DOI: 10.5061/dryad.fqz612k2j
title: Effects of species richness and turnover on ecosystem functioning in heterogeneous environments of two tropical mountains

description: Aim Progress has been made in understanding the relationship between
 biodiversity and ecosystem functioning (BEF) in both experimental and
 real-world ecosystems. Yet, we have a limited understanding of the extent
 to which biodiversity affects ecosystem functioning in heterogeneous
 environments and whether variation in ecosystem functioning between
 communities is related to variation in species richness or turnover. Here,
 we quantify the relative contribution of variation in species richness and
 species turnover to variation in ecosystem functioning between communities
 (i.e., the diversity effect) along two tropical elevational gradients.
 Location Andes (Ecuador) and Mt. Kilimanjaro (Tanzania). Taxa studied
 Woody plants, springtails, soil arthropods, ants, and frugivorous birds.
 Methods We collected data on seven ecosystem functions, including biomass
 and process rates, across six ecosystem types along the two elevational
 gradients. We then combine the ecological Price equation with the concept
 of β-diversity to quantify how the diversity effect is shaped by
 environmental heterogeneity within and across ecosystem types, and whether
 the effect of environmental heterogeneity is primarily mediated by
 variation in species richness or species turnover. Results The diversity
 effect on ecosystem functioning increased consistently with environmental
 heterogeneity on both mountains. Species richness and turnover, on
 average, contributed similarly to the diversity effect on ecosystem
 functioning in both mountain regions, but effect sizes varied across
 functions. The increase in the diversity effect with environmental
 heterogeneity was primarily mediated by species richness, while species
 turnover played a secondary role in mediating the effects of environmental
 heterogeneity. Main Conclusions Our study reveals that the diversity
 effect on ecosystem functioning increases with environmental heterogeneity
 and that species richness, rather than species turnover, primarily drives
 this relationship. The dominant role of species richness in mediating the
 effect of environmental heterogeneity indicates that BEF relationships
 along environmental gradients are strongly influenced by environmental
 filters that limit local species coexistence.
description: <em>Methods: Study area</em> The
 <strong>Ecuadorian Andes</strong> have been formed by tectonic
 activity whereby the subduction of the Pacific plate under the continental
 plate uplifted the mountain cahin with its origin in the early Miocene or
 earlier (Evenstar et al. 2015). In the Ecuadorian
 Andes, the data was collected at three sites in southern Ecuador located
 in and next to the Podocarpus National Park (PNP) (Beck et al., 2019,
 Bendix et al. 2021). Here, the annual mean temperature ranges between 19°C
 and 13°C (Richter 2003; Bendix et al. 2006). The study sites experience a
 tropical humid climate with annual precipitation ranging from
 approximately 2,300 mm at 1,850 m a.s.l. to over 6,000 mm at 3,100 m a.s.l
 (Bendix et al. 2006). The wet season, which is exceptionally moist, occurs
 from April to July, while a period with less precipitation extends from
 September to December. The central research station is located in the
 valley of Rio San Francisco (Estación Científica San Francisco; Lat.
 3°58’18’’ S (-3.971667), Long. 79°4’45’’ W (-79.079167); Beck et al.,
 2019). Study sites with premontane rainforest (at elevations of ~1,000 m
 a.s.l.) were located at the Bombuscaro area within PNP. Study sites with
 montane rainforest (at elevations of ~2,000 m a.s.l.) were located at the
 humid eastern slopes of the main Cordillera, in the valley of the Rio San
 Francisco at the border of the PNP (Reserva Biológica San Francisco).
 Study sites at the upper montane sites (elevations of ~3,000 m a.s.l.)
 were located at the Cajanuma area of PNP. Study sites in disturbed forests
 were located on private land next to the PNP, mostly embedded in pastures,
 pasture successions with southern bracken fern or exotic tree plantations
 (pines) (Knoke et al. 2014, 2016; Curatola Fernández et al.
 2015).   <strong>Mt.
 Kilimanjaro</strong> is a dormant volcano from the Pleistocene or
 earlier covering multiple climatic and cultivation zones (Wilcockson 1956;
 van der Plas et al. 2021). Here, data was collected at the southern and
 southeastern slopes (Tanzania, East Africa; 2° 45′–3° 25′ S, 37° 00′–37°
 43′ E) (Peters et al. 2019). Mt. Kilimanjaro covers lowlands with
 elevations of 700 m a.s.l. to a snow-capped summit with an elevation of
 5,895 m a.s.l. However, for this study, we focused on elevations up to
 ~3,000 m a.s.l. The mean annual temperature ranges within the studied
 elevational range between 4-18°C at the lowlands to 8.8-10°C at
 2,770-3,060 m a.s.l (Peters et al. 2019). The mean annual precipitation
 peaks at ~2,200 m a.s.l. with 2700 mm (Hemp 2006a). Mt. Kilimanjaro is
 characterized by a rainy season that lasts from March to May and short
 rains in November (Hemp 2006a; Peters et al. 2019). Mt. Kilimanjaro has
 been characterized for a long time by land use and thus natural ecosystem
 types (in particular in the lowlands) have been degraded by fire, wood
 extraction, and agroforestry practices (Hemp 2006a, b). Only the area
 above 1,800 m a.s.l. is protected and has been designated as a national
 park (Mt. Kilimanjaro National Park; (Hemp 2006b; Peters et al.
 2019). <em>Methods: Study
 design</em> Data was collected on 15 to 67 study
 sites (median = 18 study sites) in the <strong>Ecuadorian
 Andes</strong>, south-eastern Ecuador, and 12 to 30 study sites
 (median = 29 study sites) on <strong>Mt. Kilimanjaro</strong>,
 Tanzania. In both mountain regions, we covered an elevational gradient of
 approximately 1,000-3,000 m.a.s.l. In the <strong>Ecuadorian
 Andes</strong>, data was collected in undisturbed premontane forest
 and disturbed premontane forest at elevations of 960–1,268 m a.s.l., in
 undisturbed lower montane forest and disturbed lower montane forest at
 elevations of 1,850–2,450 m a.s.l. as well as in undisturbed upper montane
 forest and disturbed upper montane forest at elevations of 2,679–2,931 m
 a.s.l. (Supplementary Methods Table 1). At <strong>Mt.
