Metapopulation and Intertrophic Dynamics From single species population dynamics (and how to harvest them) to complex multi-species (pred-prey) dynamics in time and space.

Herons, UK BHT: fig Metapopulation and Intertrophic Dynamics stability fluctuations biotic factors? (density dependence) abiotic factors? (density independence)

Metapopulation and Intertrophic Dynamics Density DK SdrJylland Population-level analysis! A B C A+B+C Then again … where is the population-level?

Metapopulation and Intertrophic Dynamics Searocket (Cakile edentula) Dispersal – an important population process BHT: fig

Metapopulation and Intertrophic Dynamics (1) Metapopulations: living in a patchy environment (2) Intertrophic dynamics: squeezed from above and below

Metapopulation Dynamics Lawton & Woodroffe sites Slope, vegetation, heterogeneity human disturbance 10 core, 15 peripheral & 14 no-visit water vole Do animals occupy all suitable habitats within their geographic range?

Increasing bank angle and structural heterogeneity Increase in % grass Metapopulation Dynamics Lawton & Woodroffe 1991 water vole Do animals occupy all suitable habitats within their geographic range? PCA performed core sites no-visit sites 55% with suitable habitats % lack voles because... reduced colonization rates predation Know your species...!

Metapopulation Dynamics Hanski & Gilpin and know your landscape!

Metapopulation Dynamics Metapopulation theory Equilibrium “population” of species (extinction - recolonization) The MacArthur-Wilson Equilibrium theory

Metapopulation Dynamics Metapopulation theory Mainland-Island model (Single-species version of the M-W multi-species model) Metapopulation

Metapopulation Dynamics Metapopulation theory Mainland-Island model (Single-species version of the M-W multi-species model) Metapopulation Levins’s metapopulation model (no mainland; equally large habitat patches)

Metapopulation Dynamics Metapopulation theory Levins’s model P : fraction of patches occupied (1-P) : fraction not occupied m : recolonization rate e : extinction rate recolonization – increases with BOTH the no of empty patches (1-P) AND with the no of occupied patches (P). extinction – increases with the no of patches prone to extinction (P). (equal patch size)

Metapopulation Dynamics Metapopulation theory Levins’s model P : fraction of patches occupied (1-P) : not occupied m : recolonization rate e : extinction rate

Metapopulation Dynamics Metapopulation theory Levins’s model P : fraction of patches occupied (1-P) : not occupied m : recolonization rate e : extinction rate Given that (m – e) > 0, the metapop will grow until equlibrium: dP/dt = 0 => P* = 1 – e/m ( trivial: P* = 0) P time 1-e/m

Metapopulation Dynamics Metapopulation theory NOTE: the metapop persists, stably, as a result of the balance between m and e despite unstable local populations! Hanski et al Melitaea cinxia local patches the metapop persists: ln(1991) = ln(1993)

Metapopulation Dynamics Metapopulation theory Levins’s metapopulation model Mainland-Island model Levins M-I

Metapopulation Dynamics Metapopulation theory Levins’s metapopulation model Mainland-Island model Variable patch size

Metapopulation Dynamics Metapopulation theory Levins’s metapopulation model Mainland-Island model Variable patch size model Increasing a, the freq of larger patches decreases a = 0 a = 

Metapopulation Dynamics Metapopulation theory dP/dt = 0 => P 1 * = 1 – e/m P 2 * = 0 Levins’s model: Melitaea cinxia Hanski et al Hanski & Gyllenberg (1993) Two general metapopulation models and the core-satellite species hypothesis. American Naturalist 142, across metapops Value of a!

Intertrophic Dynamics (2) Intertrophic dynamics: squeezed from above and below (i) Predation on prey are biased BHT: fig. 8.9 Thomson’s Gazelle

Intertrophic Dynamics (2) Intertrophic dynamics: squeezed from above and below (ii) Predators AND prey are also ”squeezed from the side” mates territories There is density dependence (crowding), which may influence or be influenced buy predation!

Intertrophic Dynamics Demonstrating the effect of predation is NOT straight forward Hokkaido multiannual cyclic seasonal fluctuations Short winter Long winter DD intense DD weak

Vito Volterra ( ) Italian mat-phys Alfred J Lotka ( ) American mat-biol % pred fish The Lotka - Volterra model Intertrophic Dynamics

Predator (P) Prey (N) q : mortality a' : hunting eff. per predator f : ability to convert food to offspring r : intrinsic rate of increase - a’PN+ fa’PN fa’PN - qP rN - a’PN Intertrophic Dynamics The Lotka-Volterra model

isoclines, dN/dt = dP/dt = 0 rN* - a’P*N* = 0 fa’P*N* - qP* = 0fa’P*N* = qP* rN* = a’P*N* => N* = q/fa’ P* = r/a’ predator mortality offpring/prey hunting effeciency prey reproduction Intertrophic Dynamics The Lotka-Volterra model (Predator isocline) (Prey isocline)

N* N P P* N* P* N P N* = q/fa’ P* = r/a’ predator mortality offpring/prey hunting effeciency prey reproduction isoclines, dN/dt = dP/dt = 0 Intertrophic Dynamics The Lotka-Volterra model

N* = q/fa’ P* = r/a’ N* P* N P BHT: fig Intertrophic Dynamics The Lotka-Volterra model Predator isocline: Prey isocline:

Intertrophic Dynamics Crowding in the Lotka-Volterra model N* = q/fa’ Predator isocline: P* = r/a’ Prey isocline: N P P* N* Hunting effeciency (a’ ) decreases with increasing P Crowding in predators:

Intertrophic Dynamics Crowding in the Lotka-Volterra model N* = q/fa’ Predator isocline: P* = r/a’ Prey isocline: P P* N* Hunting effeciency (a’ ) decreases with increasing P Crowding in predators: Reproduction rate (r ) decreases with increasing N Crowding in prey: N

Intertrophic Dynamics Crowding in the Lotka-Volterra model N* = q/fa’ Predator isocline: P* = r/a’ Prey isocline: P P* N* Hunting effeciency (a’ ) decreases with increasing P Crowding in predators: Reproduction rate (r ) decreases with increasing N Crowding in prey: N KNKN

Intertrophic Dynamics Crowding in the Lotka-Volterra model N* = q/fa’ Predator isocline: P* = r/a’ Prey isocline: Prey isocline Predator isocline Less effecient predator Predator isocline Prey isocline Combining DD in predator and prey Prey isocline Predator isocline Strong DD in predator BHT: fig The greater the distance from Eq, the quicker the return to Eq!

