large-scale synchronisation of life-history events esa ranta

Large-scale synchronisation oflife-history events

Esa Ranta

Large-scale synchronisation oflife-history events

Esa RantaVeijo Kaitala

Per Lundberg

Jan Lindström

Contents:

• What is meant with synchrony?

• Examples of synchrony

• Explanations of synchrony

• An IBM model on synchronisation of life history events in perennial plants

What is meant by synchrony?

• Temporal (year-to-year) match in large-scale population fluctuations of a given target species

Time

Po

pu

lati

on

siz

e

Time

Inc

ide

nc

e

What is meant by synchrony?

• Temporal (year-to-year) match in large-scale population fluctuations of a given target species

• Temporal match in occurrence (incidence, extent) of life history events (flowering, seed set, ...)

Examples of synchrony:QuickTime™ and aGraphics decompressorare needed to see this picture.

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1960 1970 1980

Lappi

Oulu

Vaasa KuopioKeski-Suomi

Mikkeli

Pohjois-Karjala

HämeTurku-Pori

Uusimaa

Kymi

Years

Black grouse

Examples of synchrony:

QuickTime™ and aGraphics decompressorare needed to see this picture.

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1964 1969 1974 1979 1984

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(A) Black grouse (B) (C)

Years Distance, km n


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(A) Mountain hare (B) Red fox (C) Pine marten

(D) Red squirrel (E) Stoat (F) Least weasel

0 5 10 0 5 10 0 5 10

Distance, km n Distance, km n Distance, km n

FINNISH DATA (A-F)


SNOWSHOE HARE IN CANADA

(B)

(A)

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1

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Distance, in grid units


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20 J InsectsÉ Fish, crabH Birds

U Terrestrial vertebrates

A

Key:

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-1 -0.8 -0.6 -0.4 -0.2 0 0.2

B

r = –0.34

0 10 20

C

Correlation betweensynchrony and distance, rD

Frequency, %

Two explanations of synchrony:

• P.A.P. Moran suggested (1953) that stochastic density-independent but correlated processes may cause local populations with a common structure of density dependence to fluctuate synchronously

X1(t+1) = aX1(t) + bX1(t–1) + (t)

X2(t+1) = aX2(t) + bX2(t–1) + (t)

– a and b are identical for X1 and X2

– the random elements and are different but correlated


• The Moran effect

• Dispersal– redistribution of individuals between breeding

seasons synchronise populations

– dispersal is negatively distance dependent


The Moran effect and dispersal may act alone or in concert


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Distance

(A) No MoranNo Dispersal

(B) Yes MoranNo Dispersal

(C) No MoranYes Dispersal

(D) Yes MoranYes Dispersal

Conclusion:

• Many animal populations (insects, fish, crustacean, mammals, birds) display synchronised population fluctuations over large geographical ranges

Conclusion:

• Many animal populations (insects, fish, crustacean, mammals, birds) display synchronised population fluctuations over large geographical ranges

• Often the level of synchrony goes down with increasing distance between the localities where the population data are collected

Conclusion:• Many animal populations (insects, fish, crustacean, mammals, birds) display synchronised population

fluctuations over large geographical ranges

• Often the level of synchrony goes down with increasing distance between the localities where the population data are collected

• These conclusions appear to be valid for seed set and flowering in perennial plants (Koenig et al., Post et al. in [too] numerous papers 1998 - 2001)

Comment:

• As to flowering plants,– Moran effect can synchronise life history events (flowering, seed set [masting])

– Dispersal is less likely to be valid here, unless there is local pollen limitation and pollen dispersal is negatively distance dependent

Comment:• As to flowering plants,

– Moran effect can synchronise life history events (flowering, seed set [masting])


• The question is:

Can we build a simple model to explain life history synchronisation in perennial flowering plants?

Comment:• As to flowering plants,

– Moran effect can synchronise life history events (flowering, seed set [masting])


• The question is:

Can we build a simple model to explain life history synchronisation in perennial flowering plants?

