DOI: 10.5061/dryad.05qfttf9z
title: Barriers decouple population dynamics of riverine fish, and asynchrony of subpopulations promotes stability within fragments

description: The spatial synchrony framework suggests that asynchrony among
 subpopulations in different branches of a river network should stabilise
 the metapopulation. However, how barriers affect this framework remains
 poorly understood. This is a significant knowledge gap given that
 population synchrony arises from dispersal and environmental similarity,
 both of which are influenced by barriers. Here, we empirically evaluated
 how barriers impact fish population synchrony and, subsequently, the
 associations between synchrony and metapopulation persistence,
 productivity, stability, and trajectory within fragments. We found that
 barriers demographically decouple populations by decreasing synchrony in
 brown trout (Salmo trutta) and Eurasian minnow (Phoxinus phoxinus) but not
 northern pike (Esox lucius), suggesting species-specific responses to
 fragmentation. Additionally, asynchrony had a stabilising portfolio effect
 on metapopulation stability at the fragment level that was statistically
 significant for S. trutta. Higher fragment synchrony also made S. trutta
 and P. phoxinus populations less stable. The impact of barriers on
 riverine fish population synchrony emphasises the need to include barriers
 in future studies on the causes and consequences of synchrony in rivers.
 That asynchrony stabilises populations in some riverine fishes suggests
 that conservation prioritisations should lie in restoring or retaining
 larger fragment sizes and higher branching complexity with intact
 connectivity.
description: <em>Study species, data acquisition and river
 structure</em>   Fish
 density data was acquired from Swedish Electrofishing RegiStry (SERS) at
 Swedish University of Agricultural Sciences (SLU). Electrofishing is a
 non-lethal fish sampling method mainly conducted in streams where it is
 possible to wade. Electric current (DC) is used to attract fish to swim
 towards a handheld anode where they are caught with a dipping net. It is
 an established and reliable method for quantifying fish density[1] in
 rivers, see the Swedish and European Standard[2] for detailed descriptions
 on the method. To evaluate generality and improve inference space, we used
 three model species – Salmo trutta (brown trout), Phoxinus phoxinus
 (Eurasian minnow), and Esox lucius (northern pike). These species
 represent three families of freshwater fish (Salmonidae, Esocidae and
 Cyprinidae) that are widely distributed in the northern hemisphere.
 Although coexisting in riverine habitats, these species require different
 habitats to complete their life cycles and sustain local populations. S.
 trutta is an obligate lotic spawner laying their eggs on gravel[3], E.
 lucius has a strong preference for spawning in lentic habitats with
 vegetated soft bottoms[4], whereas the P. phoxinus is intermediate,
 preferably spawning on hard bottoms in slow flowing lotic
 habitats[5].   Because of
 the extensive requirement on spatial and temporal coverage of sampling
 sites to answer our questions, an initial filtering was done where we
 removed all electrofishing sites with less than 6 sampling occasions. This
 allowed us to visually select 24 catchments with sufficient spatial and
 temporal coverage throughout Sweden (Fig. 1) with sites located between
 56.62 to 66.83 degrees latitude and 12.10 to 21.82 degrees longitude.
 Temporal span of sampling data was 1951 to 2021, but 90% of the sampling
 occasions occurred after 1988. Vectored polylines of the rivers in these
 24 catchments were downloaded from Lantmäteriet (Land Survey). The spatial
 distribution of barriers was downloaded from Swedish Meteorological and
 Hydrological Institute (SMHI). These three geographic information layers
 were integrated in R package riverdist[6], which was used to generate
 tables with the segment and vertex location of all barriers and
 electrofishing sites. Watercourse routes between all pairwise sites were
 recorded, and if the route crossed a segment and vertex of a dam, the two
 sample sites were assigned to different fragments. A matrix was then
 constructed with this information which clustered connected sites into
 fragments. The riverdist package also recorded watercourse distance,
 Euclidean distance, and flow-connectivity between all sites. See Fig. 1b
 for a visualisation of a catchment with sites split into fragments by
 barriers.   Of the total
 1505 dam occurrences within in the study area, 224 were classified as
 removed and were thus filtered away before the spatial data extraction
 process. The metainformation in the registry for barrier occurrences was
 very patchy. Of the remaining 1281 dam occurrences, only 301 specify a dam
 height: the average height of those dam constructions was 6.4 (± 19 SD)
 meters. Information on whether barriers had the capacity to regulate the
 flow, or if they were barriers for fish, was also rarely specified. Rather
 than designing questions dependent on such patchy data, all remaining
 barriers were assumed to be barriers for fish.
