Spatial synchrony and extinction risk in metapopulations: a spatial “hydra effect”
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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Vasseur & Fox 2009; Fox et al. 2011, unpublished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