Here the IBM models may come to a rescue

An IBM model for life history synchronisation:

• The model is built on individual-level accumulation of energy reserves i,k(t) in a given site k for flowering and reproduction



• The reserves are annually updated due to solar energy received during growing season




• The energy received is stand-level Ek(t) radiation topped off with i,k(t), variation individuals are experiencing due to, e.g., shading and wind factors affecting local spots





• Reproduction takes place once the accumulated reserve exceeds the threshold k for reproduction





• Reproduction takes place once the accumulated reserve exceeds the threshold k for reproduction

• The reserves are depleted during reproductive bouts


Threshold for flowering

Individual# 1

Individual# 2

En

erg

y le

vel

En

erg

y le

vel



Individual# 1

Individual# 2

En

erg

y le

vel

En

erg

y le

vel

An

nu

al E

An

nu

al E



Individual# 1

Individual# 2

En

erg

y le

vel

En

erg

y le

vel

An

nu

al E

An

nu

al E

Local



Individual# 1

Individual# 2

En

erg

y le

vel

En

erg

y le

vel

An IBM model for life history synchronisation:QuickTime™ and aGraphics decompressorare needed to see this picture.

Locality, k

Locality, k + 1

Locality, k + N

...

Πi,k + N(t)

Individual treesinluenced by

εi,k+ N(t)

Πi,k + 1(t)


εi,k+1(t)

Πi,k(t)


εi,k(t)

Inluenced bythe

Moran effect

Inluenced bythe

Moran effect

Inluenced bythe

Moran effect

Receiving Ek + N(t)

Threshold Φk + N

Receiving Ek + N(t)

Threshold Φk + 1

Receiving Ek + N(t)

Threshold Φk

Structure of the threshold model for reproduction


0 10 20 30 40 50 60 70 80 90 1000

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0 10 20 30 40 50 60 70 80 90 1000

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Individuals 1 - 100

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TIME

Ene

rgy

afte

r flo

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befo

re f

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erin

g%

flo

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An IBM model for life history synchronisation:QuickTime™ and aGraphics decompressorare needed to see this picture.

-1

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1(a) E(t) = 100, Φ = 199

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0 2 4 6 8 10

(b) E(t) = 100, Φ = 201

(c) E(t) = 100, Φ = 300

0 2 4 6 8 10

(d) E(t) = 100, Φ = 500No

stochasticity

With 5% of εi,k(t)

Time lag, years

• With no annual variation in Ek(t) and with no individual differences in energy accumulation due to local differences we find the following:

• When Ek(t) > all individuals in all sites will reproduce every year, with < Ek(t) < 2k reproduction in each k is synchronous with period two

• Whereas with Ek(t) << k the period length starts to increase



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1 0.9 0.8 0.7 0.6 0.5 1 0.9 0.8 0.7 0.6 0.5

NO STOCHASTICITY INDIVIDUALSTOCHASTICITY

Gradient similarity, d

1 0.9 0.8 0.7 0.6 0.5

MORAN EFFECT &INDIVIDUAL

STOCHASTICITY

Gradient differences in reproduction threshold,

Φ

Gradient differences in annual radiation, Ek(t)

Gradient differences in Φ and Ek(t)Matching

slope

Slope

differences

(a)

(d)

(g)

(b)

(e)

(h)

(c)

(f)

(i)

• By introducing differences (a) in Ek(t), assuming, e.g., a south – north gradient, will break down synchronous reproduction between any two groups where the difference in Ek(t) is large enough to cause flowering periodicities among the sites to differ.

• With gradient differences (b) in k reproduction will be asynchronous. Naturally, Ek(t) and k can (c) covary along the gradient

• Synchronous reproduction will be maintained among the sites until site-specific periodicities will start to change


• Introducing stochasticity in i,k(t) under (a), (b) or (c) will break down regional reproductive synchrony

• Introducing a global modulator, the Moran effect, influencing i,k(t) of each individual in a matching manner, recovers synchronicity


Conclusions:• We have created an individual based model on

reproduction in flowering plants

• With Moran effect the model is capable of producing synchronised life reproduction among separate populations

• With an environmental gradient in energy received or threshold of energy needed for reproduction one can get the level of synchrony going down against distance along the gradient

• This matches observations with real plants (seed set: W. Koenig et al.; flowering: E. Post et al.)

large-scale synchronisation of life-history events esa ranta

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