Intertrophic Dynamics Functional response and prey-switching P N (this prey) KNKN P Switch of prey eat this prey eat another prey

Intertrophic Dynamics Functional response and prey-switching P N (this prey) KNKN P Switch of prey eat this prey eat another prey At low N there’s no effect of predator P N (this prey)

Intertrophic Dynamics Functional response and prey-switching P N (this prey) KNKN P Switch of prey eat this prey eat another prey At low N there’s no effect of predator P N (this prey) Independent of prey (DD still in work) Degree of DD determines level

Intertrophic Dynamics Functional response and prey-switching Prey isocline Predator isocline BHT: fig Predator isocline (high DD) Stable pattern with prey density below carrying capacity

Intertrophic Dynamics Functional response and prey-switching Many other combinations! Despite initial settings they all become stable! Prey isocline Predator isocline Less effecient predator Predator isocline Prey isocline Combining DD in predator and prey Prey isocline Predator isocline Strong DD in predator BHT: fig. 10.7

Intertrophic Dynamics Crowding in practice Heterogeneous media Structural simple media Indian Meal moth BHT: fig time Log density

Intertrophic Dynamics Crowding in practice Indian Meal moth Heterogeneous media Structural simple media Intrinsic and extrinsic causes of population cycles (fluctuations)

Intertrophic Dynamics Population cycles and their analysis

pattern: the distinct 10-year cycle (hunting data!) processes?: obscure! hypotheses: (1) vegetation-hare (2) hare-lynx (3) vegetation-hare-lynx (4) sunspots lynx Sunspot + Intertrophic Dynamics Lynx – hare interactions

pattern: the distinct 10-year cycle (hunting data!) processes?: obscure! hypotheses: (1) vegetation-hare (2) hare-lynx (3) vegetation-hare-lynx (4) sunspots Sunspot lynx - Intertrophic Dynamics Lynx – hare interactions

pattern: the distinct 10-year cycle (hunting data!) processes?: obscure! hypotheses: (1) vegetation-hare (2) hare-lynx (3) vegetation-hare-lynx (4) sunspots Sunspot lynx + Intertrophic Dynamics Lynx – hare interactions

Factorial design large-scale experiment: (1) control blocks (2) ad lib supplemental food blocks (3) predator exclusion blocks (4) 2+3 blocks monitored everything over 15 years (species composition, population dynamics, life histories...) Intertrophic Dynamics Lynx – hare interactions: The Kluane Project

Non-additive response 10-fold Increased cycle period... … but neither food addition and predator exclosure prevented hares from cycling - Why? Vegetation-hare-predator year Hare density (-pred, + food) (-pred) (+food) (control) Intertrophic Dynamics Lynx – hare interactions: The Kluane Project

Forest/Grassland Closed forest Open forest Atlantic Continental Pacific NAO Intertrophic Dynamics Lynx – hare interactions: A spatial perspective

N t = f(N t-1,N t-2,..., N t-11 )!... Kluane indicates that hare- predator interactions are central. lynx hare year density f( N t-1, N t-2 ) decrease N t = f( N t-1, N t-2 ) increase … dynamics non-linear! High dependence (80%) on hare density... Intertrophic Dynamics Lynx – hare interactions: the lynx perspective

Intertrophic Dynamics A geographical gradient in rodent fluctuations: a statistical modelling approach Ottar Bjørnstad Lemmus Clethrionomys Microtus 27 populations Bjørnstad et al Hanski et al BHT: fig Effect of predators?

Intertrophic Dynamics A geographical gradient in rodent fluctuations: a statistical modelling approach Lemmus Clethrionomys Microtus Bjørnstad et al Hanski et al Two hypotheses (1)The specialist predator hypothesis (predator numerically linked to prey, that is through reproduction; variations come from variations in predator efficiency) (2)The generalist predator hypothesis (more generalist predators in south than north) delayed effect on prey direct effect on prey Analysis of prey population dynamics: AR(2): N t = f(N t-1,N t-2 ) AR(1): N t = f(N t-1 ) BHT: fig efficiency no of pred

Intertrophic Dynamics A geographical gradient in rodent fluctuations: a statistical modelling approach Lemmus Clethrionomys Microtus Bjørnstad et al Ottar analysed 19 time series (>15 years) using autoregression (AR): 17 (89%) time series best described by: AR(2): N t = f(N t-1,N t-2 ) N t-2 N t-1 The generalist predator hypothesis Increasing no of gen pred increases the direct negative effect on prey

Metapopulation and Intertrophic Dynamics Combining metapopulation and predator-prey theory BHT section Comins et al. (1992) The spatial dynamics of host- parasitoid systems. Journal of Animal Ecology 61,

Fagprojekter (1) Harvesting natural populations Niels (2) Cohort variation and life histories Toke (3) Climate and density dependence in population dynamics Mads Max 3-4 pax/groupMax pp + figs/tabs