A quantitative review of abundance‐based species distribution models

Spatial abundance data

We obtained standardised estimates of species abundance across large regions for birds and shallow‐water reef fishes from the Breeding Bird Survey of the USA (BBS) and Reef Life Survey (RLS), respectively (for detailed sampling schemes, see Pardieck et al. 2019 for birds and Edgar and Stuart‐Smith 2014 for fishes). For birds, abundance data comprise of 3‐min counts of individuals sighted and heard within a 400‐m stop radius along a transect of 50 stops. We summed bird species abundance across 50 stops within a sampled year and mean‐averaged abundances for a given species in a repeated site across the years 2014–2018. We aggregated abundances across years to better generalise our results to the structure of most abundance datasets, whereby yearly values across broad geographic regions are unlikely to be available (see the Supporting information for exploration of this assumption). We filtered out all samples that did not meet BBS‐established weather, date, time, route completion, randomised sampling and sampling protocol criteria (i.e. using BBS data with a run type of 1). For fishes, abundance data are counts of individuals sighted along 50‐m‐long underwater transects (summed across 2 × 5‐m‐wide blocks on either side of the transect line). We mean‐averaged RLS abundance estimates across multiple transects within sites, with sites defined as sets of transects <200 m apart (Edgar and Stuart‐Smith 2014, Cresswell et al. 2017). As such, where sites are surveyed in multiple years, abundances were mean‐averaged. We filtered sites geographically between 3°S to 50°S and 110°E to 165°E to select for Australian and Indo‐Pacific survey locations where sampling effort was most intensive and comprehensive in the RLS dataset. For both BBS and RLS datasets, we removed species without full scientific names and fewer than 50 abundance records. We required species absences for two‐stage models and abundance–absence models. We generated absences for each species by taking observations where species were present and finding all observations within a 1000‐km buffer where species were not present. A lack of observed presence is not necessarily a ‘true absence' but instead suggests species were undetectable with a reasonable sampling effort (Guillera‐Arroita 2017). We analysed a total of 264 474 observations of 385 species in 3890 sites for birds in the BBS dataset and 567 669 observations of 495 species in 2137 sites for reef fishes in the RLS dataset.

Covariates

We matched site locations to gridded environmental variables representing climate, biogeochemistry, land‐use, depth, habitat area and human populations, retaining only variables with expected a priori relationships with abundance (see the Supporting information for details). Because of the high number of similar climate‐related variables, and to avoid multicollinearity in these, we first applied robust principal component analysis (PCA) using package pcaMethods(ver. 1.76.0; Stacklies et al. 2007) which is shown to be a good approach to reduce multicollinearity in species distribution models (SDM) (Cruz‐Cárdenas et al. 2014, De Marco and Nóbrega 2018, Osorio‐Olvera et al. 2020). Furthermore, we focused on predictive power to ensure our results were more robust to potential multicollinearity. We ran a separate robust PCA on 19 variables characterising climates across the bird survey locations (bio1–bio19) and on 15 variables characterising climatic and biogeochemical properties across the fish survey locations (mean, minimum and maximum of pH, salinity, chl‐a, net primary productivity, degree heating weeks; indicated in the Supporting information). For each dataset, we retained three principal components, explaining 87.8% and 77.8% variation, respectively, and used these principal component scores as predictor variables to summarise the dominant climate and biogeochemical regimes of the data in each set of models (three PCA variables for birds and three PCA variables for fishes; Supporting information). In addition to the climatological variables, we also included additional environmental variables as predictors in our model that we expected to act independently. All non‐PCA variables were mean‐centred, normalised to a variance of 1 and transformed according to the Supporting information before modelling.

