Species 1 (victim V) Species 2 (predator P) + - EXPLOITATION

Classic predation theory is built upon the idea of time constraint (foraging theory): A 24 hour day is divided into time spent unrelated to eating: social interactions mating rituals grooming sleeping And eating-related activities: searching for prey pursuing prey subduing the prey eating the prey digesting (may not always exclude other activities)

foraging other essential activities Foraging time The time constraints on foraging

other essential activities search handling Foraging time Handling time Search time The time constraints on foraging

Search time: all activities up to the point of spotting the prey searching Handling time: all activities from spotting to digesting the prey pursuing subduing, killing eating (transporting, burying, regurgitating, etc) digesting Caveat: not all activities may be mutually exclusive ex. Digesting and non-eating related activities

other essential activities search eating pursuing & subduing Foraging time Handling time Search time eating time pursuit & subdue time The time constraints on foraging

Different species will allocate foraging time differently: Filter feeder: eating digesting Sit & wait predator (spider) subduing eating waiting

Time allocation also depends on victim density and predator status: Well-fed mammalian predator: eating pursuing & subduing searching Starving mammalian Predator (victims at low dnsity): searching eating pursuing & subduing

The math of predation: (After C.S. Holling) C.S. (Buzz) Holling Total search time per day Total handing time per day Total foraging time is fixed (or cannot exceed a certain limit).

1) Define the per-predator capture rate as the number of victims captured ( n ) per time spent searching ( t s ): 2) Capture rate is a function of victim density ( V ). Define  as capture efficiency. 3) Every captured victim requires a certain time for “processing”.

n/t = capture rate

Capture rate Prey density (V) Capture rate limited by prey density and capture efficiency Capture rate limited by predator’s handling time.

Damselfly nymph (Thompson 1975)

The larger the prey, the greater the handling time. Decreasing prey size Asymptote: 1/h (Thompson 1975)

Three Functional Responses (of predators with respect to prey abundance): Holling Type I: Consumption per predator depends only on capture efficiency: no handling time constraint. Holling Type II: Predator is constrained by handling time. Holling Type III: Predator is constrained by handling time but also changes foraging behavior when victim density is low.

Per predator consumption rate victim density Type I (filter feeders) Type II (predator with significant handling time limitations) Type III (predator who pays less attention to victims at low density) Type I: Type II Type III

Daphnia (Filter feeder on microscopic freshwater organism) Type I functional response Thin algae suspension culture Daphnia path Thick algae suspension culture Holling Type I functional response:

Slug eating grassCattle grazing in sagebrush grassland Holling Type II functional response:

Paper wasp, a generalist predator, eating shield beetle larvae: The wasp learns to hunt for other prey, when the beetle larvae becomes scarce. Holling Type III functional response:

The dynamics of predator prey systems are often quite complex and dependent on foraging mechanics and constraints.

Didinium nasutum eats Paramecium caudatum : Gause’s Predation Experiments:

1)Paramecium in oat medium: logistic growth. 2) Paramecium with Didinium in oat medium: extinction of both. 3) Paramecium with Didinium in oat medium with sediment: extinction of Didinium.

A fly and its wasp predator: Greenhouse whitefly Parasitoid wasp (Burnett 1959) Laboratory experiment

Spider mites Predatory mite spider mite on its ownwith predator in simple habitat with predator in complex habitat (Laboratory experiment) (Huffaker 1958)

(Laboratory experiment) Azuki bean weevil and parasitoid wasp (Utida 1957)

collared lemmingstoat lemming stoat (Greenland) (Gilg et al. 2003)

Possible outcomes of predator-prey interactions: 1.The predator goes extinct. 2.Both species go extinct. 3.Predator and prey cycle: prey boom Predator bust predator boom prey bust 4.Predator and prey coexist in stable ratios.

Putting together the population dynamics: Predators (P): Victims (V): Victim consumption rate * Victim  Predator conversion efficiency - Predator death rate Victim renewal rate – Victim consumption rate

Victim growth assumption: exponential logistic Functional response of the predator: always proportional to victim density (Holling Type I) Saturating (Holling Type II) Saturating with threshold effects (Holling Type III) Choices, choices….

The simplest predator-prey model (Lotka-Volterra predation model) Exponential victim growth in the absence of predators. Capture rate proportional to victim density (Holling Type I).

Isocline analysis:

Victim density Predator density Victim isocline: Predator isocline:

Victim density Predator density Victim isocline: Predator isocline: dV/dt < 0 dP/dt > 0 dV/dt > 0 dP/dt < 0 dV/dt > 0 dP/dt > 0 dV/dt < 0 dP/dt < 0 Show me dynamics

Victim density Predator density Victim isocline: Predator isocline:

Victim density Predator density Victim isocline: Preator isocline:

Victim density Predator density Victim isocline: Preator isocline: Neutrally stable cycles! Every new starting point has its own cycle, except the equilibrium point. The equilibrium is also neutrally stable.

Logistic victim growth in the absence of predators. Capture rate proportional to victim density (Holling Type I).

Victim density Predator density Predator isocline: Victim isocline: rr rcrc

P V Stable Point ! Predator and Prey cycle move towards the equilibrium with damping oscillations.

Exponential growth in the absence of predators. Capture rate Holling Type II (victim saturation).

Victim density Predator density Predator isocline: Victim isocline: r kD

P V Unstable Equilibrium Point! Predator and prey move away from equilibrium with growing oscillations.

No density-dependence in either victim or prey (unrealistic model, but shows the propensity of PP systems to cycle): P V Intraspecific competition in prey: (prey competition stabilizes PP dynamics) P V Intraspecific mutualism in prey (through a type II functional response): P V

Predators population growth rate (with type II funct. resp.): Victim population growth rate (with type II funct. resp.):

Victim density Predator density Predator isocline: Victim isocline: Rosenzweig-MacArthur Model

Victim density Predator density Predator isocline: Victim isocline: Rosenzweig-MacArthur Model If the predator needs high victim density to survive, competition between victims is strong, stabilizing the equilibrium!

Victim density Predator density Predator isocline: Victim isocline: Rosenzweig-MacArthur Model If the predator drives the victim population to very low density, the equilibrium is unstable because of strong mutualistic victim interactions.

Victim density Predator density Predator isocline: Victim isocline: Rosenzweig-MacArthur Model However, there is a stable PP cycle. Predator and prey still coexist!

The Rosenzweig-MacArthur Model illustrates how the variety of outcomes in Predator-Prey systems can come about: 1)Both predator and prey can go extinct if the predator is too efficient capturing prey (or the prey is too good at getting away). 2)The predator can go extinct while the prey survives, if the predator is not efficient enough: even with the prey is at carrying capacity, the predator cannot capture enough prey to persist. 3)With the capture efficiency in balance, predator and prey can coexist. a) coexistence without cyclical dynamics, if the predator is relatively inefficient and prey remains close to carrying capacity. b) coexistence with predator-prey cycles, if the predators are more efficient and regularly bring victim densities down below the level that predators need to maintain their population size.