ ), Medium ( $33\text{--}45 \text{ s}$ ), and Long ( $52\text{--}95 \text{ s}$ ).
- Result: Starlings brought back significantly larger loads from distant feeders, validating MVT predictions.
Broad Biological Applications:
- Whelk size-class selection by foraging crows.
- Root biomass allocation in plants responding to soil nutrient patches.
Human Behavioral Ecology Studies:
- Applies optimal foraging models to human decision-making in prehistoric and modern societies.
- Intertidal shellfish harvesting studies in Micronesia and Mozambique demonstrated that diet breadth and prey choices strictly maximized energy return rates.
- Extended to analyze mating tactics, parenting strategies, and resource conservation.

Practice Problems, Quizzes, and Step-by-Step Solutions

Question 2.24: Which of the following is NOT an advantage of using optimality models to study behavior?
- Correct Answer: The models always perfectly predict an individual's behavior. (This statement is false, as models are simplified hypotheses).
Question 2.25: House martins feeding young in the nest are central-place foragers. According to MVT, how should a martin behave when visiting a distant patch compared to a close patch?
- Correct Answer: It should stay longer in and collect a larger load from the more distant patch.
House Martin Insect Dataset:
- Stonefly ( $i=1$ ): $E_1 = 0.9 \text{ kcal}$ , $h_1 = 3 \text{ s}$ , $S_1$ (Variable)
- Caddisfly ( $i=2$ ): $E_2 = 0.4 \text{ kcal}$ , $h_2 = 2 \text{ s}$ , $S_2 = 3 \text{ s}$
- Mayfly ( $i=3$ ): $E_3 = 0.2 \text{ kcal}$ , $h_3 = 2 \text{ s}$ , $S_3 = 1 \text{ s}$
Question 2.26 Calculation (Caddisfly Profitability):

$\text{Profitability} = \frac{E_2}{h_2} = \frac{0.4 \text{ kcal}}{2 \text{ s}} = 0.2 \text{ kcal/s}$

Question 2.27 Calculation (Stonefly Critical Search Time over Caddisfly):
- Given available prey: Stonefly (Prey 1) and Caddisfly (Prey 2).
- Formula: $S_1^* = \frac{E_1 h_2}{E_2} - h_1$
- Substitution:

$S_1^* = \frac{0.9 \times 2}{0.4} - 3 = \frac{1.8}{0.4} - 3 = 4.5 - 3 = 1.5 \text{ s}$

Correct Answer: $1.5 \text{ s}$
- Question 2.28 Calculation (Late Season Selection between Caddisfly and Mayfly):
Caddisfly (Prey 2, now primary): Profitability = $0.2 \text{ kcal/s}$
Mayfly (Prey 3, secondary): Profitability = $\frac{0.2 \text{ kcal}}{2 \text{ s}} = 0.1 \text{ kcal/s}$
Caddisfly critical search time threshold:

$S_2^* = \frac{E_2 h_3}{E_3} - h_2 = \frac{0.4 \times 2}{0.2} - 2 = \frac{0.8}{0.2} - 2 = 4 - 2 = 2 \text{ s}$

Given that critical search time is $2 \text{ s}$ , if actual search time $S_2 \frac{E_1 h_2}{E_2} - h_1$
- Central-Place Foraging (MVT): $H = \frac{L}{T_t + T_f}$