Predictability and transferability of local biodiversity environment relationships

Introduction

Local biodiversity on land is known to vary with environmental heterogeneity (Hillebrand, 2004; Stein & Kreft, 2015; Holt et al., 2017), often quantified as difference in availability and variability of resources available to a species. These resources, such as nutrients, water, energy characterize the suitable habitat where the population of a species can persist and commonly include the key availability and diversity of components of ecosystem functioning (Stein & Kreft, 2015; Regos et al., 2022). Several theories have been postulated as possible source of the relationship of environmental heterogeneity with local biodiversity. These include, among others, the widely tested species-energy (Hurlbert, 2004; Evans, Warren & Gaston, 2005; Duncan et al., 2015), the species spectral-heterogeneity (Oldeland et al., 2010; Rocchini et al., 2010) or the species-geodiversity hypotheses (Alahuhta, Toivanen & Hjort, 2020). The assumption is that habitats with greater heterogeneity provide more niches for diverse sets of species and species population expansions. However, despite a number of global meta-analyses on the relationship between environmental heterogeneity and local biodiversity for plant, bird and mammal species (Stein, Gerstner & Kreft, 2014; Duncan et al., 2015), it has rarely been comprehensively investigated how predictable and transferable these relationships are, especially across taxonomic groups and different biodiversity measures more generally.

Predictions made by statistical models are key for our understanding of the living world and for the creation of outputs relevant for conservation management (Miller et al., 2004; Houlahan et al., 2017). Because of the evermore increasing demand for scenarios and spatial maps by policy makers and land managers, biodiversity modellers often need to rely on inter- and extrapolations of model predictions across space and time (Miller et al., 2004). These predictions need to be precise and accurate enough for the context and decisions they are meant to inform (Santini et al., 2021). Thus model predictions should be investigated for their predictability, e.g., a model’s ability to accurately predict correlative relationships within the same spatial and/or temporal context by withholding some parts of the data (as in cross-validation procedures), and transferability, e.g., the capacity to produce accurate predictions for conditions dissimilar to those of the data for which a model was trained by withholding data outside the range used for calibration or making use of independently collected data (Petchey et al., 2015; Jung et al., 2017; Yates et al., 2018; Tredennick et al., 2021). And yet, model predictability and transferability is rarely consistently assessed and, when studied in more detail, results rarely look promising.

There is increasing evidence that models using variables of environmental heterogeneity, in the context of this work defined as characterizations of local habitats by vegetation and land-surface conditions, often fail to accurately predict and transfer local biodiversity measures. Studies have found that the predictability of local biodiversity as function of a difference in environmental heterogeneity are highly variable between geographic regions (Phillips, Newbold & Purvis, 2017) and local contexts (Duncan et al., 2015; Jung et al., 2017). Similarly, transferability of model predictions to spatial or temporally distinct regions has long been recognized as key issue for species distribution models (Zurell, Elith & Schröder, 2012; Mesgaran, Cousens & Webber, 2014; Regos et al., 2019) or models using local and regional biodiversity measures (Parmentier et al., 2011; Schmidtlein & Fassnacht, 2017). Despite the development of techniques for assessing the novel parameter space of a model (Zurell, Elith & Schröder, 2012; Meyer & Pebesma, 2021), the limited uptake of modellers to evaluate and present model uncertainty can hinder the application and affect trust in biodiversity model predictions (Rapacciuolo, 2019). Here, one key reason and shortcoming in doing so in macroecological studies are the various and context-specific ways in which environmental heterogeneity is quantified (Stein & Kreft, 2015), preventing assessments of predictability and transferability.

