Foraging Behavior and Ideal Free Distribution

• Foraging behavior refers to the methods an animal uses to acquire energy and nutrients
• Foraging can be broken down into several steps: encounter, detect/recognize, decision making (herbivore), predation sequence (predator), and deciding whether to stay or move

Ideal Free Distribution

• Individuals will distribute themselves among resource patches based on the payoffs
• Steps to Ideal Free Distribution: encounter, stay vs. move
• Key assumptions include:
• Food patches differ in quality
• Several individuals forage in the patches
• Individuals share food equally within a patch
• Individuals can freely choose patches and aim for the highest payoff
• Ideal Free Distribution (Fretwell & Lucas, 1969) posits that if individuals choose patches based on payoffs, they'll distribute themselves according to resource distribution
• Newcomers will aim to settle where the payoff rate is greatest
• A patch becomes crowded and individual payoffs decrease, individuals should relocate to a patch with better payoff
• Individuals will have approximately equal payoff over time
• The number of individuals in a patch is proportional to the quality of the patch

Adding Complexities to the Models

• Optimal foraging theory states there are costs and benefits to different foraging decisions
• Animals should choose the foraging strategy with the highest net benefit (benefit – cost difference or ratio)
• Assumes costs and benefits are independent of what others are doing
• Evolutionary Game theory assumes costs and benefits are primarily determined by what other individuals are doing
• Optimality models predict organisms behave to maximize net benefit gain (benefit minus cost)
• Assumes costs and benefits are independent of what others are doing

Optimal Foraging Theory

• Benefits of energy intake include maintenance, growth, and reproduction
• Costs include opportunity cost (time spent performing a behavior), energy expended, and risk of injury or death
• Optimal prey selection models maximize energy intake per time unit (efficiency)
• Different food options have different benefits and costs related to time and energy to search, pursue, and handle the food
• As prey density increases, the opportunity cost of going after smaller prey becomes higher
• Bluegill sunfish are most selective for prey size in high-density treatments during optimal foraging
• Sunfish foraging was studied by Werner & Hall (1974) by allowing sunfish to forage in experimental ponds with high, medium, and low densities of daphnia
• Encounter rate is how close the fish are to prey which implies that fish preferentially chase after larger prey in high/medium density
• Diet was predicted using a model
• The observed diet can also be described

Optimal Patch Use Models

• Animals can forage in multiple patches of food
• Animals experience diminishing returns, where it becomes harder to find food over time
• Traveling between patches takes time that can’t be used for foraging
• An animal should leave a patch according to the Marginal Value Theorem
• The Marginal Value Theorem states that if we draw a line connecting the start and end of each patch foraging bout, the slope represents energy intake per unit time (i.e., efficiency)
• Leaving early is often the better strategy because it gathers energy more efficiently
• The optimal time to leave correlates to when the slope is largest
• Individuals should stay in a patch for 10 minutes to maximize foraging efficiency
• Maximizing slope is finding the tangent line
• The best time to leave is the tangent point
• All else being equal, when patches are further away, animals should spend more time in each patch before leaving
• According to marginal value theorem, animals should spend longer time foraging in a patch for scenario B where food gathering efficiently within a patch diminishes slowly as opposed to scenario A where it diminishes drastically with time

Optimal Foraging Theory: Take Away

• Optimality models assume animals make choices that maximize their net fitness gain while foraging; cost and benefit are independent of other individual's decisions
• Has applications in optimal prey choice models and optimal patch use models

Evolutionary Game theory

• Economically, this refers to mathematical models of strategic interactions among rational agents
• Rational agents use strategies that gives them the highest benefit
• The benefit depends on what the other agents are doing
• In biology, this is the application of game theory in evolving populations
• Natural selection favors behaviors that lead to the highest fitness, which depends on what others are doing
• Ex.) Fishing vs. Pirating, Hawk-Dove Game, Prisoner's Dilemma, and Tragedy of the Commons
• Assumes that costs and benefits are determined by what other individuals are doing

Fisher Pirate Example

• Pirates do better in a population dominated by fishers, because they can easily steal food and in turn have higher fitness
• Fishers do better in a population dominated by pirates, because pirates can't find targets
• The fitness of a foraging strategy thus depends on the relative proportion of fisher and pirates in the population

Hawk-Dove Game Example

• Hawks fight to get resources
• Doves share resources but retreat when they encounter hawks
• The value of resource (V) describes cost of losing a fight (C)
• The payoff chart is read as follows: when doves meets hawk: Dove retreats, getting nothing (payoff = 0). While Hawk gets all (payoff = V)
• Whether hawk or dove is a better strategy depends on how many doves and how many hawks there are in a population
• Payoff is calculated as:
• 1. calculate payoff in each encounter
• 2. calculate the strategy payoff based on encounter frequency
• 3. the strategy that has higher payoff has a higher fitness, in this case, Dove.

Calculating Payoff of a Strategy:

• In a population with 50% hawk and 50% dove, which strategy has a higher fitness?
• Consider the Hawk-Dove game with V=2, and the fight cost C=10, in an all-dove population hawk has a higher fitness
• Payoff = Sum of encounter frequency x payoff
• In an all dove population:
• hawk strategy performs better and will increase in number
• When the population is all hawk, a dove strategy performs better and increase in number
• Evolutionary Stable State – where both have the same fitness (payoff = 0.8)

Negative Frequency Dependent Selection

• NFDS – relative fitness of a phenotype increases as it becomes rarer in the population
• Doves have higher fitness when they are rare
• Hawks have higher fitness when they are rare
• Leads to an Equilibrium ratio (ESS)
• Ex.) Fruit fly larvae foraging:
• Sedentary sitter: stays a long time in a patch
• Active rover: moves from patch to patch frequently
• Varies vary the relative frequency of two phenotypes and measure fitness (survival % to adult)
• The fitness of a sitter decreases with the frequency of the sitters in a population
• Example: Scale-Eating Cichlid where right and left-jawed chichlids are maintained in the population

More Complexities

• Food doesn't want to be Eaten which leads to a Predator-Prey Arms Race where the efficiency of predator foraging depends on how well your food (prey) can elude you
• Landscape of fear is the spatial distribution of where prey forage is shaped by the predation risks they perceive, influence both prey foraging and predator foraging.
• Prey practice antipredator behavior to avoid being eaten
• Predators practice foraging behavior to overcome prey defense
• Predator/prey battles can happen at different levels:
• Sensory ability, Avoiding detection, Escape ability, and Weapons & Counters
• Bats vs. Moths is a key example. Bats engage in echolocation (night foraging), aerial maneuvers, and use their webbed tail to wrap around prey. In contrast, moths engage in ultrasound hearing
• Aggressive Mimicry involves a predator mimicking profitable signals (e.g. food, mates) to lure prey towards it
• Aphaenogaster ants use tool use to place debris into liquid food and then carry the soaked debris back to their nest
• Ants are selective in materials, and can learn to use with materials they've never encountered in nature
• Due to the Landscape of Fear animals must make trade-offs between finding food and avoiding predators/diseases
• When there are predators around, animals change when and where they forage

Yellowstone Wolf Reintroduction

• Predator effect on ecosystem is described by:
• Lethal effect
• Non-lethal effect
• Landscape of fear describes the non-lethal effect
• Changes in foraging behavior can lead to community and ecosystem level consequences