Analytical design

We analysed a large diversity of species abundance models that spanned a gradient in model complexity and different formulations of abundance data. Further, we assessed model performance for interpolation and extrapolation of cross‐validation scenarios (Fig. 1). Given that data requirements are a major challenge in fitting species abundance models, we chose species‐level statistical models that were suitable for our goal of comparing predictive performance (i.e. not mechanistic, hierarchical or multispecies/joint/multivariate SDMs). In total, we fitted and evaluated 68 types of species abundance model (24 model frameworks by 3 response variable (abundance) formulations, less 4 models of zero‐inflation that are not valid for abundance‐only models = 68 models; see Supporting information for full model list). Combining models and cross‐validations for 1547 species led to 59 840 models to evaluate.

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Our full species abundance model set comprises different statistical algorithms, response transformations, error distributions and formulations of abundance data. We used 24 model variants from common statistical distributions and transformations for abundance data that were available within statistical software packages in R (e.g. Poisson, negative binomial, zero‐inflated, Tweedie, multi‐nominal, log10‐Gaussian, log‐Gaussian; Supporting information). We chose statistical treatments of abundance data that are common in the literature and valid to the error distribution of abundance. We fitted these 24 model variants using four statistical model fitting procedures: generalised linear models (GLMs), generalised additive models (GAMs; Wood 2011), gradient boosting machine (GBM; Friedman 2001) and random forests (RF; Breiman 2001). This model set varied in complexity of the relationship between abundance and environmental variables (linear to highly complex) and the behaviour of interactions within the models (none to many; Merow et al. 2014). For GLMs and GAMs, we used a range of error distributions rather than determining a priori the most appropriate error distribution for each species. This follows previous species abundance model comparisons (Potts and Elith 2006), which assumed that incorrect model specification leads to poor predictive ability, and we focused our comparison of model performance on predictive ability (which also provided standardised assessment criteria across statistical algorithms). For all models, we included the same initial set of predictor variables, although each model framework had a different underlying variable selection procedure that identified independent sets of final predictors. The full model fitting procedure, algorithm parameters and justification for each modelling approach and software used are provided in the Supporting information.

In addition to model variants, we used three formulations of response data: abundance‐when‐present (for 20 model variants, less 4 zero‐inflated models), abundance–absence (for 24 model variants) and an indirect two‐stage modelling approach (for 24 model variants). For abundance‐when‐present models, we removed all absences. Abundance–absence models were analogous to classic presence–absence data in species distribution models but using abundance estimates instead of presences. In abundance–absence models, we standardised prevalence (the number of absences compared to presences) across species, which can influence the estimation of response curves from data characteristics alone when there are many more absences than presences (Meynard et al. 2019). To do so, we bootstrap‐subsampled the number of absences to be twice the number of presences, repeating this procedure 10 times and averaging abundance predictions across bootstraps. Finally, our indirect two‐stage modelling approach first modelled habitat suitability as a traditional SDM by converting abundance–absences into presence–absences. Next, we used the habitat suitability predictions from this model as a single covariate to predict abundance. Note, this is not a hurdle approach but instead tests the assumption that habitat suitability correlates to, and predicts, local abundance (Vanderwal et al. 2009). Details for fitting SDMs to produce occupancy predictions are provided in the Supporting information.

Model evaluation: accuracy, discrimination and precision

We evaluated the consistency between predicted and observed abundance using metrics of: 1) accuracy; 2) discrimination and 3) precision (see Fig. 1 for equations; Norberg et al. 2019). Accuracy is the degree of proximity to a known truth, measured here using mean absolute error between observed and predicted abundance, expressed as a proportional error by dividing the mean absolute error by the mean observed abundance for a species (A_mae). Discrimination measures how well model predictions discern low values from high values of observed abundance, e.g. in the correct overall ordering of abundances. This is a continuous analogue of occurrence SDMs discerning between present and absent. We measured discrimination using both Spearman's rank correlation (D_Spearman) and Pearson's correlation (D_Pearson) between predicted and observed abundance. In addition, we estimated the slope and intercept of a linear model between predicted and observed abundance (D_slope, D_intercept). Precision measures the information content in the predictions as the variation in predicted abundance relative to the variation in the observed abundances. Precision differs from accuracy because estimates can be precise with high information content even if overall predictions were biased. Here, we measured precision as the SD of the predicted abundances (Norberg et al. 2019). However, we compared this value to a reasonable expectation of precision because each species has a different range of abundance values. Therefore, we estimated the SD of predicted abundance and divided this by the SD of observed abundance and call this property P_dispersion.

