Results from studies examining changes in the abundance of fish species in French rivers.

dat.maire2019

Format

The object is a list containing a data frame called dat that contains the following columns and distance matrix called dmat:

sitecharacterstudy site
stationcharactersampling station at site
site_stationcharactersite and station combined
s1numericMann-Kendal trend statistic for relative abundance of non-local species
vars1numericcorresponding sampling variance (corrected for temporal autocorrelation)
s2numericMann-Kendal trend statistic for relative abundance of northern species
vars2numericcorresponding sampling variance (corrected for temporal autocorrelation)
s3numericMann-Kendal trend statistic for relative abundance of non-native species
vars3numericcorresponding sampling variance (corrected for temporal autocorrelation)
constnumericconstant value of 1

Details

The dataset includes the results from 35 sampling stations (at 11 sites along various French rivers) examining the abundance of various fish species over time (i.e., over 19-37 years, all until 2015). The temporal trend in these abundance data was quantified in terms of Mann-Kendal trend statistics, with positive values indicating monotonically increasing trends. The corresponding sampling variances were corrected for the temporal autocorrelation in the data (Hamed & Rao, 1998).

The distance matrix dmat indicates the distance of the sampling stations (1-423 river-km). For stations not connected through the river network, a high distance value of 10,000 river-km was set (effectively forcing the spatial correlation to be 0 for such stations).

The dataset can be used to illustrate a meta-analysis allowing for spatial correlation in the outcomes.

Source

Maire, A., Thierry, E., Viechtbauer, W., & Daufresne, M. (2019). Poleward shift in large-river fish communities detected with a novel meta-analysis framework. Freshwater Biology, 64(6), 1143--1156. https://doi.org/10.1111/fwb.13291

References

Hamed, K. H., & Rao, A. R. (1998). A modified Mann-Kendall trend test for autocorrelated data. Journal of Hydrology, 204(1-4), 182--196. https://doi.org/10.1016/S0022-1694(97)00125-X

Examples

### copy data into 'dat' and examine data
dat <- dat.maire2019$dat
dat[-10]
#>      site station site_station  s1      vars1   s2      vars2   s3      vars3
#> 1   site1    sta1   site1_sta1 168  3502.7424    9  2301.0000 -109  2301.0000
#> 2   site1    sta2   site1_sta2 123  2301.0000   -9  2301.0000  -71  1603.4889
#> 3   site2    sta1   site2_sta1 302  5846.0000 -213 13738.9074   -1  5846.0000
#> 4   site2    sta2   site2_sta2 220 12815.9330 -306  8523.6120  162 10331.2344
#> 5   site2    sta3   site2_sta3 350  3154.7614 -220 15295.4021   56  5846.0000
#> 6   site2    sta4   site2_sta4 337  1890.6559 -336 11428.8040  180  7707.7479
#> 7   site2    sta5   site2_sta5 233  8644.3041 -389 10296.2071  231  2577.2668
#> 8   site2    sta6   site2_sta6 283  5846.0000 -460  9629.2758  148  5846.0000
#> 9   site2    sta7   site2_sta7 353 10344.5677 -320 12964.8288  300  5846.0000
#> 10  site3    sta1   site3_sta1 177  2562.0000 -140  2562.0000  -97  2562.0000
#> 11  site3    sta2   site3_sta2 229  4301.7270 -111  2562.0000   29  2562.0000
#> 12  site4    sta1   site4_sta1 248  4606.0582 -126   955.6867  117  3338.5788
#> 13  site4    sta2   site4_sta2 197  5436.9501  -34  2301.0000  -16  2301.0000
#> 14  site5    sta1   site5_sta1  93   950.0000  -14  1160.7161   21   950.0000
#> 15  site5    sta2   site5_sta2  34   468.8432    3   697.0000  -21   446.6578
#> 16  site5    sta3   site5_sta3  61   594.4956  -16   950.0000   47   950.0000
#> 17  site5    sta4   site5_sta4  61   950.0000   96   950.0000   44   950.0000
#> 18  site6    sta1   site6_sta1 271  4165.3333 -187  6756.4437 -167  4165.3333
#> 19  site6    sta2   site6_sta2 319  4165.3333 -182  2885.4519  -98  3567.5292
#> 20  site7    sta1   site7_sta1  14   817.0000  -41   817.0000 -115   817.0000
#> 21  site7    sta2   site7_sta2  61  1499.0587  -59   817.0000  -75   817.0000
#> 22  site8    sta1   site8_sta1 305  9035.2651 -123  2842.0000  -68  2842.0000
#> 23  site8    sta2   site8_sta2 315  5096.2897   58  2842.0000   41  2842.0000
#> 24  site8    sta3   site8_sta3 195  2842.0000  -31  2842.0000  117  2842.0000
#> 25  site9    sta1   site9_sta1 308 11395.6877  243  5497.1710   -3  1568.0952
#> 26  site9    sta2   site9_sta2 345  5395.0077  316  3461.6667 -139  3461.6667
#> 27  site9    sta3   site9_sta3 294  3461.6667  -89  3461.6667 -193  3461.6667
#> 28  site9    sta4   site9_sta4 318  5212.0340  -78  3461.6667 -123  8405.0704
#> 29 site10    sta1  site10_sta1 114   739.1046  -37   950.0000    0   950.0000
#> 30 site10    sta2  site10_sta2  92  2640.7189  -62  1096.6667  -46  1096.6667
#> 31 site11    sta1  site11_sta1  50  2021.0911  -24  1096.6667   79  1096.6667
#> 32 site11    sta2  site11_sta2 309  4550.3333 -112  4550.3333  -12  4550.3333
#> 33 site11    sta3  site11_sta3 225  3107.6097  -75  4550.3333   -6  4550.3333
#> 34 site11    sta4  site11_sta4  37  1096.6667  -44  1096.6667   11  1096.6667
#> 35 site11    sta5  site11_sta5  44  1661.3690   -5   950.0000   46   950.0000