 Kilimanjaro</strong>, Tanzania, sampling was performed in
 undisturbed and disturbed lower montane forest (i.e., chagga home gardens)
 at elevations of 1,171–2,097 m a.s.l., undisturbed and disturbed
 <em>Ocotea</em> forest at elevations of 2,150–2,741 m a.s.l.,
 <em>Podocarpus</em> forest at elevations of 2,720-2,970 m
 a.s.l. as well as in undisturbed and disturbed podocarpus forest at
 elevations of 2,753–3,009 m a.s.l. (Supplementary Methods Table
 1). <em>Methods: Environmental
 variables</em> The methods for measuring the
 environmental variables in this study were previously explained in detail.
 We offer a concise summary with a reference to the respective publications
 (Appelhans et al. 2016; Peters et al. 2019).
 <em>Methods: Soil variables</em>
 In the Ecuadorian Andes, soil properties were determined to
 represent the upper 0.5 m of the mineral soil. Two sampling designs were
 used depending on the location: Soils were sampled from three profiles on
 18 study sites along the elevation gradient from 1,000-3,000 m a.s.l. and
 at 8-10 profiles along transects in four micro-catchments at 1,900-2,200 m
 a.s.l. Soil profiles were excavated down to 1 m depth and representative
 samples were taken from each horizon of the mineral soil. The samples were
 dried at 40 °C, sieved to &lt;2 mm and an aliquot milled in a
 planetary ball mill (PM400, Retsch, Haan, Germany). Total C and N content
 were measured by elemental analysis (Flash 2000 HT Plus, Thermo
 Scientific, Bremen, Germany) via thermal combustion at 1020 °C. The total
 P content was determined after microwave digestion (Mars 6, CEM,
 Kamp-Lintfort, Germany) with HNO3, H2O2, and HF by ICP-OES (5100 OES VDV,
 Agilent Technologies, Waldbronn, Germany). We calculated a weighted
 average of the measured element contents to 0.5 m mineral soil depth by
 considering the thickness and density of each soil layer. Because the
 soils were free of carbonates, total C corresponds to organic carbon
 (Corg). To determine the content of soil organic carbon at Mt.
 Kilimanjaro, samples of the organic horizon and the mineral soil (0-5cm)
 were collected at five locations per study site. Mineral soil and organic
 horizon materials were air-dried until constant weight. Soil was sieved to
 2 mm with visible root fragments being further removed, while the organic
 horizon material was shredded prior to grinding with a mixer mill (MM200,
 Retsch, Haan, Germany) (Peters et al. 2019). All samples were analyzed
 using dry combustion elemental analyzer (Flash EA1112, Thermo Scientific,
 Bremen, Germany) to determine the C content (i.e., Corg, because all soils
 were carbonate-free) at 950 °C. Individual element contents of soil and
 the organic layer were averaged across the five locations for each study
 site. To quantify the C/N and N/P ratios, mineral soil samples were
 collected from soil pits at 10 cm intervals using a standard soil auger.
 Mineral soil samples were dried at 60 °C for 24 h and root and plant
 materials removed by sieving to &lt; 2 mm before grinding them for
 further analysis. The total C and N concentrations of the soils were
 measured using an elemental analyzer (Vario EL, Elementar) at 950 °C. The
 total P content was determined using inductively coupled plasma optical
 emission spectrometry (Spectro Analytical Instruments) after pressure
 digestion with concentrated HNO3. <em>Methods:
 Climate variables</em> In the
 <strong>Ecuadorian Andes</strong>, temperature and
 precipitation information was gathered for each 1-ha site. The average
 monthly temperature (i.e., the monthly mean of daily mean temperatures)
 was acquired using an air temperature regionalization tool developed
 specifically for the study region (Fries et al. 2012). Monthly mean
 precipitation (i.e., the average of the monthly precipitation sum) was
 gathered with a hybrid approach blending ground-based and space-born
 remote sensing data (using local area weather radar and satellite imagery)
 with observation data of the meteorological gauge network (Rollenbeck
 & Bendix, 2011, Bendix et al. 2017). To assess
 the climatic conditions at the study sites at <strong>Mt.
 Kilimanjaro,</strong> mean annual temperature and mean annual
 precipitation was assessed. To measure annual temperature, we installed
 temperature sensors approximately 2 meters above the ground at all study
 sites (Peters et al. 2019). The sensors recorded temperature at 5-minute
 intervals for about 2 years. The mean annual temperature (°C) was
 calculated by averaging all the measurements per study site. Mean annual
 precipitation (mm yr<sup>−1</sup>) was estimated by
 interpolating a 15-year dataset from a network of about 70 rain gauges on
 Mt. Kilimanjaro using a co-kriging approach (Appelhans et al. 2016; Peters
 et al. 2016). <em>Methods: Ecosystem
 functions</em> In each mountain region, data on
 seven ecosystem functions belonging to either biomass stock or process
 rates were collected (Supplementary Methods Table 2). We were able to
 directly measure the species-specific functional contributions for 5 out
 of 7 functions in each community. However, we did not have direct
 estimates for the functional contributions of litter decomposition by
 oribatid mites and springtails. Instead, we assumed that the functional
 contribution of a species was proportional to its relative abundance or
 biomass at each site. <em>Methods: Biomass
 stocks</em> To determine the biomass stocks of
 <strong>springtails, oribatid mites, ants, and birds</strong>
 in the **Ecuadorian Andes <strong>and</strong> at Mt.
 Kilimanjaro at each study site, we combined data on species abundances
 with data on species-specific per capita mass. Species abundances at each
 study site were assessed using standardized methods with taxon-specific
 sampling techniques, which have been detailed in previous studies (for
 Ecuador: Marian et al., 2018; Santillán et al., 2018; Tiede et al., 2017;
 for Kilimanjaro: Peters et al., 2016). To estimate the per capita mass for
 birds, we used existing literature (Dunning 2008; Wilman et al. 2014). For
 ants and springtails, we applied allometric equations to morphometric
 measures (i.e., head length for ants, and total body length for
 springtails) to derive species-specific estimates of per capita mass.
 Morphometric measurements were taken from up to ten randomly selected
 individuals per species using a binocular microscope with a calibrated
 ocular micrometer. The individual biomass estimated using allometric
 equations closely matched the true biomass determined with a precision
 scale. In the <strong>Ecuadorian
 Andes</strong>, we included only trees (no shrubs) with a diameter
 at breast height greater than or equal to 10 cm (Homeier &
 Leuschner, 2021). We used basal area as a proxy for aboveground biomass
 (AGB). We calculated the species-specific basal area by summing the
 individual basal area measurements for each species at each study site. To
 determine the aboveground <strong>biomass stocks</strong> of
 <strong>woody plants</strong> at <strong>Mt.