Accuracy, discrimination and precision capture different facets of model performance and so could be considered together or separately depending on the purposes of the modelling exercise. For example, a model can predict mean abundance of a species well (high accuracy) but poorly discriminate between high and low abundances (low discrimination). We focused our results mostly on discrimination because identifying changes in spatial and temporal variation in abundance, a goal of conservation and wildlife management, depends on good discrimination of abundance values between sites or time periods. Further, accuracy and precision may depend on the quality of sampling, but inaccurate sampling may still provide reasonable estimates of spatial and temporal differences in abundance. We identified an ‘optimal model' based on the most discriminatory model for each species. To do so, we rescaled the four discrimination metrics between 0 and 1, averaged the score across the scaled metrics and identified the model with the highest average score per species – we report this as the ‘optimal model' throughout.

Note that we avoid confounding performance in predicting presence–absences from performance in predicting abundance by only evaluating predictions for species abundances when present (i.e. we exclude any abundance values predicted in sites where species are absent in the observed data). Although many reviews exist identifying the best occupancy‐based frameworks for predicting presence or absences (Norberg et al. 2019), our novel contribution focuses on predicting species abundance. In practice, to obtain abundance estimates, both occupancy and abundance predictions should be combined (Denes et al. 2015).

We assessed whether a rescaling correction could improve the biases in abundance predictions between predicted and observed abundance. This bias appears systematically in quantitative ecological predictions (Pearce and Ferrier 2001, Fukaya et al. 2020, Ploton et al. 2020). We rescaled predicted values to take the range of observed values using the following formula

and assessed how this procedure affected model performance indicated by our evaluation metric set.

Model cross‐validations and transferability to novel climates

We evaluated model performance using two cross‐validation strategies. We evaluated how well models predict abundance when 1) interpolating within environments (within‐sample) and 2) extrapolating into novel climate conditions (out‐of‐sample). The first scenario applies when models are interpolated to fill geographic gaps in sampling within a species range. The second scenario applies, for example, when modelling species abundance under climate change. When testing interpolation within sample environments, we randomly held out 20% of the abundance data and fitted models to the remaining 80%. This within‐sample model evaluation used a random subset of sites within the full covariate space.

Our second cross‐validation strategy tested model transferability in novel conditions. Transferability measures if models can be projected beyond environments found within bounds of the covariate data. Given the rate of anthropogenic environmental change, models will be best applied when they are also accurate in novel conditions with no past analogues (Evans 2012, Sequeira et al. 2018a). Model transferability can be low if models are overfitted, exhibit non‐stationarity or are missing important covariates (Yates et al. 2018). We built separate models following the above protocol to test model transferability. To do so, we non‐randomly sampled 20% data from above the 80th quantile of sea‐surface temperature in reef fishes and above the 80th quantile of the climatological PCA‐1 in birds and fitted our abundance models to the remaining 80%. We estimated all evaluation metrics within the out‐of‐sample cross‐validation sets as above. In both scenarios, we assumed that cross‐validation frames were independent of the training data frames (Randin et al. 2006, Roberts et al. 2017).