   <em>Quantifying
 synchrony</em>  
 <em>Between sites</em>
   Synchrony between all sites in each
 catchment was quantified using Spearman’s correlations with at least 6
 matching pairwise years for each species (n = 9998, n = 4653 and n = 2033
 for S. trutta, P. phoxinus and E. lucius, respectively). Correlation
 analyses have been used to analyse spatial synchrony in several previous
 studies (Spearman’s correlations[7–9] and Pearson’s correlations[10]). We
 found that site-pairs that did not have any matching years with &gt;0
 density lead to negatively biased correlations, so to improve data quality
 all such site-pairs were excluded.  
 To evaluate whether the results and conclusions based on
 estimates of synchrony were robust or influenced to any important degree
 by the length of the time period, we also performed a sensitivity analysis
 using only site-pairs with at least 10 matching years (instead of at least
 6 matching years). The results were qualitatively similar as no
 significances nor direction of effects were altered; these results are
 available in the Supplementary Material but we report the results based on
 analyses of at least 6 matching years in the main text below.
   Because distances between site-pairs
 across fragments have the potential to be longer than those within
 fragments, the distance of between-fragment site-pairs was truncated to
 the maximum distance of site-pairs within fragments (for each catchment
 respectively). This resolves the statistical issue of unequal variances
 (and ranges) between groups, which can be problematic in models with
 interactions.   Linear mixed
 models were performed with R package lme4[11]. Because each “observation”
 in this dataset is based on information obtained from two sites, the data
 has a “pairwise” correlation structure (one row equals the synchrony,
 Euclidean distance, watercourse distance, etc. between two sites). Thus,
 each site (e.g., A, B, C, D) is used for the calculation of multiple
 synchrony values (e.g., A-B, A-C, A-D, etc) and that the same site
 sometimes occurs in different columns (e.g., A-B, B-C). To account for
 this non-independency issue, we used a multimembership random effect added
 using lme4-wrapper LmerMultiMember[12]. With this approach, a synchrony
 value can be seen as a group with the two sites as “members”, and some
 part of the variation can be partitioned to the sites across
 groups.   In light of recent
 studies[7], accounting for dendritic structure is critical in analyses of
 synchrony in river networks. To evaluate the influence of spatial
 distribution, flow-connectedness and fragmentation on site-pair synchrony,
 we constructed a linear mixed model with site-pair synchrony as the
 response variable, and the main effects of, and the three-way interaction
 between, ‘water course distance’, ‘flow-connectedness’ and ‘fragment
 border passing’ as explanatory variables. Random intercept for catchment
 identity and multimembership effect for site were included as random
 effects in the models. We analysed the data for each of the three species
 separately. To ensure that our model maintains the expected Type I error
 rate under the null hypothesis, we conducted a simulation-based evaluation
 outlined in the Supplementary Materials. Reassuringly, the proportion of
 p-values below the alpha level (0.05) was approximately 5% across all
 model terms except the intercept (Supplementary Fig. S1), confirming that
 our approach maintains appropriate Type I error rates.
   To improve interpretability of
 results, we also performed models with flow-unconnected (n = 6632, n =
 2561 and n = 1243 for S. trutta, P. phoxinus and E. lucius; Fig. 2a-c) and
 flow-connected site-pairs (n = 3366, n = 2092 and n = 790 for S. trutta,
 P. phoxinus and E. lucius; Fig. 2d-f) separately. Linear mixed models
 (LMMs) with ‘site-pair synchrony’ as response and ‘watercourse distance’,
 ‘fragment border passing’, and their interaction, as explanatory variables
 were performed for each species. Random intercept for catchment identity
 and multimembership effect for site were included as random effects. For
 flow-connected sites, the interaction effect between ‘watercourse
 distance’ and ‘fragment border passing’ was not significant (interaction
 term: t = 0.028) for pike so an additional model with only main effects
 was performed (Table 2; Fig. 2).  