### copy distance matrix into 'dmat' and examine first 5 rows/columns
dmat <- dat.maire2019$dmat
dmat[1:5,1:5]
#>            site1_sta1 site1_sta2 site2_sta1 site2_sta2 site2_sta3
#> site1_sta1          0          6      10000      10000      10000
#> site1_sta2          6          0      10000      10000      10000
#> site2_sta1      10000      10000          0          1          1
#> site2_sta2      10000      10000          1          0          1
#> site2_sta3      10000      10000          1          1          0

# \dontrun{

### load metafor package
library(metafor)

### fit a standard random-effects model ignoring spatial correlation
res1 <- rma.mv(s1, vars1, random = ~ 1 | site_station, data=dat)
res1
#> 
#> Multivariate Meta-Analysis Model (k = 35; method: REML)
#> 
#> Variance Components:
#> 
#>                 estim      sqrt  nlvls  fixed        factor 
#> sigma^2    10522.1760  102.5777     35     no  site_station 
#> 
#> Test for Heterogeneity:
#> Q(df = 34) = 191.4837, p-val < .0001
#> 
#> Model Results:
#> 
#> estimate       se    zval    pval     ci.lb     ci.ub     ​ 
#> 187.5809  20.0424  9.3592  <.0001  148.2984  226.8633  *** 
#> 
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 

### fit model allowing for spatial correlation
res2 <- rma.mv(s1, vars1, random = ~ site_station | const, struct="SPGAU",
               data=dat, dist=list(dmat), control=list(rho.init=10))
res2
#> 
#> Multivariate Meta-Analysis Model (k = 35; method: REML)
#> 
#> Variance Components:
#> 
#> outer factor: const         (nlvls = 1)
#> inner term:   ~site_station (nlvls = 35)
#> 
#>                estim     sqrt  fixed 
#> tau^2      8945.8842  94.5827     no 
#> rho          15.0568              no 
#> 
#> Test for Heterogeneity:
#> Q(df = 34) = 191.4837, p-val < .0001
#> 
#> Model Results:
#> 
#> estimate       se    zval    pval     ci.lb     ci.ub     ​ 
#> 176.5775  26.3986  6.6889  <.0001  124.8372  228.3178  *** 
#> 
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 

### add random effects for sites and stations within sites
res3 <- rma.mv(s1, vars1, random = list(~ 1 | site/station, ~ site_station | const), struct="SPGAU",
               data=dat, dist=list(dmat), control=list(rho.init=10))
res3
#> 
#> Multivariate Meta-Analysis Model (k = 35; method: REML)
#> 
#> Variance Components:
#> 
#>                estim     sqrt  nlvls  fixed        factor 
#> sigma^2.1  7158.3492  84.6070     11     no          site 
#> sigma^2.2     0.0000   0.0039     35     no  site/station 
#> 
#> outer factor: const         (nlvls = 1)
#> inner term:   ~site_station (nlvls = 35)
#> 
#>                estim     sqrt  fixed 
#> tau^2      3425.5862  58.5285     no 
#> rho          12.8755              no 
#> 
#> Test for Heterogeneity:
#> Q(df = 34) = 191.4837, p-val < .0001
#> 
#> Model Results:
#> 
#> estimate       se    zval    pval     ci.lb     ci.ub     ​ 
#> 182.1199  31.2808  5.8221  <.0001  120.8107  243.4291  *** 
#> 
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 

### likelihood ratio tests comparing the models
anova(res1, res2)
#> 
#>         df      AIC      BIC     AICc    logLik     LRT   pval       QE tau^2 
#> Full     3 402.3380 406.9171 403.1380 -198.1690                191.4837    NA 
#> Reduced  2 423.8050 426.8577 424.1921 -209.9025 23.4670 <.0001 191.4837    NA 
#> 
anova(res2, res3)
#> 
#>         df      AIC      BIC     AICc    logLik    LRT   pval       QE tau^2 
#> Full     5 403.7355 411.3673 405.8783 -196.8677               191.4837    NA 
#> Reduced  3 402.3380 406.9171 403.1380 -198.1690 2.6025 0.2722 191.4837    NA 
#> 

### profile likelihood plots for model res2
profile(res2, cline=TRUE)
#> Profiling tau2 = 1 

#> Profiling rho = 1 


### effective range (river-km for which the spatial correlation is >= .05)
sqrt(3) * res2$rho
#> [1] 26.07908

### note: it was necessary to adjust the starting value for rho in models
### res2 and res3 so that the optimizer does not get stuck in a local maximum
profile(res2, rho=1, xlim=c(0,200), steps=100)


# }