Spatial synchrony and extinction riskin metapopulations:

a spatial “hydra effect”Jeremy Fox

University of Calgarydynamicecology.wordpress.com

David VasseurYale University

The “hydra effect”

The usual story: intermediate dispersal rates maximize metapopulation persistence

Met

apop

ulati

on p

ersis

tenc

e tim

e

Dispersal rateZero/low Intermediate High

Indep. patches(async.)

Coloniz.-extinction(async.)

“One big patch”(sync.)

Big patch persistent

Big patch extinction-prone

Yaari et al. 2012

Intermediate dispersal rates maximize metapopulation persistence

Huffaker 1958

Intermediate dispersal maximizes metapopulation persistence

Holyoak and Lawler 1996:

Euplotes patella

Tetrahymena pyriformis

Protist microcosms: a model system for spatial synchrony

Day

Pre

y de

nsity

(ml-1

)

0 720

1500

0 72

Vasseur & Fox 2009; Fox et al. 2011, unpublished

Cyclic dynamics are easily synchronized (“phase locked”) by dispersal

• Dispersal rates <0.5%/prey generation can give synchrony

Spatial synchrony in nature

Lynx Gypsy moth

0

10

1994 1995 1996 1997 1998 1999 2000

Year

Lem

min

g ab

unda

nce

inde

x Collared lemming

Measles

Blasius et al. 1999, Johnson et al. 2006, Rohani et al. 1999, Paradis et al. 2000, Krebs et al. 2002

Wren

A puzzle: How are asynchronous colonization-extinction dynamics possible?

An answer: A spatial hydra effect

Local extinctions are desynchronizing• Anything that reduces synchrony promotes recolonization,

and thus persistence

• Empirical examples of colonization-extinction dynamics involve extinction-prone subpopulations

• Empirical examples of synchrony at low dispersal rates involve persistent subpopulations

An illustration of the spatial hydra effect

• Nicholson-Bailey host-parasitoid model with demogr. stochas. (Yaari et al. 2012)

• 4 patches

• Global density-independent dispersal of both spp. after births & deaths

• At end of timestep: random subpop. destruction

Subpopulation dynamics under low dispersal, no subpop. destruction

0 10 20 30 40

020

040

060

080

0

Index

n.h[

, 1]

Timestep

Hos

t sub

popu

latio

n ab

unda

nce

Subpopulation dynamics under intermediate dispersal, no subpop. destruction

0 50 100 150

050

010

0015

00

Index

n.h[

, 1]

Timestep

Hos

t sub

popu

latio

n ab

unda

nce

0 10 20 30 40

010

0020

0030

0040

00

Index

n.h[

, 1]

Subpopulation dynamics under high dispersal, no subpop. destruction

Timestep

Hos

t sub

popu

latio

n ab

unda

nce

0 10 20 30 40 50 60

010

020

030

040

050

060

0

Index

n.h[

, 1]

Subpopulation dynamics under high dispersalwith random subpopulation destruction

Timestep

Hos

t sub

popu

latio

n ab

unda

nce

0

90

0.0001 0.001 0.01 0.1 1Dispersal rate (log scale)

Met

apop

ulat

ion

pers

iste

nce

time

(mea

n)

Subpopulationdestruction rate

00.0250.50.0750.1

A spatial hydra effect

Conclusions and future directions• Hydras are real

• Effect can vary in strength, be swamped by other effects-Matter & Roland 2010 Proc Roy Soc B

• Biological details only matter via effects on colonization and extinction rates

Really exists.

0

800

0 1 0 1Dispersal rate

Mea

n m

etap

op. p

ersi

st. t

ime

Stochastic Ricker Stochastic logistic map

00.0250.050.0750.1

Destruct. rate

Weak spatial hydra effect

Moran Disp. n n y n n y y y

Low rates of “stepping stone” dispersal phase lock entire metapopulations

0

0.9

1.8

1 2 3 4 5Spatial lag

Mea

n pr

ey s

ynch

rony

±S

E

Fox et al. 2011 Ecol. Lett.

0 2 4 6 8 10 12

0.0

0.2

0.4

0.6

0.8

1.0

Dispersal rate (% per event)

Pre

y sy

nchr

ony

Even low dispersal rates can rapidly synchronize cycling populations

Fox et al. unpublished