 <em>Scaling up site-synchrony to
 fragment-level</em>  
 To quantify and compare synchrony at the level of fragments all
 site-pairs with different fragment identities were filtered away (leaving
 n = 4747, n = 2412 and n = 730 for S. trutta, P. phoxinus and E. lucius).
 The level of synchrony for each fragment (i.e., the metapopulation of the
 fragment) was then estimated by calculating the arithmetic mean[13,14].
 This metric disregards spatial sampling density or dendritic structure so
 it is likely that fragments that contain sites that are more spaced out,
 or that are located in different branches, will have lower synchrony
 values, for example. While being dependent on the spatial sampling
 distribution, this metric does give an accurate view of the synchrony of
 the sampled sites.  
 <em>Consequences of synchrony for
 populations</em>  
 <em>The portfolio effect</em>
   To quantify the stability (i.e., the
 portfolio effect response variable; PE) of each fragment metapopulation we
 chose the metric and calculated the PE as outlined by the practical guide
 by Anderson and colleagues[15]. The PE is defined as the ratio of the
 observed metapopulation CV to the CV the population as if it was one
 uniform population[15]. A value of 1.5 in this metric signifies a
 metapopulation that is 1.5 times more stable than a theoretically uniform
 population. Noteworthy is that “This metric does not address the benefit
 of increases in portfolio size (e.g., metapopulation size) itself”[15],
 implying that unequal sampling in fragments ought not to be a
 problem.   To choose the
 appropriate PE metric, we first plotted the mean and variance of each
 subpopulation time series across all metapopulations on log-log axes,
 which showed a linear (as opposed to non-linear) relationship, and
 retrieved species-specific slopes of z_strutta = 1.61, z_pphoxinus = 1.68,
 and z_elucius = 1.43. Since all of these z are different from z = 2 (an
 assumption of the average-CV PE), we used the more conservative PE metric,
 the mean-variance CV[15]. To make the estimation of the PE as accurate as
 possible, the data inclusion criteria were set at similar levels of the
 salmon example in Anderson et al. (2013)[15]: Only fragments with at least
 4 subpopulations where each of the subpopulations had at least 10 sampled
 occasions were included. This resulted in a dataset of n = 40 fragments
 for trout, n = 33 fragments for minnow, and n = 26 fragments for pike. The
 mean ± SD number of sites per fragment was 13.7 ± 11.6 for S. trutta, 14.8
 ± 12.4 for P. phoxinus, and 16.6 ± 13.32 for E. lucius.
   We used linear mixed models to
 evaluate the relationship between fragment mean synchrony and the
 mean-variance portfolio effect response variable. Because some catchments
 might be represented by several fragments, we added catchment identity as
 a random effect to the model to account for any residual geographical
 non-independence.  
 <em>Other population performance
 metrics</em>   We also
 quantified five other population performances; (i) occurrence rate, (ii)
 mean log-density + 1, (iii) standard deviation in log-density, (iv)
 residual standard deviation (RSD), and (v) population trajectory slope,
 for all respective sites using all the available data (i.e., the entire
 time series of each site) (Table 1). These metrics thus have a larger
 sample size than for the portfolio effect above. The first three
 measurements were calculated at site level and then aggregated to fragment
 level by averaging the values from all sites with the same fragment
 identity. The last two measurements (residual standard deviation and
 population trajectory slope) were calculated through performing a model
 per fragment: the residual standard deviation is calculated, per fragment,
 from regressing all containing sites’ time series of log-density on years
 in interaction with site identity and using the residuals to calculate a
 population variability (Please see Supplementary Fig. S2 for visual
 explanation). An important advantage of this last way to estimate
 variability of sites in fragments is that it also detrends the data (i.e.,
 preventing longer-term trends in data from being included in estimations
 of year-to-year variability). The mean fragment trajectory slope was used
 to evaluate if level of synchrony is associated with population
 trajectory. This resulted in a dataset of n = 101 fragments for trout, n =
 70 fragments for minnow, and n = 62 fragments for pike. The mean ± SD
 number of sites per fragment was 7.35 ± 9 for S. trutta, 8.9 ± 10.2 for P.
 phoxinus, and 8.8 ± 10.8 for E. lucius.
