#optimal foraging

Predator Prey Model

According to MVT, a forager should leave a patch when:

The marginal value theorem states that a forager should leave a patch when its instantaneous capture or energy-gain rate has declined to the average rate attainable across the environment, including travel time between patches. Early in a patch visit, profitable items are readily found and marginal return is high. Continued exploitation depletes the patch, so each additional unit of time yields less. Once the marginal return equals the habitat-wide average, staying longer would lower long-term intake; departing for a new patch raises it. Maximum total energy within the current patch is not the objective because reaching complete depletion can waste substantial time. “Falls below minimum” lacks a defined comparison, and handling time need not become zero. Graphically, the optimal point is where a tangent drawn from the negative travel-time intercept touches the cumulative gain curve. This rule assumes knowledge or evolved estimation of patch quality and average environmental profitability. Predation risk, competition, and incomplete information may shift actual departure, but the equality of marginal and average gain is the theoretical benchmark.

Ref: Ecology: Concepts and Applications, Molles, 9th Ed., Ch. 14

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PREDATOR

Patch residence time is maximized when:

When travel between patches takes a long time, leaving the current patch imposes a large period with no resource intake. The marginal value theorem therefore predicts that a forager should exploit each reached patch more thoroughly and remain there longer before departing. With short travel, frequent movement is less costly and earlier departure can be optimal. Resource-poor patches generally support shorter visits unless travel costs are extreme, and low energetic rewards do not by themselves maximize residence. The relationship arises because the optimal departure tangent is calculated over both patch exploitation and between-patch travel, so greater travel time lowers the environmental average gain rate and delays departure. From an evolutionary perspective, traits persist when their net effects improve inclusive or direct fitness under prevailing conditions. The ecological terminology therefore summarizes both an immediate mechanism and its likely consequences across generations. A careful interpretation retains the assumptions of the underlying model and avoids extending it beyond available evidence. Within those assumptions, the keyed concept gives the most consistent account of the biological pattern and its expected outcome.

Ref: Ecology: From Individuals to Ecosystems, Begon et al., 5th Ed., Ch. 10

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PREDATOR

The term 'marginal value' in foraging refers to:

The marginal value theorem evaluates the rate at which a forager gains energy while exploiting a depleting patch. Early in a visit, abundant accessible resources produce rapid gains; as the patch is depleted, the instantaneous gain rate falls. Departure is favored when that marginal rate declines to the average rate obtainable across the environment after accounting for travel time between patches. Thus the relevant quantity is energy gained per unit time, not energy per bite or the identity of a least-preferred prey. The theory predicts longer residence in richer patches and when travel is costly, linking diminishing returns within patches to landscape-level foraging efficiency. Mechanistic reasoning is essential here: classifications should follow measurable consequences for survival, reproduction, resource acquisition, or detection. Context can modify interaction strength, but it does not erase the defining contrast among the alternatives presented. At population level, this mechanism can influence abundance, coexistence, and evolutionary selection. Separating immediate individual effects from longer-term community outcomes gives the selected concept a clearer ecological meaning and avoids relying only on memorized terminology.

Ref: Ecology: From Individuals to Ecosystems, Begon et al., 5th Ed., Ch. 10

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PREDATOR

What reduces profitability of a prey item?

Prey profitability is commonly measured as energetic value E divided by handling time h. A long handling interval lowers E/h because the predator spends more time capturing, subduing, opening, or consuming the same energy package. High energy raises profitability, while rapid capture tends to shorten handling and increase it. Search time affects the habitat-wide rate of intake and whether lower-ranked prey should be accepted, but it is not part of the basic post-encounter profitability ratio. Natural defenses such as shells, spines, toxins requiring careful processing, or difficult body size can therefore make prey less profitable even when their tissues contain substantial energy. The distinction is biologically useful because ecological labels summarize mechanisms that generate testable predictions. Evaluating costs, benefits, timing, and the identities of interacting organisms prevents confusion between terms that may look similar in a short description. Mechanistic reasoning is essential here: classifications should follow measurable consequences for survival, reproduction, resource acquisition, or detection. Context can modify interaction strength, but it does not erase the defining contrast among the alternatives presented.

Ref: Ecology: From Individuals to Ecosystems, Begon et al., 5th Ed., Ch. 10

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PREDATOR

In OFT, if prey2 is more abundant but less profitable, predator should:

A lower-ranked prey should not be accepted merely because it is abundant. In the classic optimal diet model, acceptance depends on whether its energy per handling time exceeds the average return expected from rejecting it and searching for more profitable prey. If prey 1 remains sufficiently available, consuming prey 2 would occupy handling time that could be spent obtaining a better item, so prey 2 is rejected. The density of prey 2 itself has little effect on this encounter decision because the choice is made after prey 2 has already been found. However, the statement is conditional: if preferred prey become scarce enough, the optimal diet broadens and the less profitable prey can be included. This interpretation follows ecological definitions based on effects on fitness, energy flow, behavior, and population performance. It also shows why superficially similar alternatives can represent different mechanisms once the direction of benefit, harm, or resource transfer is considered.

Ref: Ecology: From Individuals to Ecosystems, Begon et al., 5th Ed., Ch. 10

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PREDATOR

Which model component represents handling time?

In optimal foraging notation, h denotes handling time: the interval required to pursue, subdue, process, and consume a prey item after encounter. Profitability is often expressed as E/h, so the same energetic reward becomes less attractive as handling time increases. S conventionally denotes search time, E the energetic return, and P may represent encounter probability, prey density, or another model-specific parameter. Distinguishing search from handling is important because a predator can change diet breadth when preferred prey become difficult to find even if their handling profitability remains high. The symbol h specifically captures the post-encounter time cost attached to a prey item. A careful interpretation retains the assumptions of the underlying model and avoids extending it beyond available evidence. Within those assumptions, the keyed concept gives the most consistent account of the biological pattern and its expected outcome. This interpretation follows ecological definitions based on effects on fitness, energy flow, behavior, and population performance. It also shows why superficially similar alternatives can represent different mechanisms once the direction of benefit, harm, or resource transfer is considered.

Ref: Ecology: From Individuals to Ecosystems, Begon et al., 5th Ed., Ch. 10

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PREDATOR

Search time S1 affects decision to eat:

Search time S1 is the expected time needed to locate the more profitable prey type. It affects whether rejecting a lower-ranked prey 2 is worthwhile. When S1 is short, the predator can bypass prey 2 and soon obtain a better return from prey 1. When S1 becomes long because prey 1 is scarce, waiting is costly and prey 2 may enter the optimal diet. By contrast, prey 1 remains worth accepting on encounter because it already has the higher profitability E1/h1. Thus S1 changes the acceptance threshold for prey 2 rather than the decision to consume the preferred prey type itself. The alternatives can be separated by asking what changes for each participant and which process causes that change. That approach is more reliable than treating familiar examples as fixed labels, because many interactions shift with environmental context. From an evolutionary perspective, traits persist when their net effects improve inclusive or direct fitness under prevailing conditions. The ecological terminology therefore summarizes both an immediate mechanism and its likely consequences across generations.

Ref: Ecology: From Individuals to Ecosystems, Begon et al., 5th Ed., Ch. 10

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