bioRxiv2018
Because biodiversity is multidimensional and scale-dependent, it is challenging to estimate its change. However, it is unclear (1) how much scale-dependence matters for empirical studies, and (2) if it does matter, how exactly we should quantify biodiversity change. To address the first question, we analyzed studies with comparisons among multiple assemblages, and found that rarefaction curves frequently crossed, implying reversals in the ranking of species richness across spatial scales. Moreover, the most frequently measured aspect of diversity--species richness--was poorly correlated with other measures of diversity. Second, we collated studies that included spatial scale in their estimates of biodiversity change in response to ecological drivers and found frequent and strong scale-dependence, including nearly 10% of studies which showed that biodiversity changes switched directions across scales. Having established the complexity of empirical biodiversity comparisons, we describe a synthesis of methods based on rarefaction curves that allow more explicit analyses of spatial and sampling effects on biodiversity comparisons. We use a case study of nutrient additions in experimental ponds to illustrate how this multi-dimensional and multi-scale perspective informs the responses of biodiversity to ecological drivers.\n\nStatement of AuthorshipJC and BM conceived the study and the overall approach, and all authors participated in multiple working group meetings to develop and refine the approach. BM collected the data for the meta-analysis that led to Fig. 2,3; JC collected the data for the metaanalysis that led to Figure 4 and S1; SB and FM did the analyses for Figures 2-4; DM, FM and XX wrote the code for the analysis used for the recipe and case study in Figure 6. JC, BM and NG wrote first drafts of most sections, and all authors contributed substantially to revisions.\n\nO_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=200 SRC=\"FIGDIR/small/275701_fig2.gif\" ALT=\"Figure 2\">\nView larger version (20K):\norg.highwire.dtl.DTLVardef@485725org.highwire.dtl.DTLVardef@151643corg.highwire.dtl.DTLVardef@8bc9e0org.highwire.dtl.DTLVardef@1729374_HPS_FORMAT_FIGEXP M_FIG O_FLOATNOFigure 2.C_FLOATNO Bivariate relationships between N, SPIE and S for 346 communities across the 37 datasets taken from McGill (2011b)(see Appendix 1). (A) S as a function of N; (B) S as a function of SPIE. (N vs SPIE not shown). Black lines depict the relationships across studies (and correspond to R2 fixed); colored points and lines show the relationships within studies. All axes are log-scale. Insets are histograms of the study-level slopes, with the solid line representing the slope across all studies. Gray bars indicate the study-level slope did not differ from zero, blue indicates a significant positive slope, and red indicates a significant negative slope.\n\nC_FIG O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=116 SRC=\"FIGDIR/small/275701_fig3.gif\" ALT=\"Figure 3\">\nView larger version (22K):\norg.highwire.dtl.DTLVardef@12ee0e9org.highwire.dtl.DTLVardef@affc46org.highwire.dtl.DTLVardef@1db6453org.highwire.dtl.DTLVardef@97ab06_HPS_FORMAT_FIGEXP M_FIG O_FLOATNOFigure 3.C_FLOATNO Representative rarefaction curves, the proportion of curves that crossed, and counts of how often curves crossed. (A) Rarefaction curves for different local communities within two datasets: marine invertebrates (nematodes) along a gradient from a waste plant outlet (Lambshead 1986), and trees in a Ugandan rainforest (Eggeling 1947); axes are log-transformed. (B) Counts of how many times pairs of rarefaction curves (from the same community) crossed; y-axis is on a log-scale.\n\nC_FIG O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=122 SRC=\"FIGDIR/small/275701_fig4.gif\" ALT=\"Figure 4\">\nView larger version (20K):\norg.highwire.dtl.DTLVardef@15d497borg.highwire.dtl.DTLVardef@18354fforg.highwire.dtl.DTLVardef@1413a54org.highwire.dtl.DTLVardef@15c8451_HPS_FORMAT_FIGEXP M_FIG O_FLOATNOFigure 4.C_FLOATNO Results of a meta-analysis of scale-dependent responses to a number of different ecological drivers (see Appendix 2). Points represent the log response ratio comparing species richness in control compared to treatments in a given comparison measured at the smallest (x-value) and largest (y-value) scale. The solid line indicates the 1: 1 line expected if effect sizes were not scale-dependent. Points above and below this line indicate effect sizes that are larger or smaller, respectively, as scale increases; points in the upper left and lower right quadrats represent cases where the direction of change shifted from positive to negative, or vice versa, with increasing scale. The dashed line indicates the best fit correlation, which is significantly different than the 1:1 line (P<0.01), indicating that overall, effect sizes tend to be larger at smaller scales than at larger scales. Colors for points indicate categorizations into different ecological drivers.\n\nC_FIG O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=200 SRC=\"FIGDIR/small/275701_figS1.gif\" ALT=\"Figure 1\">\nView larger version (15K):\norg.highwire.dtl.DTLVardef@f30150org.highwire.dtl.DTLVardef@1db2db9org.highwire.dtl.DTLVardef@970507org.highwire.dtl.DTLVardef@cb37e6_HPS_FORMAT_FIGEXP M_FIG O_FLOATNOFigure S1.C_FLOATNO Results showing the ratio of log-response ratio effect sizes from experiments where species richness responses were measured at two spatial scales (small scale/large scale). The dashed line at 0 would indicate studies where the effect sizes were the same at the smaller and larger scale. For each category of ecological driver, the means are above 1, indicating that the measured effect size is larger at the smaller relative to larger size, and this difference is statistically significant for land use, invasive species, and grazing/predation.\n\nC_FIG O_FIG O_LINKSMALLFIG WIDTH=158 HEIGHT=200 SRC=\"FIGDIR/small/275701_fig6.gif\" ALT=\"Figure 6\">\nView larger version (21K):\norg.highwire.dtl.DTLVardef@1c313d0org.highwire.dtl.DTLVardef@49df71org.highwire.dtl.DTLVardef@1ec92a3org.highwire.dtl.DTLVardef@8f1693_HPS_FORMAT_FIGEXP M_FIG O_FLOATNOFigure 6.C_FLOATNO Effect of nutrient additions on several measurements of biodiversity from Table 1 (see data in Appendix 3). Each biodiversity measure was calculated at the -scale (1 mesocosm) (Panels A,B), {gamma}-scale (15 mesocosms) (Panels C,D), as well as the -scale (i.e. turnover across scales, {gamma}/)(Panels D,E,F). See Chase (2010) for details on the experimental design and the mobr package (McGlinn et al. submitted, https://github.com/MoBiodiv/mobr) for details on the statistical methods\n\nC_FIG\n\nO_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=99 SRC=\"FIGDIR/small/275701_fig1.gif\" ALT=\"Figure 1\">\nView larger version (15K):\norg.highwire.dtl.DTLVardef@133d65org.highwire.dtl.DTLVardef@123b3faorg.highwire.dtl.DTLVardef@fce7ccorg.highwire.dtl.DTLVardef@1d62dab_HPS_FORMAT_FIGEXP M_FIG O_FLOATNOFigure 1.C_FLOATNO A. Individual-based rarefaction curves of three hypothetical communities (labelled A,B, C) where ranked differences between communities are consistent across scales. B. Individual-based rarefaction curves of three hypothetical communities (labelled A,B, C) where rankings between communities switch because of differences in the total numbers of species, and their relative abundances. Dotted vertical lines illustrate sampling scales where rankings switch. These curves were generated using the sim_sad function from the mobsim R package (May et al. 2018).\n\nC_FIG\n\n\n\nData accessibility statementAll data for meta-analyses and case study will be deposited in a publically available repository with DOI upon acceptance (available in link for submission).