   A justification for using a range of
 different metrics is that they all capture slightly different ecological
 aspects of population performance[13]. Some, but not all, of the metrics
 of population performance were positively correlated, and the pairwise
 correlations differ somewhat between the three species (Supplementary
 Figs. S3, S4, S5)   To
 evaluate the association between synchrony and these population
 performance metrics, we performed linear mixed models with mean fragment
 synchrony as explanatory variable, and the five different measures of
 performance as responses, respectively, for each species. The test
 statistics were recorded in Table 3.  
 The Benjamini-Hochberg method was used to adjust the p-values
 for all population metrics, including the portfolio effect in the previous
 section.   <em>Does
 adding information on barriers improve a previous
 framework?</em>   To
 investigate if adding barriers adds significantly to the predictive power
 of the recent development of a “geography of spatial synchrony in
 dendritic river networks”[7], we replicated the fluvial synchrogram
 variables defined therein in our dataset. The synchrograms developed by
 Larsen and colleagues in 2021[7] offer insights into the effects of both
 hydrological connectivity and upstream dependence among populations, while
 also capturing relationships among populations across adjacent tributaries
 and the broader landscape context. They calculate Euclidean distance (dE)
 and watercourse distance (dW) and their quotient (dE/dW) between all
 pairwise sites and subsequently recognise that sites can be separated by
 four functionally different distances: D1, D2, D3 and D4. The authors
 present four major expectations based on these four combinations of
 pair-wise distances: D1: Populations with
 small and similar dE and dW values are likely on the same network branch,
 displaying high synchrony. They are close both in terms of physical
 distance and water flow, suggesting a strong potential for interaction and
 shared dynamics. D2: Populations with large and equal
 dE and dW values are likely located on the same branch but are more
 distant. They are still expected to show intermediate synchrony,
 influenced by a combination of dispersal and a Moran effect.
 D3: Populations with small dE but much larger dW values are
 likely situated in separate but nearby branches. They should display
 intermediate synchrony, primarily driven by a Moran effect. This suggests
 that even though they may not be directly connected by water flow, there
 might still be shared environmental influences. D4:
 Populations with large dE and much larger dW values are positioned on
 distant and separate branches. They are expected to show the lowest degree
 of synchrony due to their significant spatial and hydrological
 separation. We set out to explore
 whether and how the inclusion of barriers enhances the predictive capacity
 of this framework within our dataset. Euclidean distance, watercourse
 distance and their quotient (dE/dW) were calculated for all sites. The
 classification was then done river-catchment-wise, so that the delineation
 into short or long dE, and high or low dE/dW, was set at the
 catchment-wise median values, and all pairwise observations in the present
 study were subsequently categorised into the four classes of distance (D1,
 D2, D3, D4). Two models were then performed per species, one that modeled
 the synchrony main effect of the synchrogram category, and another model
 that included main effect of synchrogram and its interaction effect with
 fragment border crossing (1/0). Akaike Information Criterion (AIC) was
 then used to compare the parsimony of these two (per species) models[16].
 We hypothesised that closely located sites (those separated by D1) would
 show the largest divergence in synchrony when either separated or not
 separated by barriers. Because of the nature of synchrony decay with
 distance, we hypothesised that differences between models would be smaller
 for D2 through D4.  
 <em>Softwares and packages used</em>
   All data manipulations, calculations
 and analyses were done in R language[17]. Widely used packages include
 those in the tidyverse ecosystem[18], lme4[11], PerformanceAnalytics[19],
 and riverdist[6]. We used the R package car[20] with the Anova function to
 estimate p-values. We used the R package performance[21] with the r2
 function to estimate conditional and marginal R2 values. Correction for
 multiple testing was done using Benjamini-Hochberg with the p.adjust
 function from stats[17] package.  
 <em>References</em>
   1.                   Bohlin T, Hamrin
 S, Heggberget TG, Rasmussen G, Saltveit SJ. 1989 Electrofishing — Theory
 and practice with special emphasis on salmonids. Hydrobiologia 173, 9–43.
 (doi:10.1007/BF00008596)  
 2.                   2003 SS‐EN 14011:2003 Water quality –
 Sampling of fish with electricity.  