 Kilimanjaro</strong>, we included all woody plant individuals that
 were taller than 1.3 m and had a diameter at breast height greater than or
 equal to 10 cm (trees) or less than 10 cm (shrubs) (Ensslin et al. 2015).
 We applied pantropical allometric equations to measures of plant height,
 diameter at breast height, and wood density (Ensslin et al. 2015). We
 calculated species-specific aboveground biomass stocks by summing
 individual biomass estimates for each species at each study
 site. <em>Methods: Process
 rates</em> To measure seed dispersal by birds,
 resource use by ants, and litter decomposition by microorganisms,
 process-specific protocols were used. The approach for <strong>seed
 dispersal</strong> measurement by birds followed standardized
 methods, which have been previously described in the literature (Ecuador:
 Quitián et al., 2018; Mt. Kilimanjaro: Albrecht et al., 2018). In the
 <strong>Ecuadorian Andes as well as at Mt.
 Kilimanjaro</strong>, bird-fruit interactions were monitored on a
 site measuring 30 m x 100 m at each study site. Birds were observed over
 four consecutive days, for a total of 25 hours, using binoculars to record
 interactions with fruiting plants. For each bird species, the number of
 visits to each fruiting plant species was recorded, as well as their
 behavior. We calculated species-specific contributions to seed dispersal
 as the number of visits to all fruiting plants by each bird species,
 considering only those visits that involved legitimate seed removal
 events, such as swallowing or carrying away fruits from the mother
 plants. To assess <strong>resource use by
 ants</strong>, bait experiments were conducted at each study site.
 In the <strong>Ecuadorian Andes</strong>, six 50 ml Falcon
 tubes were used at five subplots, respectively (Tiede et al. 2017). At
 <strong>Mt. Kilimanjaro</strong>, thirty 50 ml Falcon tubes
 were placed along three 50-m transects at ground level (Peters et al.
 2014). In the Ecuadorian Andes, each tube contained 15 mL and at
 <strong>Mt. Kilimanjaro</strong> 10 mL of nutrient solutions,
 such as sugar, sugar-protein, protein, water, salt, or oil, with five
 replicates per nutrient. In the <strong>Ecuadorian
 Andes</strong>, ant data was collected at 1,000, 1,500, 2,000,
 2,500, and 3,000 m a.s.l. after 2, 3, 4, 4.5, and 5 hours, respectively.
 Based on the occurrence of ants at the baits, the species-specific
 contributions to resource use were calculated as the proportion of baits
 detected by each ant species. In cases where more than one ant species was
 recorded at a bait, we assigned species-specific contributions to resource
 use in proportion to the relative abundance of each ant species at that
 bait. At <strong>Mt. Kilimanjaro</strong>, the baits were
 collected after two hours and the number of individuals of each ant
 species that were present at each bait were recorded.
 To study net <strong>litter decomposition
 rates</strong>, standardized litter bags with leaves or roots (with
 a 4 mm mesh and containing 10 g of leaves or roots) were utilized in the**
 Ecuadorian Andes**. 120 litterbags were placed at each study site, with
 one at each elevational level, and collected after 6, 12, 24, 36, and 48
 months. We followed an established protocol to process the leaves and
 roots (Marian et al. 2017). Decomposition rates were calculated based on
 the remaining carbon (CR) in the litterbags at the sampling dates (n)
 expressed as a percentage of the initial amount of carbon placed in the
 litterbags (C0). Changes in the remaining nitrogen (NR) were similarly
 expressed as a percentage of the initial amount of nitrogen placed in the
 litterbags (N0). We used the following formulas: CR [%] = (Cn/C0) × 100
 and NR [%] = (Nn/N0) × 100, with Cn and Nn being the amount of carbon and
 nitrogen remaining at each sampling date n. We calculated the contents of
 carbon (CC) and nitrogen (NC) in the litter using the following equations:
 CC [%] = (Cn/DWn) × 100 and NC [%] = (Nn/DWn) × 100, with DWn being the
 dry weight of litter remaining at sampling date n. At
 **Mt. Kilimanjaro **litter decomposition rates were assessed using
 litterbags filled with dried maize straw (10 cm x 15 cm, 20 μm x 20 μm
 mesh size, and containing 5 ± 0.05 g of maize husks; Peters et al., 2019).
 Three bags were placed at each study site and collected after 69 to 86
 days. To process the leaves, established protocols were applied. Due to
 logistical reasons, bags at lower elevations were exposed for a longer
 time than bags at higher elevations. To adjust for these differences,
 decomposition rates per day were calculated using the equation k =
 −ln(m<sub>LOI</sub> / m<sub>OAF</sub>) / t, where
 m<sub>LOI</sub> is the weight after loss-on-ignition,
 m<sub>OAF</sub> is the original ash-free weight, and t is the
 number of days the bags have been exposed. The decomposition rates per
 study site were averaged. In both the
 <strong>Ecuadorian Andes and at Mt. Kilimanjaro</strong>, we
 did not have direct measures of species-specific contributions to litter
 decomposition. Thus, we estimated the specific contribution of each
 species to decomposition at each site based on the relative abundance of
 each species at that site. In the <strong>Ecuadorian
 Andes</strong>, decomposition rates were related to the abundance of
 oribatid mites (Marian et al. 2018) and at <strong>Mt.
 Kilimanjaro</strong> to springtails (Peters et al. 2016).
