Spatial synchrony of population fluctuations: causes and consequences

Jeremy FoxUniversity of Calgary

Website: homepages.ucalgary.ca/~jefox/Home.htm

Blog: dynamicecology.wordpress.com

With thanks to: Tara Janes, Jessica Scharein, Joyce MacNeil,Stephen Hausch, Jodie Roberts, Geoff Legault

Collaborator: David Vasseur, Yale University

"An odd kind of sympathy": Huygens' clocks

Synchrony

Spatial synchrony in population ecology

Lynx Gypsy moth

0

10

1994 1995 1996 1997 1998 1999 2000

Year

Lem

min

g a

bu

nd

ance

ind

ex Collared lemming

Measles

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

Wren

Causes of spatial synchrony

•Dispersal

•Spatially-synchronous environmental fluctuations (Moran effect)

•Interspecific interactions

Stochastic predator-prey model

N1

P1

N2

P2

Dispersal

Patch 1 Patch 2

iPijiPi

iii

iNiji

iiiNii

i

PtPPdPtmhN

PeaN

dt

dP

NtNNdhN

PaNNtmNN

dt

dN

ii

ii

1

Envi. flucts. Envi. flucts.

Growth Mortality Predation DispersalDemogr.stochas.

Model predictions for prey synchrony

•Dispersal is synchronizing

•Moran effect is synchronizing

•Predation increases the synchronizing effect of dispersal

Vasseur & Fox 2009 Nature

Sync. envi., + dispersal

Time (arbitrary units)

Mod

el p

rey

dens

ity

Sync. envi., no dispersal

Patch 1 Patch 2

Predator-prey oscillations are synchronized (‘phase locked’) by dispersal

• No predatorsno cycleslittle effect of dispersal

Summary of model predictions

•Dispersal is synchronizing

•Moran effect is synchronizing

•Predators that generate oscillations greatly increase the synchronizing effect of dispersal

-Statistical signature of phase locking

Protist microcosm experiment

•Prey: Tetrahymena pyriformis

•Predator: Euplotes patella

•Microcosms: 80 ml, semi-continuous cultures

•Small samples taken on weekdays

•Dispersal of 10% of individuals, 3x/week

•Daily temperature fluctuations (independent or perfectly synchronous)

•6 replicate bottle pairs/ttmt. combination

•Experimental units: pairs of bottles

•2x2x2 factorial design crossing pres./abs. of dispersal, Moran effect, predator

Conducting dispersal events

102

103

104

0 9 18 27 36 45 54 63

2030

Tem

p. (°C)T

et./

ml

(log

scal

e)

Day

Illustrative population dynamics

Day

0

600

1200

0 9 18 27 36 45 54 630

10

20

30

Tem

p. (°C)

Eupl./m

lTet

./m

l

Experimental results vs. model predictions

Vasseur & Fox 2009 Nature

Phase-locked oscillations

0 630

700

Day

Tet

rahy

men

a/m

l Patch 1Patch 2

102

103

104

0 9 18 27 36 45 54 63

2030

Tem

p. (°C)T

et./

ml

(log

scal

e)

Day

Prey densities did not track temperature fluctuations

Summary so far

Synchrony

Dispersal Moran effect

Species interactions

Population dynamics(cyclic vs.

not)

Lynx

Phase drift at low dispersal rates: data

Day

Pre

y de

nsity

(m

l-1)

Fox et al. in press Plos One

Phase drift at low dispersal rates: model

Fox et al. in press Plos One

Scaling up

Synchrony usually decays with distance

Syn

chro

ny

Distance between populations

Ranta et al. 1995

•Links between pattern of decay and underlying mechs.?

Questions

• Why does synchrony decay with distance?– Decay of environmental synchrony– Limited dispersal distance

• Phase locking across long distances?

Methods

1 2 3 4 5 6•Exptl. units:

•2 x 2 factorial design (y/n Moran effect, y/n dispersal)

•Stepping-stone dispersal

•Moran effect with spatially-decaying synchrony

•Predators + prey

Illustrative prey dynamicsLo

g(T

etra

./m

l + 1

)

Time

+M +D +M -D -M +D -M -D

Moran Disp. n n y n n y y y

Prey synchrony

0

0.9

1.8

1 2 3 4 5Spatial lag

Mea

n pr

ey s

ynch

rony

±S

E

•High mean sync. (init. conds.)•Higher sync. at even lags (init. conds.)

+ dispersal

- dispersal

•Dispersal increases sync.•Same effect at all lags (phase locking)•Moran eff. increases short-distance sync.•Spat. decay of sync. in +Moran ttmts.•No Moran x disp. interaction

Fox et al. 2011 Ecol. Lett.