 3.                   Jonsson B. 1989 Life history and habitat
 use of Norwegian brown trout (Salmo trutta). Freshwater Biology 21,
 71–86.   4.                 
  Nilsson J, Engstedt O, Larsson P. 2014 Wetlands for northern pike (Esox
 lucius L.) recruitment in the Baltic Sea. Hydrobiologia 721,
 145–154.   5.               
    Frost WE. 1943 The natural history of the minnow, Phoxinus phoxinus.
 The Journal of Animal Ecology , 139–162.
   6.                   Tyers M. 2022
 riverdist: River Network Distance Computation and Applications. See
 https://CRAN.R-project.org/package=riverdist.
   7.                   Larsen S et al.
 2021 The geography of metapopulation synchrony in dendritic river
 networks. Ecology Letters 24, 791–801. (doi:10.1111/ele.13699)
   8.                   Vendrametto
 Granzotti R, Agostinho AA, Bini LM. 2022 Drivers and spatial patterns of
 population synchrony of fish species in a floodplain. Freshwater Biology
 67, 857–872. (doi:10.1111/fwb.13886)  
 9.                   Chevalier M, Laffaille P, Grenouillet G.
 2014 Spatial synchrony in stream fish populations: influence of species
 traits. Ecography 37, 960–968. (doi:10.1111/ecog.00662)
   10.                 Terui A, Ishiyama
 N, Urabe H, Ono S, Finlay JC, Nakamura F. 2018 Metapopulation stability in
 branching river networks. Proc. Natl. Acad. Sci. U.S.A. 115.
 (doi:10.1073/pnas.1800060115)  
 11.                 Bates D, Mächler M, Bolker B, Walker S.
 2015 Fitting Linear Mixed-Effects Models Using lme4. Journal of
 Statistical Software 67, 1–48. (doi:10.18637/jss.v067.i01)
   12.                 Paridon J van,
 Bolker B, Alday P. 2022 lmerMultiMember: Multimember Random Effects
 Wrapper for lme4.   13.     
            Yang Q, Hong P, Luo M, Jiang L, Wang S. 2022 Dispersal
 Increases Spatial Synchrony of Populations but Has Weak Effects on
 Population Variability: A Meta-analysis. The American Naturalist 200,
 544–555. (doi:10.1086/720715)  
 14.                 Abbott KC. 2011 A dispersal-induced
 paradox: synchrony and stability in stochastic metapopulations. Ecology
 Letters 14, 1158–1169. (doi:10.1111/j.1461-0248.2011.01670.x)
   15.                 Anderson SC,
 Cooper AB, Dulvy NK. 2013 Ecological prophets: quantifying metapopulation
 portfolio effects. Methods Ecol Evol 4, 971–981.
 (doi:10.1111/2041-210X.12093)  
 16.                 Zuur AF, Ieno EN, Smith GM, others. 2007
 Analysing ecological data. Springer.  
 17.                 R Core Team. 2022 R: A Language and
 Environment for Statistical Computing. Vienna, Austria: R Foundation for
 Statistical Computing. See https://www.R-project.org/.
   18.                 Wickham H et al.
 2019 Welcome to the tidyverse. Journal of Open Source Software 4, 1686.
 (doi:10.21105/joss.01686)  
 19.                 Peterson BG, Carl P. 2024
 PerformanceAnalytics: Econometric Tools for Performance and Risk Analysis.
 See https://CRAN.R-project.org/package=PerformanceAnalytics.
   20.                 Fox J, Weisberg S.
 2019 An R Companion to Applied Regression. Third. Thousand Oaks CA: Sage.
 See https://www.john-fox.ca/Companion/.
   21.                 Lüdecke D,
 Ben-Shachar MS, Patil I, Waggoner P, Makowski D. 2021 performance: An R
 Package for Assessment, Comparison and Testing of Statistical Models.
 Journal of Open Source Software 6, 3139.
