Large-scale synchronisation of life-history events Esa Ranta

Large-scale synchronisation of life-history events Esa Ranta Veijo 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 Population size

Time Incidence 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:

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 X 1 (t+1) = aX 1 (t) + bX 1 (t–1) +  (t) X 2 (t+1) = aX 2 (t) + bX 2 (t–1) +  (t) –a and b are identical for X 1 and X 2 –the random elements  and   are different but correlated

Two explanations of synchrony: The Moran effect Dispersal –redistribution of individuals between breeding seasons synchronise populations –dispersal is negatively distance dependent

Two explanations of synchrony: The Moran effect and dispersal may act alone or in concert

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 )

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

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

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 E k (t) radiation topped off with  i,k (t), variation individuals are experiencing due to, e.g., shading and wind factors affecting local spots

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 E k (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

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 E k (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 The reserves are depleted during reproductive bouts

An IBM model for life history synchronisation: Threshold for flowering Individual # 1 Individual # 2 Energy level

An IBM model for life history synchronisation: Threshold for flowering Individual # 1 Individual # 2 Energy level Annual E

An IBM model for life history synchronisation: Threshold for flowering Individual # 1 Individual # 2 Energy level Annual E Local 

An IBM model for life history synchronisation: Threshold for flowering Individual # 1 Individual # 2 Energy level

An IBM model for life history synchronisation:

Energy after flowering before flowering % flowering

An IBM model for life history synchronisation:

With no annual variation in E k (t) and with no individual differences in energy accumulation due to local differences we find the following: When E k (t) >  all individuals in all sites will reproduce every year, with  < E k (t) < 2  k reproduction in each k is synchronous with period two Whereas with E k (t) <<  k the period length starts to increase An IBM model for life history synchronisation:

By introducing differences (a) in E k (t), assuming, e.g., a south – north gradient, will break down synchronous reproduction between any two groups where the difference in E k (t) is large enough to cause flowering periodicities among the sites to differ. With gradient differences (b) in  k reproduction will be asynchronous. Naturally, E k (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 An IBM model for life history synchronisation:

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 An IBM model for life history synchronisation:

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.)