Recent advances in remote sensing and cloud-processing have enabled the robust quantification of environmental heterogeneity at high spatial and temporal resolution (Gorelick et al., 2017; Randin et al., 2020; Regos et al., 2022). Through repeated satellite observations, measures of environmental heterogeneity, such as differences in photosynthetic activity or spectral variability as proxies for vegetation cover, vegetation condition and structure and overall variability of land surfaces (Rocchini et al., 2010; Radeloff et al., 2019), can be robustly quantified. On their own they can be considered continuous representations of contrasts in land cover and land use (Hansen et al., 2000; Jung, Scharlemann & Rowhani, 2020) and ecosystem functioning (Regos et al., 2022), while also being related to key species population processes (Pettorelli et al., 2005). Although such remotely-sensed measures do not cover all types of environmental heterogeneity (Stein, Gerstner & Kreft, 2014), they can be exogenously quantified in space and time and have often been incorporated in statistical models for the prediction of species distributions (Cord et al., 2013; He et al., 2015; Regos et al., 2022) or to infer differences in local biodiversity measures (Oldeland et al., 2010; Goetz et al., 2014; Rocchini, Hernández-Stefanoni & He, 2015; Jung et al., 2019; Jung, Scharlemann & Rowhani, 2020). Remote sensing measures of environmental heterogeneity can therefore–opposed to study-specific predictors commonly included in ecological meta-analysis–serve as a globally consistent predictor for evaluating biodiversity environment relationships (Duncan et al., 2015). With the availability of new global databases on local biodiversity in-situ observations (Hudson et al., 2017), it has become possible to comparably investigate the predictability and transferability of biodiversity environment relationships across taxonomic groups and biodiversity measures.

There are a number of shortcomings in previous analyses on the predictability and transferability of local biodiversity environment relationships. Most studies have (a) focussed on effect sizes among studies (e.g., strength of inference), rather than the predictability and transferability of this relationships (Tredennick et al., 2021), (b) tended to focus mostly on species richness (Stein, Gerstner & Kreft, 2014), thus ignoring other biodiversity measures such as abundance or differences in species assemblage composition, (c) used variables of varying origin to capture effects of changes in environmental heterogeneity on biodiversity (Supp & Ernest, 2014; Shackelford et al., 2017) or have (d) focussed only on regional extents and single taxonomic groups such as birds, butterflies or plants (Kerr, Southwood & Cihlar, 2001; Oldeland et al., 2010; Goetz et al., 2014; Schmidtlein & Fassnacht, 2017). Quantitatively addressing these issues is key, if we are to understand in which cases spatial and/or temporal predictions of local biodiversity measures are reliable and accurate.

In this study I investigate the predictability and transferability of model-based predictions on local biodiversity environment relationships. The expectation is that (i) predictability is generally stronger than transferability, (ii) transferability of species-environment relationships affects some biodiversity measures and taxonomic groups more than others, and that (iii) unexplained variation in the tested relationships is predominantly linked to differences in study design, e.g., spatial scale and sampling duration. To test this, I combine local biodiversity data from globally distributed surveys with remotely-sensed environmental predictors quantifying photosynthetic activity (Evans, Warren & Gaston, 2005; Stein, Gerstner & Kreft, 2014; Duncan et al., 2015) and spectral variability (Rocchini et al., 2010); predictors that represent a continuous characterization of the availability of resources and land surface modifications. Using variations of generalized linear and additive models, I assess the predictability, quantified as overall and within-study reduction in prediction error, and transferability, quantified as reduction in prediction error between different studies of comparable design but identical taxonomic groups (Fig. 1). The aim of this work is thus to comparatively assess the strength and generality of local biodiversity-environment relationships at a global scale, which hopefully stimulates a debate on whether predicted local biodiversity measures, such as total site-based abundance or richness, can accurately be predicted or transferred to unsampled regions.

Materials and Methods

Results

The explanatory power of environmental predictors–photosynthetic activity and spectral variability–in explaining differences in biodiversity varied across biodiversity measures and individual studies. Models fitted with photosynthetic activity explained on average slightly more variance than models fitted with spectral variability, the former having an average R² of 0.21 (±0.285 SD) compared to an average R² of 0.19 (±0.284 SD) in the latter. There was considerable variation of R² values across studies and biodiversity measures (Fig. 2), with species richness on average being best explained by photosynthetic activity (R² = 0.246 ± 0.311 SD) or spectral variability (R² = 0.22 ± 0.306 SD). Notably, correlations with species abundance were particularly low, with the R² being close to 0 (R² < 0.001) for more than a quarter of all studies (Fig. 2). Meanwhile the difference in explained variance between models using photosynthetic activity compared to spectral variability was lowest for differences in assemble composition (Pearson’s R = 0.922). There were no obvious spatial (Fig. S2) or directional patterns (Fig. S3) in the average explained variance, although some studies notably had high explanatory power regardless of the considered biodiversity measure (Fig. S2).