 <em>Methods: Analytical approach</em>
 <em>Quantifying the effect of diversity on ecosystem
 functioning.</em> The framework is generally applicable to any
 ecosystem function that is determined by the summed functional
 contributions of individual species. It is based on a community matrix
 <strong>F</strong> (<em>n</em> ×
 <em>s</em>), which summarizes the contribution of
 <em>s</em> species to a given ecosystem function in
 <em>n</em> study sites (which we refer to as communities;
 Albrecht et al., 2021). Each element *f<sub>ij</sub> *of
 matrix <strong>F</strong> represents the contribution of
 species <em>j</em> to a given ecosystem function at study site
 <em>i.</em> Using matrix <strong>F</strong>, we
 constructed three binary matrices <strong>P</strong>,
 <strong>Q</strong>, and <strong>O</strong>. Matrix
 <strong>P</strong> is a binary species incidence matrix (with
 the same dimensions as F, in which *p<sub>ij</sub> *= 1 if
 <em>f<sub>ij *&gt; 0 and *pij</sub></em> = 0
 otherwise). Further, matrix <strong>Q</strong> is the
 complement of matrix <strong>P</strong>
 (<strong>Q</strong> = 1 – <strong>P</strong>), so
 that <em>q<sub>ij</sub></em> = 1 if
 <em>f<sub>ij *= 0 and *qij</sub></em> = 0
 otherwise. And finally, matrix <strong>O</strong> is given by
 the sum of matrices <strong>P</strong> and
 <strong>Q</strong>, so that all elements
 <em>o<sub>ij</sub></em> = 1. The total difference
 in the magnitude of a given ecosystem function between two communities
 <em>i</em> and <em>j</em> is given by the element
 ∆<em>f<sub>ij</sub></em> of the
 <em>n</em> × <em>n</em> square matrix
 <strong>∆F</strong> =
 <strong>FO</strong><sup>T</sup> –
 <strong>OF</strong><sup>T</sup>. The difference in
 the magnitude of an ecosystem function between two communities
 <em>i</em> and <em>j</em> caused by changes in the
 functional contributions of shared species is given by the element
 ∆s<sub>ij of the n × n square matrix <strong>∆S</strong>
 = <strong>FP</strong><sup>T</sup> –
 <strong>PF</strong><sup>T</sup>. Lastly, the
 difference in the magnitude of a given ecosystem function between two
 communities i and j caused by differences in species richness and species
 turnover between communities is represented by the element
 ∆*dij</sub> of the n × n square matrix
 <strong>∆D</strong> =
 <strong>FQ</strong><sup>T</sup> –
 <strong>QF</strong><sup>T</sup>.
 Equation (1) comprises three components that possess the
 dimension of the corresponding ecosystem function and an expected value of
 zero if there is no overall difference in this function between
 communities <em>i</em> and <em>j</em>
 (∆<em>f<sub>ij</sub></em> = 0), no difference in
 function because of differences in species richness and species turnover
 (∆<em>d<sub>ij</sub></em> = 0), or no difference
 in function because of differences in the functional contributions of
 shared species (∆<em>s<sub>ij</sub></em> = 0). The
 components can be positive or negative, and the diversity and shared
 species components may cancel each other out, resulting in a net
 difference in the function of zero. Note that the formula presented in
 equation (1) represents a simplified version of the of the 5-part and
 3-part Price equation presented in Fox and Kerr (2012) and Bannar-Martin
 et al. (2018). However, the formulation described here overcomes an
 important limitation of previous frameworks (Fox and Kerr 2012;
 Bannar‐Martin et al. 2018), as it can be applied to any pair of
 communities, regardless of whether they have species in common.
 Using equation (1), we calculated the relative contribution of
 the diversity of the focal taxa to variation in their ecosystem functions
 between communities, which we refer to as the diversity effect
 (Y). Where the absolute values of
 ∆<em>d<sub>ij</sub></em> and
 ∆<em>s<sub>ij</sub></em> are denoted as
 |∆<em>d<sub>ij</sub></em>| and
 |∆<em>s<sub>ij</sub></em>|, respectively. Absolute
 values are used because ∆<em>d<sub>ij</sub></em>
 and ∆<em>s<sub>ij</sub></em> can either be
 positive or negative, thus computing the mean of these values would mask
 the total contribution of both factors. The diversity effect is a
 dimensionless measure that ranges from 0 to 1. The diversity effect equals
 0 if all differences in ecosystem functioning between communities result
 from differences in the functional contributions of shared species, which
 can be attributed to differences in abundance or individual performance.
 Conversely, the diversity effect equals 1 if all differences in ecosystem
 functioning result from the combined effects of differences in species
 richness and turnover between communities. For worked example scenarios of
 how changes in species richness, species turnover, or the functional
 contribution of shared species are related to the diversity effect see
 Fig. S1.1 in Supporting Information. Because our metric
 for the diversity effect is an absolute measure, we also quantified the
 correlations of the raw values of
 ∆<em>f<sub>i</sub></em> with
 ∆<em>d<sub>i</sub></em> and
 ∆<em><sub>si</sub></em> to assess how strongly
 total variation in ecosystem functioning between communities
 (∆<em>f<sub>i</sub></em>) is related to variation
 in ecosystem functioning, due to differences in species richness and
 turnover (∆<em>d<sub>i</sub></em>), and to
 variation in ecosystem functioning, due to changes in the contributions of
 shared species (∆<em>s<sub>i</sub></em>; Fig.
 S1.3). Across all 14 functions as well as for individual functions, we
 observed a strong positive correlation between
 ∆<em>f<sub>i</sub></em> and
 ∆<em>d<sub>i</sub></em>~ (Fig. S1.3 and Table
 S1.11). Moreover, across the 14 ecosystem functions, the diversity effect
 was strongly positively related to the correlations between
 ∆<em>fi</em> and ∆<em>di</em> of individual
 functions (r = 0.78; Fig. S1.3) and strongly negatively related to the
 correlation between ∆*fi~ *(and
 ∆<em>s<sub>i</sub></em>~ ~(r = -0.89; Fig. S1.3).
 This indicates that our metric of the diversity effect is able to quantify
 the contribution of differences in species richness and turnover to the
 total variation in ecosystem functioning between communities.
 <em>Quantifying variation in species richness and
 turnover.</em> We used the Jaccard index to partition the variation
 in species composition (<em>β</em>) into variation resulting
 from differences in species richness (<em>R</em>) and species
 turnover (<em>T</em>) between <em>n</em>
 communities (Albrecht et al. 2021). The species richness and turnover
 components form an additive partition of the total variation in species
 composition, meaning that <em>β = R + T</em> (Legendre 2014).
 To estimate the total variation in species composition and its two
 components, we calculated the number of shared species, unique species in
 community* i*, and unique species in community* j*, using the species
 incidence matrix <strong>P</strong> and its complement
 <strong>Q</strong>. The number of shared species between
 communities* i* and <em>j</em> is represented by element
 <em>a<sub>ij</sub></em> of the
 <em>n</em> × <em>n</em> matrix
 <strong>A</strong> =
 <strong>PP</strong><sup>T</sup>, the number of
 species unique to community <em>i</em> by element
 <em>b<sub>ij</sub></em> of the
 <em>n</em> × <em>n</em> matrix
 <strong>B</strong> =
 <strong>PQ</strong><sup>T</sup>, and the number of
 species unique to community <em>j</em> by element
 c<em><sub>ij</sub></em> of the
 <em>n</em> × <em>n</em> matrix
 <strong>C</strong> =
 <strong>QP</strong><sup>T</sup>. Using these
 matrices, we can express the total variation in species composition
 (<em>β</em>), the richness component (<em>R</em>),
 and the turnover component (<em>T</em>).
