Metapopulation predator-prey modeling with nonconsumptive effects

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Method synopsis

Mathematical modeling approach extending classic Levins metapopulation models to incorporate both consumptive and nonconsumptive effects of generalist predators on prey colonization and extinction dynamics. Uses differential equations to analyze patch occupancy dynamics and equilibrium conditions.

Synthesized from method descriptions across 1 paper using this protocol.

Procedure as described in the canonical source

Steps below were extracted from the paper that introduces this protocol — Consumptive and non-consumptive effects of predators on metacommunities of competing prey (2008), Ecology. Implementations in other papers (listed below) may differ.

1. Develop basic metapopulation model
   Established baseline single-species metapopulation model using Levins (1969) framework with differential equation dp/dt = cp(1-p) - ep, where p is proportion of patches occupied, c is colonization rate, and e is extinction rate
   Quantities: Single prey species across multiple patches in landscapeDuration: Not applicable - theoretical model developmentConditions: Assumes random encounters between predators and prey, independent patch dynamics
   Equipment: Mathematical modeling
2. Incorporate generalist predator effects
   Modified basic model to include predator visitation parameter b (proportion of patches visited), predator effect on colonization r, and predator effect on extinction m, yielding equations 3a-3b for patches with and without predators
   Quantities: Parameters b, r, m representing predator density and behavioral effectsDuration: Not applicable - theoretical model developmentConditions: Assumes predator encounters are random and predator abundance changes slowly relative to prey
   Equipment: Mathematical modeling
3. Extend to two-species competition model
   Developed competition model with superior competitor (species 1) and inferior competitor (species 2) using Tilman (1994) approach, incorporating colonization rates c1, c2 and extinction rates e1, e2, with species 1 displacing species 2

Typical Equipment

• Mathematical modeling
• Mathematical analysis

Output Measurements

• equilibrium patch occupancy
• invasion criteria
• extinction thresholds

Papers Using This Protocol (1)

Species Studied With This Protocol

Places Where Used