Description Usage Arguments Details Value Author(s) References See Also Examples

The function calculates spatial synchrony from a `list`

of fitted mixed models with variance-covariance structures of the type as produced by `dendro.varcov`

. Within- and between- `varGroup`

level synchrony are calculated, quantifying the degree to which the values of N chronologies contain a common temporal signal. Different models allow for the estimation of intraclass correlations either at the intragroup or intergroup level. The underlying idea is to split the mean correlation estimated between all possible pairs of chronologies drawn from the whole dataset into: (i) a mean correlation between pairs of chronologies for every group; and (ii) a mean correlation between pairs of chronologies for pairs of groups.

1 2 |

`modelList` |
a |

`modname` |
a |

`trend.mBE` |
a |

The function calculates the within- and between-group synchrony. For the more general (unstructured) model, the correlation of pairs of chronologies `i`

and `i*`

belonging to group `r`

is:

*rho(Wi,Wi*) = cov(Wi,Wi*)/sqrt(Var(Wi)*Var(Wi*)) = sigma^2yr/sigma^2yr+sigma^2e*

Where `Wi`

is tree-ring width of `i`

th chronology, `sigma^2yr`

is a covariance between observations `Wi`

and `Wi*`

belonging to a group `r`

, `sigma^2e`

is a random deviation within the `r`

th group.
Conversely, the correlation of pairs of chronologies `i`

and `i*`

belonging to groups `r`

and `r*`

is:

*rho(Wi,Wi*) = cov(Wi,Wi*)/sqrt(Var(Wi)*Var(Wi*)) =*

*sigma^2yr*/sqrt((sigma^2yr+sigma^2e)+(sigma^2yr*+sigma^2e))*

Note that if no `modname`

is provided a warning message appears indicating that synchrony will be only calculated for the first `modname`

vector element, i.e. broad evaluation model (mBE).

The function returns a `list`

containing the following components:

for within-group synchrony:

`Modname` |
a column indicating the variance-covariance mixed models fit type: |

mBE: null (or broad evaluation) structure.

mNE: homoscedastic variant of banded main diagonal (or narrow evaluation) structure.

mCS: homoscedastic variant of compound symmetry structure.

mUN: homoscedastic variant of unstructured (or full) structure.

mHeNE: heteroscedastic variant of banded main diagonal (or narrow evaluation) structure.

mHeCS: heteroscedastic variant of compound symmetry structure.

mHeUN: heteroscedastic variant of unstructured (or full) structure.

`a_Group` |
a column representing the within-group synchrony. |

`SE_Group` |
standard error of each observation. |

for between-group synchrony:

`Modname` |
a column indicating the model fit type. See previous desription. |

`GroupName` |
a column indicating between-group |

`a_betw_Grp` |
a column indicating between-group |

`SE_betw_Grp` |
standard error of each observation. |

Josu G. Alday, Tatiana A. Shestakova, Victor Resco de Dios, Jordi Voltas

Shestakova, T.A., Aguilera, M., Ferrio, J.P., Gutierrez, E. & Voltas, J. (2014). Unravelling spatiotemporal tree-ring signals in Mediterranean oaks: a variance-covariance modelling approach of carbon and oxygen isotope ratios. *Tree Physiology* 34: 819-838.

Shestakova, T.A., Gutierrez, E., Kirdyanov, A.V., Camarero, J.J., Genova, M., Knorre, A.A., Linares, J.C., Resco de Dios, V., Sanchez-Salguero, R. & Voltas, J. (2016). Forests synchronize their growth in contrasting Eurasian regions in response to climate warming. *Proceedings of the National Academy of Sciences of the United States of America* 113: 662-667.

`dendro.varcov`

for models details.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 | ```
## Calculate synchrony for null.model (broad evaluation, mBE) and homoscedastic variant
# of unstructured model (or full, mUN) for conifersIP data,
# and heteroscedastic variant for 1970-1999 period.
data(conifersIP)
##Fit the homoscedastic set of varcov models (mBE, mNE, mCS, mUN)
#using taxonomic grouping criteria (i.e. Species)
ModHm <- dendro.varcov(TRW ~ Code, varTime = "Year", varGroup = "Species",
data = conifersIP, homoscedastic = TRUE)
summary(ModHm)# Class and length of list elements
#Synchrony for mBE and mUN models
sync(ModHm, modname = "mBE")
sync(ModHm, modname = "mUN")
##Chop the data from 1970 to 1999.
conif.30 <- conifersIP[conifersIP$Year>1969 & conifersIP$Year<2000,]
summary(conif.30$Year)
#Fit the heteroscedastic set of variance covariance mixed models (mBE, mHeNE, mHeCS, mHeUN)
# using taxonomic grouping criteria (ie. Species)
ModHt30 <- dendro.varcov(TRW ~ Code, varTime = "Year", varGroup = "Species",
data = conif.30, homoscedastic = FALSE)
sync(ModHt30, modname = "mBE")
sync(ModHt30, modname = "mHeUN")
``` |

```
Loading required package: nlme
Loading required package: ggplot2
[1] "Please wait. I am fitting the models now :)"
Length Class Mode
mBE 18 lme list
mNE 18 lme list
mCS 18 lme list
mUN 18 lme list
$Within_Group_Synchrony
Modname a_all SE
1 mBE 0.309 0.043
attr(,"class")
[1] "sync"
$Within_Group_Synchrony
Modname GroupName a_Group SE_Group
1 mUN ABAL 0.280 0.041
2 mUN PINI 0.469 0.050
3 mUN PISY 0.318 0.044
$Between_Group_Synchrony
Modname GroupName a_betw_Grp SE_betw_Grp
1 mUN ABAL/PINI 0.278 0.041
2 mUN ABAL/PISY 0.270 0.040
3 mUN PINI/PISY 0.298 0.042
attr(,"class")
[1] "sync"
Min. 1st Qu. Median Mean 3rd Qu. Max.
1970 1977 1984 1984 1991 1999
[1] "Please wait. I am fitting the models now :)"
$Within_Group_Synchrony
Modname a_all SE
1 mBE 0.319 0.058
attr(,"class")
[1] "sync"
$Within_Group_Synchrony
Modname GroupName a_Group SE_Group
1 mHeUN ABAL 0.505 0.066
2 mHeUN PINI 0.414 0.064
3 mHeUN PISY 0.297 0.055
$Between_Group_Synchrony
Modname GroupName a_betw_Grp SE_betw_Grp
1 mHeUN ABAL/PINI 0.321 0.058
2 mHeUN ABAL/PISY 0.325 0.058
3 mHeUN PINI/PISY 0.259 0.051
attr(,"class")
[1] "sync"
```

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