 <em>Quantifying environmental heterogeneity.</em> We
 used the Gower distance to determine the environmental distance
 <em>h</em> between sites based on a set of environmental
 variables. The Gower distance between two sites* i* and
 <em>j</em> equals the mean difference in environmental
 variables across all environmental variables after standardizing the
 environmental variables by their ranges. In equation
 (6), <em>n</em> is the number of environmental variables,
 <em>x<sub>ik</sub></em> and
 <em>x<sub>jk</sub></em> are the values of variable
 <em>k</em> on study sites <em>i</em> and* j.* The
 Gower distance is preferred over the Euclidean distance as it is less
 sensitive to extreme values and facilitates the inclusion of categorical
 measures. Moreover, the range standardization ensures that each
 environmental variable contributes equally to the distance metric, and the
 maximum value of the distance function is 1. As some study sites had
 missing data for some environmental variables, we calculated the pairwise
 distances by using a pairwise deletion of missing observations. We defined
 environmental heterogeneity (<em>H</em>) as the mean
 environmental distance between <em>n</em> combinations of
 study sites. Quantifying how environmental
 heterogeneity modulates the effect of diversity on ecosystem functioning.
 To quantify the direct effect of environmental heterogeneity on the
 diversity effect as well as the indirect effects that are mediated by
 variation in species richness and species turnover within and across
 ecosystem types, we segmented the distance matrices for Y, R, T and H into
 submatrices that contained comparisons within single and across multiple
 ecosystem types (Fig. 1d). Then, we averaged these submatrices to obtain
 estimates for Y, R, T and H for comparisons between sites based on
 different numbers of ecosystem types (Fig. 1e).
  
description: # Effects of species richness and turnover on ecosystem functioning in
 heterogeneous environments of two tropical mountains Dataset DOI:
 [10.5061/dryad.fqz612k2j](https://doi.org/10.5061/dryad.fqz612k2j) ##
 Description of the data and file structure ***The following environmental
 variables were assessed:*** * Soil variables:  Soil organic carbon (g/kg
 soil), Soil C:N ratio (no unit), Soil N:P ratio (no unit) * Climate
 variables: average monthly temperature (°C) and monthly mean precipitation
 (mm) ***The following ecosystem functions were assessed:*** * biomass
 stock of springtails (g), oribatid mites (g), ants (g), birds (g), and
 woody plants (mg/ha in Tanzania; m2/ha in Ecuador) * process rates: seed
 dispersal by birds (interaction frequency per 25h), resource use by ants
 (proportion of baits used per 2h) , and litter decomposition by
 mocroorganisms (mites and springtails; decomposition rate per day) For all
 datasets: NA values indicate that values are not available. ### Files and
 variables #### File: ES03_ant_biomass_data.csv **Description:** To
 determine the biomass stocks of ants in the Ecuadorian Andes and at Mt.
 Kilimanjaro at each study site, we combined data on species abundances
 with data on species-specific per capita mass. ##### Variables * id: S01 *
 variable: ant biomass (g) * species: genus species ID * plot: Plot ID *
 session: 1 * per_capita_mass: mass (g) per individual * abundance:
 abundance (N) * functional_contribution: abundance per capita mass
 (N*g/individual) #### File: ES04_bird_biomass_data.csv **Description:** To
 determine the biomass stocks of birds in the Ecuadorian Andes and at Mt.
 Kilimanjaro at each study site, we combined data on species abundances
 with data on species-specific per capita mass. ##### Variables * id: S05 *
 variable: bird biomass (g) * species: genus species ID * plot: Plot ID *
 session: 1 * per_capita_mass: mass per individual (g/individual) *
 abundance: abundance (N) * functional_contribution: abundance * per capita
 mass (N*g/individual) #### File: TR02_springtail_decomposition_data.csv
 **Description:** To determine the litter decomposition by springtails we
 combined data on species abundances with data on litter decomposition =
 litter decomposition\n(springtails). In both the Ecuadorian Andes and at
 Mt. Kilimanjaro, we did not have direct measures of species-specific
 contributions to litter decomposition. Thus, we estimated the specific
 contribution of each species to decomposition at each site based on the
 relative abundance of each species at that site. At Mt.
 Kilimanjaro decomposition rates were related to springtails. #####
 Variables * id: S15 * variable: springtail decomposition (litter
 decomposition\n(springtails)) * species: species genus ID * plot: Plot ID
 * session: 1 * per_capita_mass: litter decomposition rate/ day *
 abundance: abundance (N) * functional_contribution: litter decomposition
 rate per day* 100 / abundance #### File: TR03_ant_resource_use_data.csv
 **Description:** To assess resource use by ants (resource use/n (ants)),
 bait experiments were conducted at each study site. Based on the
 occurrence of ants at the baits, the species-specific contributions to
 resource use were calculated as the proportion of baits detected by each
 ant species. In cases where more than one ant species was recorded at a
 bait, we assigned species-specific contributions to resource use in
 proportion to the relative abundance of each ant species at that bait.
