Optimal Foraging Notes

Optimal Foraging

All behaviors have costs and benefits that impact survival and mating success, which are subject to natural selection. Optimal foraging theory suggests that animals will adopt strategies that maximize energy intake per unit time.

Optimality Models

• Optimality models predict an animal's optimal course of action under specific conditions to maximize its fitness. These models involve defining a currency (e.g., energy intake), constraints (e.g., handling time, search time), and decision variables (e.g., prey choice, patch residence time).

Territory Defense

• Optimal territory size is determined by the balance between costs and benefits. Costs include energy expenditure and risk of injury during defense, while benefits include exclusive access to resources. A larger territory may provide more resources but require more energy to defend.

• The maximum benefit is achieved where the difference between benefits and costs is greatest. This point determines the optimal territory size.

• Krebs (2009) presented a hypothetical cost-benefit model for territory size, demonstrating how territory size can be optimized based on resource distribution and competitor pressure.

Territory Size and Food Availability

• Territory size is related to the amount of available food. In areas with high food availability, territories tend to be smaller, as animals can meet their energy needs in a smaller area. Conversely, in areas with scarce food resources, territories tend to be larger.

• Animals adjust their territory size to optimize energy intake. This adjustment can be influenced by factors such as population density, resource predictability, and the presence of competitors.

Prey Selection

• Foragers must decide which food items to eat. This decision involves assessing the energy content, handling time, and encounter rate of different prey types.

  • The central question is whether to eat or move on, considering the potential for encountering more profitable prey elsewhere.

  • The currency being maximized is the rate of energy intake. Animals aim to maximize the amount of energy gained per unit of time spent foraging.

Model Assumptions

• Models assume:

  • Measurable standard currency (e.g., energy). Energy is often used as a common currency to evaluate the profitability of different foraging decisions.

  • Handling prey involves a cost. Handling time includes the time and energy required to capture, process, and consume prey.

  • A predator cannot handle prey and search for other prey simultaneously. This assumption simplifies the model by assuming that predators must fully handle one prey item before searching for another.

  • Prey are encountered sequentially. Predators encounter prey one at a time, rather than simultaneously.

  • Prey are recognized instantly and accurately. Predators can immediately identify and assess the value of potential prey items.

Rate of Energy Acquisition

• Key variables:

  • $e_i$ = energy provided by prey type i

  • $h_i$ = handling time and effort associated with prey type i

  • $\lambda_i$ = encounter rate with prey type i

  • $T_s$ = amount of time devoted to searching for prey type i

  • $T$ = total time

• Rate of energy acquisition = $e/h$

• Predators are assumed to prioritize prey with higher $e<em>i/h</em>i$ values. This ratio represents the energy gain per unit handling time and is a key factor in prey selection.

Prey Choice

• Consider two prey types: prey 1 and prey 2.

• If a predator eats both types of prey, the rate of energy acquisition is $\frac{e}{h + h<em>2}$, where $h</em>2$ is the extra handling time for prey 2.

• The decision is whether to eat only prey 1 or both prey types.

  • $\frac{e}{h}$ prey 1

  • $\frac{e}{h + h_2}$ prey 2 extra handling time for prey 2

• Should a predator eat both types of prey or just prey 1? The optimal choice depends on the relative abundance, energy content, and handling time of each prey type.

Model Predictions

• Searchers should be generalists. In environments where prey is scarce or unpredictable, it is advantageous to be a generalist and consume a wide variety of prey items.

• Handlers should be specialists. When handling time is significant, predators should specialize on the most profitable prey items to maximize energy intake.

• Specialization increases in more productive environments. In environments with abundant high-quality prey, predators can afford to specialize on these items, leading to higher energy intake rates.

• The abundance of unprofitable prey types is irrelevant. Predators should ignore prey types that offer low energy returns relative to handling time, regardless of how abundant they are.

Factors Affecting the Model

• Have we chosen the right currency? Animals may make more complex judgments about food (e.g., tits feeding spiders to chicks). Nutritional content, toxin levels, and social factors can also influence prey choice.

• The probability of finding prey may not be proportional to its density due to the search image concept (Tinbergen-warblers). Predators may develop a search image for a specific prey type, making them more efficient at finding that prey but less efficient at finding other prey.