 (doi:10.21105/joss.03139)
description: # Barriers decouple population dynamics of riverine fish, and asynchrony
 of subpopulations promotes stability within fragments
 [https://doi.org/10.5061/dryad.05qfttf9z](https://doi.org/10.5061/dryad.05qfttf9z) ## Submitted files ### 1.1 Data files: **all_data_synchrony.csv**: This is the full data set for analysing synchrony patterns in rivers (with multimember models) for all three species (S. trutta, P. phoxinus, and E. lucius). Each row is a site-pair with its associated synchrony, between site distance (both euclidean and watercourse), flow-connectedness, etc. **rawdf.csv**: This contains the raw time-series abundance data used to calculate the portfolio effect for each fragment for all three species. The code will call this dataset at the appropriate time to calculate the portfolio effect. **pop_perf_trout.csv**: This contains the population performance metrics for each fragment for S. trutta. Each row is the mean synchrony and the population metrics for all sites in a fragment. **pop_perf_minnow.csv**: This contains the population performance metrics for each fragment for P. phoxinus. Each row is the mean synchrony and the population metrics for all sites in a fragment. **pop_perf_pike.csv**: This contains the population performance metrics for each fragment for E. lucius. Each row is the mean synchrony and the population metrics for all sites in a fragment. ### 1.2 Code files: **synchrony_final.R**: This contains the annotated/commented code to reproduce the statistics, data manipulations, and figures in this study. The code will call each data file at the appropriate moment. ## Variable descriptions ### 2.1 For full data (**all\_data\_synchrony.csv**): * variable name: *explanation* [unit] * fromid: *identifier of from-site* * toid: *identifier of to-site* * fromXY: *identifier of from-site* * toXY: *identifier of to-site* * pythdist: *pythagoran/euclidean distance between site-pairs* [m] * rivdist: *watercourse distance between site-pairs* [m] * fromXKOORLOK: *X coordinate in RT90 of from-site* * fromYKOORLOK: *Y coordinate in RT90 of to-site* * toXKOORLOK: *X coordinate in RT90 of from-site* * toYKOORLOK: *Y coordinate in RT90 of to-site* * n_years: *Number of matching sampling years between site-pairs* [years] * over_frag01: *Dichotomous variable (1/0) describing whether site-pair were in different (1) or same (0) fragment (i.e., if calculation was OVER FRAGment border)* * flowconn01: *Dichotomous variable (1/0) describing whether site-pair were FLOW-CONNected.* * rivdistlg: *watercourse distance between site-pairs but log-transformed* [log-transformed meters] * river_id: *ID given to river (synonymous with catchment)* * trout_rho: *the synchrony in TROUT fluctuations between to-site and from-site* [Spearman's rho] * trout_n_gt0_two: *how many pair-wise observations where both sites have more than 0 density.* * pike_rho: *the synchrony in PIKE fluctuations between to-site and from-site* [Spearman's rho] * pike_n_gt0_two: *how many pair-wise observations where both sites have more than 0 density.* * minnow_rho: *the synchrony in MINNOW fluctuations between to-site and from-site* [Spearman's rho] * minnow_n_gt0_two: *how many pair-wise observations where both sites have more than 0 density.