 ##### Variables * id: R05 * variable: ant resource use (proportion of
 baits used per 2h) * species: species genus ID * plot: Plot ID * session:
 1 * per_capita_mass: proportion of baits used per 2h *
 abundance: abundance (N occurence at baits) *
 functional_contribution: proportion of baits used per 2h * 100 /
 abundance  #### File: TR04_bird_seed_dispersal_data.csv
 **Description:** In the Ecuadorian Andes as well as at Mt. Kilimanjaro,
 bird-fruit interactions were monitored. We calculated species-specific
 contributions to seed dispersal as the number of visits to all fruiting
 plants by each bird species, considering only those visits that involved
 legitimate seed removal events, such as swallowing or carrying away fruits
 from the mother plants. ##### Variables * id: R06 * variable: bird seed
 dispersal (seed dispersal/N (birds)) * species: species genus ID * plot:
 Plot ID * session: 1 * per_capita_mass: mass of seeds removed (g) *
 abundance: abundance (N birds) * functional_contribution: mass of seeds
 (g) removed per individual (interaction frequency) #### File:
 TS02_springtail_biomass_data.csv **Description:** To determine the biomass
 stocks of springtails we combined data on species abundances with data on
 species-specific per capita mass. ##### Variables * id: S15 * variable:
 springtail biomass (g) * species: genus species ID * plot: Plot ID *
 session: 1 * per_capita_mass: mass per individual (g/individual) *
 abundance: abundance (N) * functional_contribution: abundance (N) * per
 capita mass (g/individual) #### File: TS03_ant_biomass_data.csv
 **Description:** To determine the biomass stocks of ants we combined data
 on species abundances with data on species-specific per capita mass. #####
 Variables * id: S14 * variable: ant biomass (g) * species: genus species
 ID * plot: Plot ID * session: 1 * per_capita_mass: mass per individual
 (g/individual) * abundance: abundance (N) *
 functional_contribution: abundance (N) * per capita mass (g/individual)
 #### File: TS04_bird_biomass_data.csv **Description:** To determine the
 biomass stocks of birds we combined data on species abundances with data
 on species-specific per capita mass. ##### Variables * id: S05 * variable:
 bird biomass (g) * species: genus species ID * plot: Plot ID * session: 1
 * per_capita_mass: mass per individual (g/individual) *
 abundance: abundance (N) * functional_contribution: abundance (N) * per
 capita mass (g/individual) #### File:
 00_study_site_characteristics_combined.xlsx **Description:** Data
 containing info on elevational level, plot coordinates and temperature and
 precipitation of each plot ##### Variables * region: Tanzania or Ecuador *
 plot: Plot ID * plot2: Plot name * habitat_description: studied ecosystem
 types * belt: elevational category * lu: 0 (undisturbed), 1 (disturbed) *
 lon: longitude (Degrees, Minutes, Seconds) * lat: latitude (Degrees,
 Minutes, Seconds) * x: x coordinate * y: y coordinate * epsg_code:
 coordinate system * elev: exact elevation (m a.s.l.) * map: precipitation
 (mm) * mat: temperature (°C) #### File: 00_meta_data_combined.xlsx
 **Description:** File describing all assessed variables ##### Variables *
 idOrig: id of each variable * id: country and number of function * region:
 Tanzania or Ecuador * range: Kilimanjaro or Andes * domain: eukaryota *
 kingdom: plantae or animalia * phylum: plantae, chordata or arthropoda *
 class: plantae, aves, insecta, plantae or entognatha * taxon: plantae,
 aves, hymenoptera, collembola or oribatida * variable: variable name *
 taxon_variable: full variable name * type: biomass stock or process rate *
 direct: direct measurement false or true * description: assessment details
 * unit: unit of measurement * mass_information: literature data or
 allometric equation * per_capita*_*mass_reference: literature reference
 #### File: 00_study_site_characteristics_combined.csv
 **Description:** Data containing info on elevational level, plot
 coordinates and temperature and precipitation of each plot ##### Variables
 * region: Tanzania or Ecuador * plot: Plot ID * plot2: Plot name *
 habitat_description: studied ecosystem types * belt: elevational category
 * lu: 0 (undisturbed), 1 (disturbed) * lon: longitude (Degrees, Minutes,
 Seconds) * lat: latitude (Degrees, Minutes, Seconds) * x: x coordinate *
 y: y coordinate * epsg_code: coordinate system * elev: exact elevation (m
 a.s.l.) * map: precipitation (mm) * mat: temperature (°C) #### File:
 ER02_microarthropod_decomposition_data.csv **Description:**  To study net
 litter decomposition rates, standardized litter bags with leaves or roots
 were utilized. In both the Ecuadorian Andes and at Mt. Kilimanjaro, we did
 not have direct measures of species-specific contributions to litter
 decomposition. Thus, we estimated the specific contribution of each
 species to decomposition at each site based on the relative abundance of
 each species at that site. In the Ecuadorian Andes, decomposition rates
 were related to the abundance of oribatid mites. ##### Variables * id: R03
 * variable: microarthropod decomposition (litter decomposition rate per
 day) * species: genus species ID * plot: Plot ID * session: 1 *
 per_capita_mass: litter decomposition (rate/day) * abundance: abundance
 (N) * functional_contribution: litter decomposition rate per day* 100 /
 abundance #### File: ER03_ant_resource_use_data.csv **Description:** To
 assess resource use by ants, bait experiments were conducted at each study
 site. Based on the occurrence of ants at the baits, the species-specific
 contributions to resource use were calculated as the proportion of baits
 detected by each ant species. In cases where more than one ant species was
 recorded at a bait, we assigned species-specific contributions to resource
 use in proportion to the relative abundance of each ant species at that
 bait. ##### Variables * id: R01 * variable: ant resource use (proportion
 of baits used per 2h) * species: species genus ID * plot: Plot ID *
 session: 1 * per_capita_mass: proportion of baits used per 2h *
 abundance: abundance (N occurrence at baits) *
 functional_contribution: proportion of baits used per 2h * 100 / abundance
 #### File: ER05_ant_predation_data.csv **Description:** To assess
 predation by ants, predation experiments were conducted at each study
 site. This data was removed in the analysis because no predation data was
 available for Mt. Kilimanjaro. ##### Variables * id: R02 * variable: ant
 predation (proportion of caterpillars attacked) * species: species genus
 ID * plot: Plot ID * session: 1 * per_capita_mass: proportion of
 caterpillars attacked (%) * abundance: abundance (N) *
 functional_contribution: proportion of attacked dummies * 100 / abundance
 per plot #### File: ER04_bird_seed_dispersal_data.csv **Description:** In
 the Ecuadorian Andes as well as at Mt. Kilimanjaro, bird-fruit
 interactions were monitored. We calculated species-specific contributions
 to seed dispersal as the number of visits to all fruiting plants by each
 bird species, considering only those visits that involved legitimate seed
 removal events, such as swallowing or carrying away fruits from the mother
 plants. ##### Variables * id: R05 * variable: bird seed dispersal (mass of
 seeds removed (g)) * species: species genus ID * plot: Plot ID * session:
 1 - per_capita_mass: mass of seeds removed (g) - abundance: abundance (N
 birds) - functional_contribution: mass of seeds (g) removed per individual
 (interaction frequency) #### File: ES01_plant_basal_area_data.csv
 **Description:** We used basal area as a proxy for aboveground biomass
 (AGB). We calculated the species-specific basal area by summing the
 individual basal area measurements for each species at each study site.