• Search image refers to the ability of predators to improve their detection of a specific prey type over time by forming a mental image of it. This can lead to prey selection based on learned recognition rather than solely on energy content.

Patch Residence Time

• Foragers must decide how long to stay in a patch. This decision depends on the rate of energy gain within the patch, the travel time to other patches, and the quality of those patches.

• Gains decrease as the patch is depleted. As a forager spends more time in a patch, the rate of energy gain typically decreases due to resource depletion.

Marginal Value Theorem

• Marginal value theorem (Charnov, 1976) addresses how long a forager should stay in a patch. The theorem predicts that foragers should stay in a patch until the rate of energy gain within the patch equals the average rate of energy gain across all patches in the environment.

• Maximum net gain is achieved when energy gain balances travel time. The optimal patch residence time is the point at which the marginal rate of energy gain in the patch equals the average rate of energy gain in the environment.

  • Animal leaves too early

• Travel Time in animal is sensitive to trip length between patches. Longer travel times between patches should lead to longer patch residence times, as the forager needs to compensate for the time spent traveling.

Assumptions of the Marginal Value Theorem

1. Each patch type is recognized instantaneously. Predators can quickly assess the quality and potential yield of a patch upon arrival.

2. Travel time between patches is known by the predator. Predators have an estimate of the time required to travel between different patches in their environment.

3. The gain curve is smooth, continuous, and decelerating. The rate of energy gain within a patch decreases continuously as the patch is depleted.

4. Travel time between and searching within a patch have equal energy costs. This assumption simplifies the model by assuming that the energy cost of traveling and searching is constant.

Implications of the Marginal Value Theorem

• Longer travel times between patches should lead to longer patch residence times, and vice versa. When travel times are long, foragers should spend more time in each patch to maximize their overall rate of energy gain.

Modifications to Optimal Foraging Models

• Central Place Foraging: considers a central location (e.g., nest) with feeding areas. This model is relevant for animals that must return to a central location to feed offspring or store resources.

  • Costs include energy to/from the feeding area and carrying food. Foragers must balance the cost of traveling to and from the central place with the amount of food they can carry back.

Central Place Foraging Hypothesis

• Birds should feed differently if feeding themselves versus feeding offspring. When feeding offspring, birds should prioritize bringing back larger loads of high-quality food, even if it means traveling farther or spending more time foraging.

Risk-Sensitive Foraging

• Animals may choose between fixed and variable food sources. Risk-sensitive foraging models incorporate the variability in food availability and the animal's current energy state.

• Barnard et al. (1985) explored risk-sensitive foraging. Their experiments demonstrated that animals may prefer variable food sources when they are energy-stressed, even if the average reward is lower.

• Intake is relative to energy requirement; animals may select variable or fixed sources based on their energy needs. Animals that are below their energy requirement may prefer variable food sources in the hope of obtaining a large reward, while animals that are above their energy requirement may prefer fixed food sources to avoid the risk of starvation.

Elk Habitat and Wolf Predation

• Elk habitat use changes in the presence of wolves. Elk may avoid areas with high wolf densities, even if these areas offer high-quality forage.

• Elk behavior is influenced by the risk of predation. Elk may alter their foraging behavior, group size, and vigilance levels in response to the perceived risk of predation.

Risk Effects on Reproduction

• Wolf reintroduction can have direct and risk effects on elk survival and reproduction. Direct effects include increased mortality due to wolf predation, while risk effects include reduced foraging efficiency and increased stress levels.

• Creel and Christianson (2008) studied these effects. Their research showed that wolf reintroduction can lead to decreased elk pregnancy rates and calf survival.

• Song sparrows exposed to recordings of predators fed their young fewer times per hour (Zanette et al. 2011), indicating perceived risk influences foraging behavior. This demonstrates that the perceived risk of predation can have cascading effects on parental care and offspring survival.

Risk-Sensitive Foraging and Shrew Behavior

• Shrews preferred the station yielding the higher mean reward rate, but preference for a constant (constant reward rate) or risky (variable reward rate) station was influenced by experience of variance in reward rate at the risky station. Shrews may adjust their foraging behavior based