* * sqrt_rivdist: *watercourse distance between site-pairs but square root-transformed* [square root-transformed meters] * sqrt_pythdist: *pythagoran/euclidean distance between site-pairs but squareroot-transformed* [square root-transformed meters] * random_site3: *Random effect site identifier for LmerMultiMember to function* * unique_frag: *Unique identifier for all fragments* * dedw: *euclidean distance (ed) divided by watercourse distance (dw)* [unitless] * median_ed: *catchment specific median for ed* [unitless] * median_dedw: *catchment specific median for ed/dw* [unitless] * cat: *The synchrogram category (see Larsen et al., 2021) describing what type of distance that separates the site-pairs* ### 2.2 For raw density data (**rawdf.csv**) * variable name: *explanation* [unit] * XKOORLOK: *X coordinate in RT90 of site* * YKOORLOK: *Y coordinate in RT90 of site* * unique_frag: *Unique identifier for all fragments* * riverID: *ID given to river (synonymous with catchment)* * year: *sampled year* [year] * ÖringTOT_mean: *mean density of brown trout* [individuals per 100m²] * Elrit_mean: *mean density of Eurasian minnow* [individuals per 100m²] * Gädda_mean: *mean density of northern pike* [individuals per 100m²] ### 2.3 For fragment data (**pop\_perf\_trout.csv**, **pop\_perf\_minnow\.csv**, **pop\_perf\_pike.csv**): *(Replace "SPECIES" with either "trout", "minnow", or "pike" in the variable names below depending on the species dataset.)* * variable name: *explanation* [unit] * unique_fragment: *Unique identifier for all fragments* * river_id: *ID given to river [synonymous with catchment)* * arith_rho: *arithmetic mean synchrony of fragment* [mean rho] * SPECIES_occ: *mean occurrence of SPECIES within fragment* [mean occurrence rate] * SPECIES_mean: *mean log(density +1) of SPECIES within fragment* [log-transformed individuals per 100m^2] * SPECIES_sd: *standard deviation in log-density of SPECIES within fragment* [log-transformed individuals per 100m^2] * SPECIES_rsd: *residual standard deviation of SPECIES within fragment* [log-transformed individuals per 100m^2] * SPECIES_slope: *population trajectory (mean slope) of SPECIES within fragment* [log-transformed individuals per 100m^2] * n_occasions: *number of unique fishing occasions within fragment* [years] * n_sites: *number of sites within fragment* [sampling sites] ## 3.0 R and R package versions ``` &gt; sessionInfo() R version 4.4.2 (2024-10-31 ucrt) Platform: x86_64-w64-mingw32/x64 Running under: Windows 11 x64 (build 22631) Matrix products: default locale: [1] LC_COLLATE=Swedish_Sweden.utf8 LC_CTYPE=Swedish_Sweden.utf8 [3] LC_MONETARY=Swedish_Sweden.utf8 LC_NUMERIC=C [5] LC_TIME=Swedish_Sweden.utf8 time zone: Europe/Stockholm tzcode source: internal attached base packages: [1] stats graphics grDevices utils datasets methods base other attached packages: [1] ggplot2_3.5.1 gridExtra_2.3 flextable_0.9.7 [4] broom.mixed_0.2.9.6 lme4_1.1-36 Matrix_1.7-1 [7] stringr_1.5.1 dplyr_1.1.4 pacman_0.5.1 [10] lmerMultiMember_0.11.8 loaded via a namespace (and not attached): [1] gtable_0.3.6 xfun_0.50 insight_1.0.1 [4] lattice_0.22-6 vctrs_0.6.5 sjstats_0.19.0 [7] tools_4.4.2 Rdpack_2.6.4 generics_0.1.3 [10] datawizard_1.0.0 parallel_4.4.2 tibble_3.2.1 [13] pkgconfig_2.0.3 data.table_1.16.4 ggeffects_2.1.0 [16] uuid_1.2-1 lifecycle_1.0.4 compiler_4.4.2 [19] textshaping_1.0.0 sjmisc_2.8.10 munsell_0.5.1 [22] codetools_0.2-20 fontLiberation_0.1.0 fontquiver_0.2.1 [25] htmltools_0.5.8.1 pillar_1.10.1 furrr_0.3.1 [28] nloptr_2.1.1 tidyr_1.3.1 MASS_7.3-61 [31] openssl_2.3.1 reformulas_0.4.0 boot_1.3-31 [34] nlme_3.1-166 parallelly_1.42.0 fontBitstreamVera_0.1.1 [37] zip_2.3.2 tidyselect_1.2.1 sjlabelled_1.2.0 [40] digest_0.6.37 performance_0.13.0 stringi_1.8.4 [43] future_1.34.0 purrr_1.0.2 listenv_0.9.1 [46] forcats_1.0.0 splines_4.4.2 fastmap_1.2.0 [49] grid_4.4.2 colorspace_2.1-1 cli_3.6.3 [52] magrittr_2.0.3 broom_1.0.7 withr_3.0.2 [55] gdtools_0.4.1 scales_1.3.0 backports_1.5.0 [58] rmarkdown_2.29 officer_0.6.7 globals_0.16.3 [61] ragg_1.3.3 askpass_1.2.1 sjPlot_2.8.17 [64] evaluate_1.0.3 knitr_1.49 rbibutils_2.3 [67] rlang_1.1.5 Rcpp_1.0.14 glue_1.8.0 [70] xml2_1.3.6 rstudioapi_0.17.1 minqa_1.2.8 [73] R6_2.5.1 systemfonts_1.2.1 ```