 ##### Variables * id: S02 * variable: woody plant basal area (m2 per ha) *
 species: genus species ID * plot: Plot ID * session: 1 * per_capita_mass:
 mass per individual (m2 per ha) * abundance: abundance (N) *
 functional_contribution: sum of the individual basal area measurements for
 each species (m2 per ha*N) #### File: ES02_microarthropod_biomass_data.csv
 **Description:** To determine the biomass stocks of oribatid mites in the
 Ecuadorian Andes at each study site, we combined data on species
 abundances with data on species-specific per capita mass. ##### Variables
 * id: S03 * variable: microarthropod biomass (g) * species: genus species
 ID * plot: Plot ID * session: 1 * per_capita_mass: mass per individual (g)
 * abundance: abundance (N) * functional_contribution: abundance per capita
 mass (N * g) #### File: 00_sourceFunctions.R **Description:** R-script
 containing all functions written for the analysis. #### File:
 script_main_analysis.R **Description:** To run the analysis you simply
 need to set your working directory in R to ".../data_package/"
 and run the script file named "script_main_analysis.R" ####
 File: data_package_DDI70093.Rproj
 **Description:** 'dataSet_KilimanjaroAndes.RData' (file) -
 RData-file that contains the raw data for the analysis in R. #### File:
 correlation_data.csv **Description:** Correlation coefficients for the
 relationships between *ΔF~i~* and *ΔD~i~*, as well as for relationships
 between *ΔF~i~ *and *ΔS~i~*, for individual functions in the two mountain
 regions (Andes, Ecuador and Mt. Kilimanjaro, Tanzania). ##### Variables *
 id: region ID * region: Ecuador or Tanzania * taxon_variable: taxon
 variable * dF~dD: ΔF~i~ = mean difference in the magnitude of a given
 ecosystem function between community *i* and all other communities;
 *ΔD~i~* = mean difference in the magnitude of a given ecosystem function
 between community *i* and all other communities due to differences in
 species richness and species turnover * dF~dS:ΔF~i~ = mean difference in
 the magnitude of a given ecosystem function between community *i* and all
 other communities; ΔF~i~ = mean difference in the magnitude of a given
 ecosystem function between community *i* and all other communities; *
 dD~Rich: ΔD~i~ = mean difference in the magnitude of a given ecosystem
 function between community *i* and all other communities due to
 differences in species richness and species turnover, , Rich = average
 total difference in the magnitude of a given ecosystem function between
 community *i* and all other communities (Δ*F~i~*) with (a) average
 difference in ecosystem functioning due to changes in species richness *
 dD~Turn: ΔD~i~ = mean difference in the magnitude of a given ecosystem
 function between community *i* and all other communities due to
 differences in species richness and species turnover, Turn = average total
 difference in the magnitude of a given ecosystem function between
 community *i* and all other communities (Δ*F~i~*) with (a) average
 difference in ecosystem functioning due to changes in species turnover
 #### File: correlation_data.xlsx **Description:** Correlation coefficients
 for the relationships between *ΔF~i~* and *ΔD~i~*, as well as for
 relationships between ΔF~i~ and *ΔS~i~*, for individual functions in the
 two mountain regions (Andes, Ecuador and Mt. Kilimanjaro, Tanzania). #####
 Variables * id: region ID * region: Ecuador or Tanzania * taxon_variable:
 taxon variable * dF~dD: ΔF~i~ = mean difference in the magnitude of a
 given ecosystem function between community *i* and all other communities;
 *ΔD~i~* = mean difference in the magnitude of a given ecosystem function
 between community *i* and all other communities due to differences in
 species richness and species turnover * dF~dS:ΔF~i~ = mean difference in
 the magnitude of a given ecosystem function between community *i* and all
 other communities; ΔF~i~ = mean difference in the magnitude of a given
 ecosystem function between community *i* and all other communities; *
 dD~Rich: ΔD~i~= mean difference in the magnitude of a given ecosystem
 function between community *i* and all other communities due to
 differences in species richness and species turnover, , Rich = average
 total difference in the magnitude of a given ecosystem function between
 community *i* and all other communities (Δ*F~i~*) with (a) average
 difference in ecosystem functioning due to changes in species richness *
 dD~Turn: ΔD~i~ = mean difference in the magnitude of a given ecosystem
 function between community *i* and all other communities due to
 differences in species richness and species turnover, Turn = average total
 difference in the magnitude of a given ecosystem function between
 community *i* and all other communities (Δ*F~i~*) with (a) average
 difference in ecosystem functioning due to changes in species turnover
 #### File: environmental_summary.csv **Description:** average values,
 standard deviation, min and max values of elevation, mean annual
 temperature and annual precipitation ##### Variables *
 habitat_description: ecosystem type * region: Ecuador or Tanzania *
 elev.mean: mean of elevation (m a.s.l.) * elev.sd: standard deviation of
 elevation (m a.s.l.) * elev.min: minimum value of elevation (m a.s.l.) *
 elev.max: maximum value of elevation (m a.s.l.) * mat.mean: mean of
 temperature (°C) * mat.sd: standard deviation of temperature (°C) *
 mat.min: minimum value of temperature (°C) * mat.max: maximum value of
 temperature (°C) * map.mean: mean of precipitation (mm) * map.sd: standard
 deviation of precipitation (mm) * map.min: minimum value of
 precipitation (mm) * map.max: maximum value of precipitation (mm) *
 soilOC.mean: mean of soil organic carbon (g/kg soil) *
 soilOC.sd:  standard deviation of soil organic carbon (g/kg soil) *
 soilOC.min: minimum value of soil organic carbon (g/kg soil) *
