FW364 Ecological Problem Solving Class 18: Spatial Structure Nov. 4, 2013

Second Exam: Wednesday (Nov. 6) Midterm II Second Exam: Wednesday (Nov. 6) Review session in lab tomorrow Study items posted on website Practice exams, Concept review, & Models and assumptions table Test will cover material taught today Topics covered will be: Population regulation (i.e., density dependence) Age structure Stage structure Spatial structure (i.e., metapopulations) Can use your calculator on exam I’ll cover general study tips during the lab review

Outline for Today Shifting focus: No longer discussing a single population… …Instead, a “population of populations” Adding spatial structure to models Objective from Last class: Introduced spatial structure / metapopulation analysis In-class demo of why spatial structure is good Objectives for Today: Cover more on metapopulation theory Management of metapopulations Text (optional reading): Chapter 6

Metapopulation Theory Basic components of metapopulation theory Features of habitat within vs. outside of local populations Factors affecting extinction probability of local populations Factors affecting re-colonization of local populations How spatial correlation affects metapopulation extinction

Metapopulation Theory Basic components of metapopulation theory Features of habitat within vs. outside of local populations Factors affecting extinction probability of local populations Factors affecting re-colonization of local populations How spatial correlation affects metapopulation extinction

Metapopulation Theory - Habitat Local populations occupy suitable habitat imbedded in a matrix of unsuitable habitat Fish in lakes in a landscape Deer in an island chain Sheep living on mountains Birds in a fragmented forest Mosquitoes in pitcher plants

Metapopulation Theory - Habitat Local populations occupy suitable habitat imbedded in a matrix of unsuitable habitat California spotted owl Dispersal among patches is key to metapopulation persistence

Metapopulation Theory Basic components of metapopulation theory Features of habitat within vs. outside of local populations Factors affecting extinction probability of local populations Factors affecting re-colonization of local populations How spatial correlation affects metapopulation extinction

Metapopulation Theory – Local Extinction Four factors affect probability of local extinction (pe) You know three of these from other population growth lectures! In-class challenge: Talk to a neighbor and answer this question: What factors affect probability of local extinction?  Think about what effects extinction risk of single populations

Metapopulation Theory – Local Extinction Four factors affect probability of local extinction (pe) Population size within habitat patch (i.e., local population) Strength of edge effects Stability of dynamics within patch Growth rate within patch

Metapopulation Theory – Local Extinction Population size within habitat patch Small populations more likely to fall below some extinction threshold  demographic stochasticity Genetic effects (inbreeding, lack of diversity) Allee effects Population size determined by: size of habitat patch (i.e., spatial extent; contributes to carrying capacity) quality of habitat in patch (contributes to productivity, carrying capacity)

Metapopulation Theory – Local Extinction 2. Strength of edge effects Small patches have more edge, relative to internal (suitable) habitat “What’s so bad about edges?” Different environmental conditions in edges than within the patch E.g., forest patch edge: more light and wind, higher temperature, more human disturbance, etc. Many small habitat patches have less suitable habitat than a few larger patches of the same total area Note: some species thrive in edge habitat… … but these are not typically the species we are concerned about e.g., invasive kudzu loves edges

Metapopulation Theory – Local Extinction 2. Strength of edge effects Big patch has same total habitat as 5 smaller patches, but more than double the suitable (interior) habitat: >2x Interior habitat in 5 km2 patch = 5 * 0.64 = 3.20 km2 Interior habitat in 1 km2 patch = 1 * 0.31 = 0.31 km2 * 5 = 1.55 km2

Metapopulation Theory – Local Extinction 3. Stability of dynamics within patch Large fluctuations in population size increase extinction risk What causes fluctuations? Environmental variation Type and strength of density dependence Scramble (extreme effect) Contest

Metapopulation Theory – Local Extinction 4. Growth rate within patch Populations that are increasing (λ > 1) are less likely to go extinct than populations that are decreasing (λ < 1) Source: Local population where births are greater than deaths (λ > 1)  Can persist on its own Excess individuals are a source of colonists to other local pops Alternative definition: Emigration > Immigration Sink: Local population where births are less than deaths (λ < 1)  Must be supplied with immigrants to persist Alternative definition: Immigration > Emigration Sink λ < 1 Source λ > 1

Metapopulation Theory – Local Extinction 4. Growth rate within patch Populations that are increasing (λ > 1) are less likely to go extinct than populations that are decreasing (λ < 1) Source: Local population where births are greater than deaths (λ > 1)  Can persist on its own Excess individuals are a source of colonists to other local pops Alternative definition: Emigration > Immigration Sink: Local population where births are less than deaths (λ < 1)  Must be supplied with immigrants to persist Alternative definition: Immigration > Emigration There must be at least one source population for the metapopulation to persist!