When applying local biodiversity models to known (‘Predictability’) or different (‘Transferability’) contexts, the main issue is how accurately such models can predict local biodiversity measures in unknown situations based on the covariates of interest (Fig. 3). Regardless of whether remotely-sensed photosynthetic activity or spectral variability was used as covariate, linear models were reasonably accurate for known contexts in inferring species richness (sMAPE of 19.1%), abundance (11.8%) and evenness (10.3%), but less so when inferring differences in species assemblages (49.3%). Errors in predicting local biodiversity to different contexts were expectedly larger (Fig. 3), whereas particular species richness could be extrapolated relatively poorly (relative error 43.3%) similarly to differences in species assemblages (67.9%), compared to abundance (25.4%) or evenness (14.3%). Notably, when local biodiversity models are used to extrapolate richness to different contexts, the sMAPE was larger than 50% in 35% of all studies, compared to 8.1% and 4.7% for abundance and evenness (Fig. 3).

There were also considerable differences in prediction error, as quantified by the sMAPE, among taxonomic groups. Across taxonomic groups and biodiversity measures the sMAPE was larger when predictions were extrapolated to novel contexts compared to predictability, particularly so for reptiles (ΔsMAPE = 21.3%) and mammals (ΔsMAPE = 20.8%), with the greatest difference being for reptile species richness (ΔsMAPE = 33%) and abundance (ΔsMAPE = 28%). The transferability of fungi (sMAPE = 7.5%), and bird (sMAPE = 9.1%) assemblage evenness was overall the lowest, while predictability was best for evenness and abundance of fungi (sMAPE = 5.11%) and plants (sMAPE = 9.65%). Fungi and Plants had across biodiversity measures the lowest sMAPE in predictability and transferability (Fig. 4). Overall, assemblage composition of vertebrates was the most poorly predicted with sMAPE estimates well over 50% throughout (Fig. 4).

I also explored across studies which factors helped explain differences in prediction error, as quantified by the sMAPE (Fig. 5). Across biodiversity measures, having a greater number of samples per site most effectively reduced the sMAPE (Δβ = −3.14) for transferability, and so did sample duration but to a lesser degree (Δβ = −0.98). Meanwhile a greater number of sites per study on average increased the sMAPE (Δβ = 2.23). Patterns of comparison results were broadly similar between transferability (Fig. 5) and predictability (Fig. S5), although notably a study being more accessible resulted in an average larger reduction in the sMAPE (Δβ = −1.02) for predictability (Fig. S5). Overall variance explained by these factors in the average model was relatively low ( $R{}_{marginal}^2$ = 0.08, $R{}_{conditional}^2=0.14$).

Discussion

In this work I make use of a large database of local biodiversity survey records and remote sensing data to evaluate the predictability and transferability of biodiversity-environment relationships, e.g., the ability of models to infer local biodiversity measures in known and novel contexts. Particular emphasis is placed on differences among biodiversity measures, taxonomic groups and sampling circumstances. I found that the explanatory power of biodiversity-environment was relatively low for most studies (Fig. 2). This aligns with a previous meta-analysis that found that relationships between biodiversity measures and photosynthetic activity cannot always be established (Duncan et al., 2015). I also discovered that prediction errors are on average lowest for evenness and abundance, and, maybe unsurprisingly, generally larger when models predictions are transferred to novel contexts (Fig. 3). Biodiversity measures of sessile organisms were on average more precisely predicted (Fig. 4), although not by much with predictions errors generally larger than 25% compared to observed values, particularly so for differences in species assemblage composition. Overall these results shed some doubts on the predictability and transferability of biodiversity measures, although they have to be interpreted in the context of the individual studies (Fig. 5) and ultimately in what is an acceptable accuracy to achieve with such predictions.