Take-home points

• Dispersal generates long-distance phase locking• Distance-decay of synchrony due to Moran effect

– Same likely true in many natural systems– Short-distance dispersal either phase-locks cycles, or

produces little synchrony at all

Summary:Spatial predator-prey cycles work like this:

Consequences of synchrony for metapopulation persistence:

the spatial “hydra effect”

The “hydra effect”

The usual story: intermediate dispersal rates maximize metapopulation persistence

Met

apop

ulati

on p

ersi

sten

ce ti

me

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:

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

Subpopulation dynamics under intermediate dispersal, no subpop. destruction

0 50 100 150

05

00

10

00

15

00

Index

n.h

[, 1

]

Timestep

Hos

t su

bpop

ulat

ion

abun

danc

e

0 10 20 30 40

01

00

02

00

03

00

04

00

0

Index

n.h

[, 1

]

Subpopulation dynamics under high dispersal, no subpop. destruction

Timestep

Hos

t su

bpop

ulat

ion

abun

danc

e

0 10 20 30 40 50 60

01

00

20

03

00

40

05

00

60

0

Index

n.h

[, 1

]

Subpopulation dynamics under high dispersalwith random subpopulation destruction

Timestep

Hos

t su

bpop

ulat

ion

abun

danc

e

0

90

0.0001 0.001 0.01 0.1 1

Dispersal rate (log scale)

Met

apop

ulat

ion

pers

iste

nce

time

(mea

n)

Subpopulationdestruction rate

00.0250.50.0750.1

A spatial hydra effect

Hydra effect summary

• 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

-local extinctions affect coloniz. rate via effect on synchrony

Really exists.

Future directions• Interplay of determinism and stochasticity• Embedding of Euplotes-Tet. cycle in larger food webs• Environmental heterogeneity• Larger spatial arrays?• Hydra effect under different forms of envi. stochasticity• Comparisons with nature

-changes in synchrony as cycles collapse?

0

800

0 1 0 1

Dispersal rate

Mea

n m

etap

op.

pers

ist.

tim

e

Stochastic Ricker Stochastic logistic map

0

0.025

0.05

0.075

0.1

Destruct. rate

Weak spatial hydra effect

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

nch

ron

y

Even low dispersal rates can rapidly synchronize cycling populations

Fox et al. unpublished

Prey synchrony vs. dispersal rate

Fox et al. in press Plos One

Data analysis

1 2 3 4 5 6

r(1,2)

1. Calculate prey synchrony (cross-correl. of log abundance) for every pair of jars in an array

-predator abundances too noisy to analyze

r(3,6)

2. Calculate mean sync. at every spatial lag within an array-vector of 5 cross-correl. coeffs.

3. z-transform to normalize

4. MANOVA for treatment effects, follow-up ANOVAs

5. Spatial decay: regress z-transformed cross-correlation on spatial lag, ANOVA on slopes

Day

Log(

Eup

lote

s/m

l +1)

Illustrative predator dynamics

0

2

4

0 25 50Day

Mea

n E

uplo

tes/

ml

0

1000

2000

3000

4000

5000

0 1 2 3 4 5 6

Day

Tetrahymena

/ml

No dispersal

Direct demonstration of dispersal-generated phase locking

-2000

0

2000

4000

0 1 2 3 4 5 6

Day

De

ns

ity

dif

fere

nc

e

No dispersal

0

1000

2000

3000

4000

5000

0 1 2 3 4 5 6

Day

Tetrahymena

/ml + dispersal

-2000

0

2000

4000

0 1 2 3 4 5 6

Day

De

ns

ity

dif

fere

nc

e

+ dispersal

Desync. Sync. Little desync.

“Leading”patches

“Trailing”patches

Phase drift at the cycle nadir in the absence of dispersal

Illustrative examples of prey synchrony

0 630

1000

Day

Tet

./m

lIndep. envi., no disp.

No

pred

ator

s

0

1000

0 63Day

Tet

./m

l

+ p

reda

tors

0 630

1400

Day

Tet

./m

l

Sync. envi., + disp.

0 630

700

Day

Tet

./m

l

-pred. +pred.

Mod

el p

rey

sync

hron

y

Indep. envi. Sync. envi.

-pred. +pred.

No disp.Pred. disp.Prey disp.Both disp.

Dispersal × predator interaction not due to prey tracking synchronized predators

DispersalNo disp.

Predator synchrony

Vasseur & Fox 2009 Nature

Robust qualitative match between model and data

Monte Carlo simulns.Exptl. data

Vasseur & Fox 2009 Nature

Monte Carlo simulations: ANOVA main effects

Monte Carlo simulations: ANOVA interaction terms

-pred. +pred.

Mod

el p

rey

sync

hron

y

Indep. envi. Sync. envi.

-pred. +pred.rand. mort.

rand. mort.

No dispersalDispersal

Dispersal × predator interaction not due to increased prey variability in presence of predators

-1.2

0

0.6

0 25 50

Day

Det

rend

ed lo

g pr

ey d

ensi

ty 0

2 (=0)

Estimating prey cycle phase

Dispersal entrains the phases of predator-prey cycles(and the Moran effect doesn’t)

0

/2

3/2

0

/2

3/2

0

/2

3/2

0

/2

3/2

+M +D

-M +D

+M -D

-M -D

Fox et al. 2011 Ecol. Lett.

Var

ianc

e in

pha

se0.05

0.20

- dispersal + dispersal

- Moran eff.+ Moran eff.

Predators generated prey oscillations

No

rma

lize

d sp

ect

ral p

ow

er

Frequency (1/d)

Predator-prey cycle

Illustrative prey power spectrum