logging in or signing up 13predation Mentor Download Post to : URL : Related Presentations : Share Add to Flag Embed Email Send to Blogs and Networks Add to Channel Uploaded from authorPOINT Insert YouTube videos in PowerPont slides with aS Desktop Copy embed code: (To copy code, click on the text box) Embed: URL: Thumbnail: WordPress Embed Customize Embed The presentation is successfully added In Your Favorites. Views: 95 Category: Entertainment License: All Rights Reserved Like it (0) Dislike it (0) Added: September 14, 2007 This Presentation is Public Favorites: 0 Presentation Description No description available. Comments Posting comment... Premium member Presentation Transcript Predation and functional responsesFISH 458: Predation and functional responses FISH 458 Readings: Readings Walters, C.J. 1986. Adaptive management of renewable resources. Macmillian Publishing Co. NY. Holling, C.S. 1965. The functional response of predators to prey density and its role in mimicry and population regulation. Memoirs of the Entomological Society of Canada 45: 1-60. Overview: Overview Lotka Volterra predator prey equations Functional Responses derivation Multispecies functional response System behavior and isoclines The predators and prey: The predators and prey Slide5: Slide6: Simple predator prey theoryLotka Volterra: Simple predator prey theory Lotka Volterra Prey governed by logistic growth Simplest theory has simple exponential growth Predators deaths are density independent, births depend upon number of prey eaten Prey eaten per predator is proportional to prey density Lotka (1926) Volterra (1926): Lotka (1926) Volterra (1926) W wildebeest numbers L lion numbers r W intrinsic rate of increase e lion predation efficiency m lion natural mortality a lion assimilation efficiency Biological unrealism of Lotka Volterra: Biological unrealism of Lotka Volterra No prey self limitation No predator self limitation No limit on prey consumption per predator Known as functional response Dynamic behavior: Dynamic behavior These models are either unstable or cyclic Adding some biological realism: Adding some biological realism Dynamic behavior in time: Dynamic behavior in time Predator prey phase diagram: Predator prey phase diagram Predation dynamicsdeveloping a functional response: Predation dynamics developing a functional response Predators do a random walk, encounter and kill a fraction of what prey they encounter. Exponential model is used to correct for the fact that no prey can be killed and eaten twice. Wildebeest Lion model: Wildebeest Lion model A lion walks 10 km per day Can see 200 m in either direction Thus sees all wildebeest covering 4 km2/day This amounts to 1460 km2/year Serengeti ecosystem is 90,000 km2 A lion can chase and catch 1 in 1000 animals it sees Thus it kills 0.000016 of the population Key assumption: Key assumption Kill rate proportional to prey abundance No self regulation of predator No predator saturation Demo using lion wildebeest model The prey isoclinewhen is prey abundance constant?: The prey isocline when is prey abundance constant? The predator isocline: The predator isocline Slide19: Increasing predator, decreasing prey decreasing predator, increasing prey decreasing predator, decreasing prey increasing predator, increasing prey Experimental components analysis of predation from Holling: Experimental components analysis of predation from Holling Total time available TT Can be split into searching time (Ts) and handling time (Th). If predator spends time h handling an individual prey and consumes Na prey, then handling time is Th=h Na Slide21: Predator searches area a’ per unit time Predator has probability pc of recognizing and successfully attacking a prey in the area searched Average prey density is N Predator will on average kill a’ pc N prey per time spent searching Na= a’ pc N Ts Ts = Na/(a’ pc N ) Slide22: So Tt= Na/(a’ pc N )+h Na solving for number attached we get Behavior: Behavior Asymptote - determined by handling time Handling time can include digestive pause Initial slope - area searched times probability of successful attack times density What could be added: What could be added Lion functional response with handling time Lion self limitation Social behavior and group territoriality Spatial heterogeneity and migration of wildebeest Alternative prey Adding additional prey: Adding additional prey Assume that during the random walk the predator encounters possible alternative prey Slide26: Additional prey: Additional prey For each prey species there is a probability of detection, pursuit and killing Do the algebra and you get the Multiprey functional response: Multiprey functional response Uses: Uses This formulation is the basis for many ecosystem based models Further issues: Further issues Predators may not search at random Predators may develop a 'search image' and preferably attack more abundant prey You do not have the permission to view this presentation. In order to view it, please contact the author of the presentation.