Indeed, it is not formerly defined what makes a prediction better or worse based on quantitative measures such as the cross-validated error metrics used in this study. According to Yates et al. (2018) ‘transferability’ is broadly defined as the capacity of a model to produce predictions for a new set of predictor values that differ from those on which the model was trained. Similarly predictability can be understood as the capacity of a model to infer held-out observations (Fig. 1). In this context, a good precision could be understood as a model that demonstrates transferability errors smaller or comparable to errors inherent in model inferences or that don’t exceed an apriori set threshold. I found that the predictability of local biodiversity measures was overall reasonable good with errors being smaller than 25% in most cases (Fig. 3), although particularly differences in assemblage composition were poorly predicted. This might indicate that photosynthetic activity and spectral variability are useful predictors for quantifying differences in local biodiversity measures, although the variance explained varied considerably across studies (Fig. 2). In contrast I found that errors associated with transferability of biodiversity measures can be considerable, exceeding 50% relative to the original measure for species richness and differences in assemblage composition in many studies (Fig. 3). This is especially relevant, since a number of studies spatially extrapolated local biodiversity estimates, e.g., species richness or abundance, to unsampled areas based on environmental predictors (König, Weigelt & Kreft, 2017; Phillips et al., 2019; van den Hoogen et al., 2019). These approaches assume that local biodiversity-environment relationships are transferable to new, unsampled environments and the results by this work indicate that this often entails considerable errors. Ideally models are evaluated on their ability to accurately reproduce their data in novel contexts (Jung et al., 2017), quantify the uncertainty in doing so, or alternatively limit predictions to areas within the models applicability (Mesgaran, Cousens & Webber, 2014; Meyer & Pebesma, 2021), and the results of this work further highlight that prediction errors should be reported.

Biodiversity measures for certain taxonomic groups might be easier to predict than others owing to the dynamics, drivers and mechanisms underlying them (Magurran, 2004). Indeed previous studies have found species abundance to be stronger correlated with photosynthetic activity than other measures (Oldeland et al., 2010; Duncan et al., 2015). Similarly, I found that abundance-based biodiversity measures–e.g., abundance and evenness–had overall lowest precision errors (Fig. 3). A potential mechanism could be that a greater photosynthetic activity or spectral variability is indicative of resources available to species populations, facilitating population growth (Hurlbert, 2004; Pettorelli et al., 2006). While species richness had the largest average explained variance compared to other biodiversity measures, it performed considerably poorer when evaluated in predictions (Fig. 3). Possibly, the processes underlying patterns of local species richness, such as colonization and extinction, might cause simple predictions to fail (Chase, 2003), unless the spatial-temporal dynamics of environmental predictors are taken into account (Fernández, Román & Delibes, 2016). Similarly, the fact that both predictability and transferability errors were on average lowest for more sessile organisms such as Fungi and Plants (Fig. 4), likely indicates that similar important processes mediate biodiversity-environment relationships. Overall this study highlights the benefit of comparing relationships across a range of studies and biodiversity measures (Stein, Gerstner & Kreft, 2014; Duncan et al., 2015), revealing that biodiversity-environment relationships are not universally strong.

Investigating as to what factors best explain prediction errors can help to improve future monitoring and modelling efforts. Among the most important factors that resulted in overall smaller prediction errors was the average number of samples per sites (Fig. 5), which can be considered a simplified metric of sampling completeness. Given that errors were smaller for sites with many samples, it could be that many species communities in the PREDICTS database have not been comprehensively sampled, if one assumes that biodiversity-environment relationships are strongest in equilibrium. There are ways to account for detectability and observation biases (Royle, Nichols & Kéry, 2005), which however was not feasible for the studies in the PREDICTS database given the heterogeneity of sampling information. Thus better standards for sampling techniques and monitoring are advisable to enable better comparability (Montgomery et al., 2021).