Metapopulation Theory Basic components of metapopulation theory Features of habitat within vs. outside of local populations Factors affecting extinction probability of local populations Factors affecting re-colonization of local populations How spatial correlation affects metapopulation extinction

Metapopulation Theory – Re-colonization Re-colonization of extinct local populations is (typically) key to metapopulation persistence! Re-colonization is a function of: Distance to the nearest inhabited patch  Longer distance decreases number of dispersing individuals Population size of source populations  Patches with high density often supply more colonists more individuals more reason to leave (competition) For example: Population with contest density-dependence: At high N, more “floaters” as potential dispersers

Metapopulation Theory Basic components of metapopulation theory Features of habitat within vs. outside of local populations Factors affecting extinction probability of local populations Factors affecting re-colonization of local populations How spatial correlation affects metapopulation extinction

Metapopulation Theory – Correlation Spatial correlation: Correlation in environmental and population fluctuation across space  Affects how the probabilities of local extinction combine to determine the probability of metapopulation persistence or extinction Fluctuations in populations close to each other will be more correlated than fluctuations in populations far apart (i.e., less independent) populations close together experience similar environmental conditions Typically, less spatial correlation (greater independence) means higher probability of metapopulation persistence

Metapopulation Theory – Correlation Spatial correlation: Correlation in environmental and population fluctuation across space California spotted owl

Concept Check How does distance among populations affect metapopulation persistence? In class exercise: Add relationships to the figures below Dispersal effects Spatial correlation effects Distance Correlation low close far high Persistence Distance Dispersal low close far high Persistence

Concept Check How does distance among populations affect metapopulation persistence? In class exercise: Add relationships to the figures below Dispersal effects Spatial correlation effects high high Dispersal Correlation low low high high close far close far Distance Persistence Distance Persistence low low close far close far high high Distance Distance Persistence Persistence low low low high low high Dispersal Correlation

Concept Check How does distance among populations affect metapopulation persistence? In class exercise: Add relationships to the figures below Dispersal effects Spatial correlation effects high high Persistence Persistence low low close far close far Distance Distance Distance among local populations has two opposing effects! smaller distance means more dispersal = plus for persistence smaller distance means greater correlation = minus for persistence  Important complexity in metapopulation models

Metapopulation Management Managing fragmented populations is becoming increasingly necessary  Not an easy task! Key metapopulation management questions: 1. How many (and what size) habitat reserves are needed? 2. How many (and what size) dispersal corridors are needed? 3. How do we handle future habitat fragmentation?

Metapopulation Management 1. How many (and what size) habitat reserves are needed? Many small reserves may provide insurance against global extinction via the basic tenet of metapopulation theory  Must have some degree of independence  But also need dispersal among reserve (local) populations A few large reserves means large local population size  Less likely to go extinct due to bad luck (series of bad recruitment years)  Less likely to go extinct due to demographic stochasticity

Metapopulation Management 1. How many (and what size) habitat reserves are needed? Many small reserves may provide insurance against global extinction via the basic tenet of metapopulation theory  Must have some degree of independence  But also need dispersal among reserve (local) populations A few large reserves means large local population size  Less likely to go extinct due to bad luck (series of bad recruitment years)  Less likely to go extinct due to demographic stochasticity No (single) general answer will apply to all metapopulations! Best options depend on specifics of metapopulation

Metapopulation Management 2. How many (and what size) dispersal corridors are needed? Dispersal between suitable habitat patches is necessary for the metapopulation effect to work BUT, there is a limit to how much dispersal is needed! Do not want totally connected populations because then metapopulation is like one large population What size & other attributes are needed to make a corridor usable? Yellowstone to Yukon Initiative Trying to link fragmented wildlife habitat in the Rocky Mountains e.g., link grizzly bears and wolves in Yellowstone to larger populations in the Canadian Rockies

Metapopulation Management 3. How do we handle future habitat fragmentation? In most cases, habitat fragmentation has a negative effect on populations Loss of habitat (a bad thing) Smaller populations (a bad thing) Less dispersal due to matrix of unsuitable habitat (often bad) Reality is that habitats are only going to get more fragmented How low can we go before we’ve gone too far?

Metapopulation Models To address these management questions, we need metapopulation models Simplest models predict fraction of local populations that are extinct / not extinct  Too simple for management  But are good for understanding basic concepts More complex models can be used to determine:  Optimal number and size of reserves  Optimal dispersal And can be used to forecast effect of future fragmentation

End of material on Midterm II

Predator-prey interactions (4 classes) Looking Ahead Next Unit: Predator-prey interactions (4 classes) Lab Tomorrow REVIEW SESSION Bring copy of practice exams (or download them onto your computer to work from) along with a calculator

Metapopulations