 soilOC.max: maximum value of soil organic carbon (g/kg soil) *
 soilCN.mean: mean of C:N ratio (no unit) * soilCN.sd: standard deviation
 of C:N ratio (no unit) * soilCN.min: minimum value of C:N ratio (no unit)
 * soilCN.max: maximum value of C:N ratio (no unit) * soilNP.mean: mean of
 N:P ratio (no unit) * soilNP.sd: standard deviation of N:P ratio (no unit)
 * soilNP.min: minimum value of N:P ratio (no unit) * soilNP.max: maximum
 value of N:P ratio (no unit) ### #### File: metaDataOut.csv
 **Description:**  meta data decsription (produced by script
 'script_main_analysis.R') ##### Variables * id: country and
 number of function * region: Tanzania or Ecuador * range: Kilimanjaro or
 Andes * domain: eukaryota * kingdom: plantae or animalia * phylum:
 plantae, chordata or arthropoda * class: plantae, aves, insecta, plantae
 or entognatha * taxon: plantae, aves, hymenoptera, collembola or oribatida
 * variable: variable name * taxon_variable: full variable name * type:
 biomass stock or process rate * direct: direct measurement false or true *
 description: assessment details * unit: unit of measurement *
 mass_information: literature data or allometric equation * id2: ID name *
 selection: 1 * yR.Int: Group-specific intercept (fixed effect + random
 effect) from model `m2b`. * yR.H: Group-specific slope for variable **H**
 from model `m2b`. * vR.Int: Estimated variance (uncertainty) of the
 intercept `yR.Int`. * vR.H: Estimated variance of the slope `yR.H`. *
 yT.Int: Group-specific intercept from model `m3b`. * yT.H: Group-specific
 slope for variable **H** from model `m3b`. * vT.Int: Estimated variance of
 the intercept `yT.Int`. * vT.H: Estimated variance of the slope `yT.H`. *
 yY.Int: Group-specific intercept from model `m4b`. * yY.H: Group-specific
 slope for variable **H** from model `m4b`. * yY.R: Group-specific slope
 for variable **R** from model `m4b`. * yY.T: Group-specific slope for
 variable **T** from model `m4b`. * vY.Int: Estimated variance of the
 intercept `yY.Int`. * vY.H: Estimated variance of the slope `yY.H`. *
 vY.R: Estimated variance of the slope `yY.R`. * vY.T: Estimated variance
 of the slope `yY.T`. * pR.Int: Two-sided Wald p-value testing if `yR.Int`
 differs from 0. * pR.H: Two-sided Wald p-value testing if `yR.H` differs
 from 0. * pT.Int: Two-sided Wald p-value testing if `yT.Int` differs from
 0. * pT.H: Two-sided Wald p-value testing if `yT.H` differs from 0. *
 pY.Int: Two-sided Wald p-value testing if `yY.Int` differs from 0. *
 pY.H: Two-sided Wald p-value testing if `yY.H` differs from 0. *
 pY.R: Two-sided Wald p-value testing if `yY.R` differs from 0. *
 pY.T: Two-sided Wald p-value testing if `yY.T` differs from 0. * at: Order
 or plotting index, used to align groups visually (e.g., in plots). *
 hetRange: Maximum number of ecological types (`nEcoTypes`) per `id`
 (measure of heterogeneity). ### #### File:
 TS01_plant_aboveground_biomass_data.csv **Description:**  ##### Variables
 * id: S02 * variable: woody plant aboveground biomass (Mg per ha) *
 species: genus species ID * plot: Plot ID * session: 1 * per_capita_mass:
 mass per individual (Mg per ha) * abundance: abundance (N) *
 functional_contribution: sum of the individual basal area measurements for
 each species (Mg per ha*N) ## Code/software To run the analysis you simply
 need to set your working directory in R to ".../data_package/"
 and run the script file named "script_main_analysis.R" in the
 main folder of the package. R version 4.4.2 (2024-10-31)\ Platform:
 aarch64-apple-darwin20\ Running under: macOS Sequoia 15.6 Matrix products:
 default\ BLAS:
 /System/Library/Frameworks/Accelerate.framework/Versions/A/Frameworks/vecLib.framework/Versions/A/libBLAS.dylib\ LAPACK: /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/lib/libRlapack.dylib; LAPACK version 3.12.0 locale:\ \[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8 time zone: Europe/Berlin\ tzcode source: internal attached base packages:\ \[1] stats graphics grDevices datasets utils methods base other attached packages:\ \[1] plyr_1.8.9 performance_0.15.1 MuMIn_1.48.11 DHARMa_0.4.7 glmmTMB_1.1.12 vegan_2.7-1 permute_0.9-8\ \[8] multcomp_1.4-28 TH.data_1.1-4 MASS_7.3-65 survival_3.8-3 mvtnorm_1.3-3 qgraph_1.9.8 reshape2_1.4.4\ \[15] viridisLite_0.4.2 lattice_0.22-7 lme4_1.1-37 Matrix_1.7-3 raster_3.6-32 sp_2.2-0 loaded via a namespace (and not attached):\ \[1] DBI_1.2.3 Rdpack_2.6.4 mnormt_2.1.1 pbapply_1.7-4 gridExtra_2.3 fdrtool_1.2.18 sandwich_3.1-1\ \[8] rlang_1.1.6 magrittr_2.0.4 compiler_4.4.2 mgcv_1.9-3 png_0.1-8 vctrs_0.6.5 quadprog_1.5-8\ \[15] stringr_1.5.2 pkgconfig_2.0.3 fastmap_1.2.0 backports_1.5.0 pbivnorm_0.6.0 promises_1.3.3 rmarkdown_2.29\ \[22] nloptr_2.2.1 xfun_0.53 later_1.4.4 jpeg_0.1-11 terra_1.8-60 psych_2.5.6 parallel_4.4.2\ \[29] lavaan_0.6-20 cluster_2.1.8.1 R6_2.6.1 gap.datasets_0.0.6 stringi_1.8.7 qgam_2.0.0 RColorBrewer_1.1-3\ \[36] boot_1.3-31 rpart_4.1.24 estimability_1.5.1 numDeriv_2016.8-1.1 iterators_1.0.14 Rcpp_1.1.0 knitr_1.50\ \[43] zoo_1.8-14 base64enc_0.1-3 httpuv_1.6.16 splines_4.4.2 nnet_7.3-20 igraph_2.1.4 tidyselect_1.2.1\ \[50] viridis_0.6.5 effects_4.2-4 rstudioapi_0.17.1 abind_1.4-8 doParallel_1.0.17 TMB_1.9.17 codetools_0.2-20\ \[57] tibble_3.3.0 shiny_1.11.1 S7_0.2.0 evaluate_1.0.5 foreign_0.8-90 survey_4.4-8 pillar_1.11.1\ \[64] carData_3.0-5 gap_1.6 foreach_1.5.2 checkmate_2.3.3 renv_1.1.4 stats4_4.4.2 reformulas_0.4.1\ \[71] insight_1.4.2 generics_0.1.4 ggplot2_4.0.0 scales_1.4.0 minqa_1.2.8 xtable_1.8-4 gtools_3.9.5\ \[78] glue_1.8.0 Hmisc_5.2-3 tools_4.4.2 data.table_1.17.8 grid_4.4.2 mitools_2.4 rbibutils_2.3\ \[85] colorspace_2.1-2 nlme_3.1-168 htmlTable_2.4.3 Formula_1.2-5 cli_3.6.5 dplyr_1.1.4 corpcor_1.6.10\ \[92] glasso_1.11 gtable_0.3.6 digest_0.6.37 htmlwidgets_1.6.4 farver_2.1.2 htmltools_0.5.8.1 lifecycle_1.0.4\ \[99] mime_0.13