Interestingly, and in contrast to previous studies (Chase & Knight, 2013), differences in sample grain, e.g., the linear scale of sampling, did not help to explain why biodiversity measures could be better predicted in some studies. A likely explanation is that the contrasts between sampling extents are relatively small (most studies in the PREDICTS database were sampled at scales between ~1 and 4,000 m). Scale-dependent effects might only become apparent at spatial scales that go beyond the local scale. A spatial mismatch at the lower end, e.g., that the grain of the used MODIS data is too coarse to be matched to the extent of sampling in PREDICTS studies, could be another explanation, however previous studies that used very-high resolution satellite imagery (<10 m) did not find much more accurate predictions than presented here (Dalmayne et al., 2013; Hofmann et al., 2017). Other, non-explored factors could further explain differences in prediction error, such as for instance preceding changes in environmental predictors (Jung et al., 2019; Jung, Rowhani & Scharlemann, 2019) or a better accounting of differences in species traits (Duncan et al., 2015; Regos et al., 2019). Future efforts could evaluate if inter- and intra-specific variability of species traits can be more precisely linked to differences in environmental heterogeneity.

In this work I used photosynthetic activity and spectral variability as measures of environmental heterogeneity, acknowledging that other characterizations of environmental heterogeneity (e.g., soil, micro-climate) could be more important (Stein & Kreft, 2015). The rationale behind focusing on photosynthetic activity and spectral variability in this work was the assumption that they can serve as general broad predictive measures across taxa and regions. There are, however, also a number of other remote-sensing measures, such as for example land-surface temperature or remotely-sensed moisture (Albright et al., 2011; Regos et al., 2022), as well as different summary statistics of such measures (maximum, minimum, variation), which for some local contexts might capture important dynamics and lead to an improved prediction with lower errors. The finding that prediction errors were lowest for plants and fungi could be related to the fact that photosynthetic activity is more closer related to the abundance of these taxa, than for other taxonomic groups, where only indirect correlations (resources for herbivores, differences in land cover) could be the most likely explanation and local factors might have a deciding influence on explaining these differences (Jung et al., 2017). Yet, focussing solely on remotely-sensed variables ensures global consistency and is frequently used to predict local biodiversity measures (Dalmayne et al., 2013; Hobi et al., 2017; Hofmann et al., 2017; Randin et al., 2020).

Another key limitation is that environmental heterogeneity is not necessarily related to differences in land use and land-use intensity, for which the PREDICTS database was explicitly designed (Purvis et al., 2018). Indeed, it could be that the potential of remotely sensed environmental heterogeneity in predicting local biodiversity measures has been exaggerated, and better and more direct characterizations of land use and its management from remote sensing have to be developed. Previous studies using PREDICTS data found that even using the local land-use categorizations explained few differences in biodiversity measures, with most variance being ‘soaked up’ by study-specific differences (Newbold et al., 2015, 2018; De Palma et al., 2015). Further, given the complexities of local species community assembly (Chase, 2003; Leibold et al., 2004), any claim of a direct prediction of ‘biodiversity’ through remotely-sensed proxies should thus be interpreted with caution and only under consideration of prediction uncertainties. Remote sensing measures are at best able to capture changes in habitat extent or condition; and those changes do not necessarily correlate strongly with changes in biodiversity measures. Future work should ideally focus on the principal mechanisms of species community assembly, their practical incorporation into models and how remote sensing can assist in capturing relevant predictors.

Conclusions

The findings presented in this study have particular implications for spatial projections of local biodiversity-environment relationships. Ecological models can and should be used for predictions (Houlahan et al., 2017; Tredennick et al., 2021); however, caveats and limitations should be better identified, communicated and hopefully build upon. We need to create models that enable biodiversity-environment relationships to be more predictable across scales and novel contexts, especially when applied to conservation contexts (Santini et al., 2021). Remote sensing data can be used for global consistent characterizations of environmental heterogeneity, but given the considerable drops in precision for transferability, this work recommends that prediction errors in projecting local biodiversity measures are clearly communicated and quantified. To improve future biodiversity predictions I further propose that models (a) should be evaluated comprehensively based on their ability to create accurate predictions, (b) account better for underlying hierarchies and sampling effects, (c) ensure that environmental predictors are quantified in a globally replicable and transparent way. Quantitative correlative models might not be the most precise in many situations, but that does not invalidate their use if shortcomings are appropriately communicated.

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