13predation Mentor Download Post to : URL : Related Presentations : Share Add to Flag Embed Email Send to Blogs and Networks Add to Channel Uploaded from authorPOINT Insert YouTube videos in PowerPont slides with aS Desktop Copy embed code: (To copy code, click on the text box) Embed: URL: Thumbnail: WordPress Embed Customize Embed The presentation is successfully added In Your Favorites. Views: 95 Category: Entertainment License: All Rights Reserved Like it (0) Dislike it (0) Added: September 14, 2007 This Presentation is Public Favorites: 0 Presentation Description No description available. Comments Posting comment... Premium member Presentation Transcript Predation and functional responsesFISH 458: Predation and functional responses FISH 458 Readings: Readings Walters, C.J. 1986. Adaptive management of renewable resources. Macmillian Publishing Co. NY. Holling, C.S. 1965. The functional response of predators to prey density and its role in mimicry and population regulation. Memoirs of the Entomological Society of Canada 45: 1-60. Overview: Overview Lotka Volterra predator prey equations Functional Responses derivation Multispecies functional response System behavior and isoclines The predators and prey: The predators and prey Slide5: Slide6: Simple predator prey theoryLotka Volterra: Simple predator prey theory Lotka Volterra Prey governed by logistic growth Simplest theory has simple exponential growth Predators deaths are density independent, births depend upon number of prey eaten Prey eaten per predator is proportional to prey density Lotka (1926) Volterra (1926): Lotka (1926) Volterra (1926) W wildebeest numbers L lion numbers r W intrinsic rate of increase e lion predation efficiency m lion natural mortality a lion assimilation efficiency Biological unrealism of Lotka Volterra: Biological unrealism of Lotka Volterra No prey self limitation No predator self limitation No limit on prey consumption per predator Known as functional response Dynamic behavior: Dynamic behavior These models are either unstable or cyclic Adding some biological realism: Adding some biological realism Dynamic behavior in time: Dynamic behavior in time Predator prey phase diagram: Predator prey phase diagram Predation dynamicsdeveloping a functional response: Predation dynamics developing a functional response Predators do a random walk, encounter and kill a fraction of what prey they encounter. Exponential model is used to correct for the fact that no prey can be killed and eaten twice. Wildebeest Lion model: Wildebeest Lion model A lion walks 10 km per day Can see 200 m in either direction Thus sees all wildebeest covering 4 km2/day This amounts to 1460 km2/year Serengeti ecosystem is 90,000 km2 A lion can chase and catch 1 in 1000 animals it sees Thus it kills 0.000016 of the population Key assumption: Key assumption Kill rate proportional to prey abundance No self regulation of predator No predator saturation Demo using lion wildebeest model The prey isoclinewhen is prey abundance constant?: The prey isocline when is prey abundance constant? The predator isocline: The predator isocline Slide19: Increasing predator, decreasing prey decreasing predator, increasing prey decreasing predator, decreasing prey increasing predator, increasing prey Experimental components analysis of predation from Holling: Experimental components analysis of predation from Holling Total time available TT Can be split into searching time (Ts) and handling time (Th). If predator spends time h handling an individual prey and consumes Na prey, then handling time is Th=h Na Slide21: Predator searches area a’ per unit time Predator has probability pc of recognizing and successfully attacking a prey in the area searched Average prey density is N Predator will on average kill a’ pc N prey per time spent searching Na= a’ pc N Ts Ts = Na/(a’ pc N ) Slide22: So Tt= Na/(a’ pc N )+h Na solving for number attached we get Behavior: Behavior Asymptote - determined by handling time Handling time can include digestive pause Initial slope - area searched times probability of successful attack times density What could be added: What could be added Lion functional response with handling time Lion self limitation Social behavior and group territoriality Spatial heterogeneity and migration of wildebeest Alternative prey Adding additional prey: Adding additional prey Assume that during the random walk the predator encounters possible alternative prey Slide26: Additional prey: Additional prey For each prey species there is a probability of detection, pursuit and killing Do the algebra and you get the Multiprey functional response: Multiprey functional response Uses: Uses This formulation is the basis for many ecosystem based models Further issues: Further issues Predators may not search at random Predators may develop a 'search image' and preferably attack more abundant prey