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Community Ecology 10/27/06 Review of last time: Multiple ChoiceS Which of the following are true of the following equations: K F N F 0.2 N S dNF rF N F dt KF K S N S 5N F dNS rS N S dt KS Circle ALL correct answers: • The equations could describe competition between the two species. • The equations could describe a predator-prey relationship. • Interspecific competition dominates intraspecific competition for species F. d. When the population S is at zero, and population F is close to zero, the model predicts that population F will grow exponentially Predator-Prey Relationships •Bottom-up vs. Top-Down control •Predators can promote diversity by keeping competition in check Mutualism Both species benefit Mutualism If it is a mutually beneficial relationship, then the two populations increase each other’s size Because this is a positive term, K is increased Because this is a positive term, K is increased Population 1 N1 dN1 K1 - N1 + a12 N2 = r1 * N1 dt K1 ti Population 2 N2 dN2 K2 - N2 + a21 N1 dt = r2 * N2 K2 Commensalism One species benefits, the other is unaffected Commensalism If the relationship is commensalistic, one species benefits (the commensal) and the other is unaffected Population 1 N1 Because this is a positive term, K is increased dN1 K1 - N1 + a12 N2 = r * N 1 1 dt K1 Population 2 N2 dN2 dt = r2 * N2 Because there is no a21 term, K is unchanged K2 - N 2 K2 How would you model it??? Parasitism Assumptions of Lotka-Volterra Models All assumptions of logistic growth model for each species… plus: Interaction coefficients, carrying capacities, and intrinsic growth rates are constant. Summary of Interaction Equations: Competition: (- , -) Predator/Prey: (+, -) Mutualism: (+, +) Commensalism: (+, 0) K1 N1 ? a12 N 2 dN1 r1 N1 dt K1 K 2 N 2 ? a21 N1 dN2 r2 N 2 dt K2 Test you knowledge! What type of relationship– what equation to use? A coati eats tree fruit. Your dog has a flea You use a fast bicyclist to “draft” off of Problems with Simple Logistic Growth 1. Births and deaths not separated -you might want to look at these processes separately -predation may have no effect on birth rate 2. 3. Carrying capacity is an arbitrary, set value No age structure 1. Separate Births and Deaths dN = Births - Deaths dt Births = b*N Deaths = d*N Births and deaths may be density dependent 1. Separate Births and Deaths dN = Births - Deaths dt Births = b*N Example: Births = b*N(1- N ) K Deaths = d*N Deaths = db+a21N2 Births rate may be density dependent Death rate may be dominated by predator effects 2. Refine Carrying Capacity If the population is a herbivore, K may depend on the population of plants Kherbivore= Nplant dNH NH dt = rH * NH (1 – NP ) Remaining Problems Age Structure Space: animals rely on different parts of landscape for different parts of their life cycle Individuality: Populations are collections of individuals, not lumped pools General Notes on Using Models How complex should model be? K.I.S.S. Identify research needs: Build model structure Test model to see what it is most sensitive to Do research to find values of unknown parameters If build a model that accurately predicts dynamics, it can be used as a management tool. Look critically at assumptions! Community Dynamics Community: a group of populations (both plants and animals) that live together in a defined region. Trophic Cascade predator/ tertiary consumer Eagles 4th trophic level predator/ secondary consumer Foxes 3rd trophic level herbivore/ primary consumer Mice 2nd trophic level autotroph/ primary producer Plants 1st trophic level How would we Model the Fox Population? K F N F aFM N M aFE N E dNF rF N F dt KF Why not include the effect of the plant population? What if foxes had a competitor? Trophic Cascade if eagles go extinct, what could happen to… foxes? mice? plants? Eagles 4th trophic level Foxes 3rd trophic level Mice 2nd trophic level Plants 1st trophic level Trophic Cascade If a new predator on mice is introduced, what could happen to… mice? plants? foxes? eagles? Eagles 4th trophic level Foxes 3rd trophic level Mice 2nd trophic level Plants 1st trophic level Trophic Cascade If drought caused a dip in plant production, what would happen to… mice? foxes? eagles? Eagles 4th trophic level Foxes 3rd trophic level Mice 2nd trophic level Plants 1st trophic level Simplified Temperate Forest Food Web What happens to when it’s a WEB instead of a CHAIN? Eagle Wolf Deer Oak seedling Fox Shrews Rabbit Caterpillars Grasses Herbs In long term, balance is restored Food Web doesn’t account for Keystone Species Summary Modeling Species Interactions Competition Predator-prey Mutualism Commensalism Community Dynamics Food Webs Keystone Species GOOD LUCK ON MONDAY’S MIDTERM!!! NO BLUE BOOKS OR CALCULATORS NEEDED.