We did not perform k‐fold cross‐validation for the full span of covariate space because we wanted to gain an understanding of abundance estimates from directional environmental novelty due to climate change (e.g. predicting abundance in warmer temperatures than that fishes currently experience in the oceans). As a hypothetical example, if we split a temperature gradient from 20 to 30°C into 20–22, 22–24, 24–26, 26–28 and 28–30°C bins and examined performance on each bin, spatial autocorrelation would lead to an underestimate of model performance in novel future climates when evaluating the middle bins. Under temperature warming, we therefore only used the highest 20% bin threshold for exploring extrapolation (i.e. transferability to novel climates). To ensure cross‐validation scenarios of interpolation and extrapolation were comparable, we used only one 20% subsample for the interpolation (random) subset also. Although this procedure is not encouraged in general for SDM fitting and evaluation, for good reason (Roberts et al. 2017), it suits our specific cross‐validation goals (Sequeira et al. 2018a, Yates et al. 2018). We expected our findings to be robust to any small biases introduced by only performing one‐fold cross‐validations because of the high number of species included in the exercise. We did, however, perform 10‐fold cross‐validations when sub‐sampling species absences to ensure findings were robust to variation in the locations of species absences.

Species and data characteristics

We tested how characteristics of species abundance, frequency and data availability affected model performance. To explain variation in model performance among species, we calculated 1) the mean abundance of species when present; 2) the proportion of presence compared to absence records (within 1000 km of presence records) in the observational data (% occupied sites) and 3) the total number of presence records per species (overall observation number). Although the frequency of occurrence and the total number of presences are collinear in bird and fish datasets (rho = 0.87, rho = 0.67, respectively), we included both because unbiased estimates of coefficients are achieved through multiple regression (Morrissey and Ruxton 2018). We log10 transformed and standardised predictor variables to have unit variance and removed outliers (points > 2 SD from the mean) from the response variables. Next, we fitted multiple regressions that explained how the model evaluation metrics depended on our three measures of species characteristics. For simplicity, we present these results using D_Spearman due to the high number of comparisons and the importance of model discrimination highlighted above. We first fitted a full model, including three two‐way interactions between pairs of predictors. We performed backwards stepwise model selection and selected the model with the lowest Akakike information criterion (AIC) score using the R package MuMIn (Burnham and Anderson 2002, Barton 2017). We plotted marginal effects by predicting model effects for a given variable across the mean value of all other model covariates. We fitted these models using phylogenetic generalised least squares using the R package caper using maximum likelihood to estimate Pagel's λ (Blomberg and Symonds 2014, Orme et al. 2018). We used published bird (Jetz et al. 2012^, 2014; <https://birdtree.org/downloads/>) and fish (Rabosky et al. 2018; <https://fishtreeoflife.org/downloads/>) phylogenetic trees.

Overview of model performance

We first assessed performance by applying all frameworks to all species and evaluating interpolative prediction of within‐sample observations. Doing so, model performance was highly variable and generally low (Supporting information). For example, across all models and species, D_Spearman had a median of 0.29 (5th percentile = −0.17, 95th percentile = 0.64), median D_slope was 0.06 (−0.07 to 0.47) and median A_mae was 0.74 (0.48–1.52). As such, of the complete model set (n = 68), only 51% of species had at least one model with a D_Spearman above 0.5; 53% of species had at least one model with a D_slope between 0.5 and 1.5, and 29% of species had at least one model with A_mae predicting mean abundances within 50% of observed mean abundances. Overall, 13% of species had models fitting all the above criteria.

We next investigated the best‐fitting algorithm for each species independently, keeping only the single best model for each species (i.e. our ‘optimal model'). Random forests were most often selected as the optimal models for discrimination (precision, accuracy) being best for 51% (55%, 44%) of the species, gradient boosting machines for 22% (26%, 21%) and generalised linear models and generalised additive models for 16% (9%, 23%) and 12% (10%, 13%) of species, respectively (Fig. 2). Building models using abundance–absence data led to the best discrimination (precision, accuracy) performance for 68% (30%, 36%) of species, 19% (24%, 51%) using only species abundance and 14% (46%, 14%) using a two‐step indirect approach relating abundance to occurrence probability (Supporting information).

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When selecting an optimal model for each species, model performance was good for most metrics (Fig. 3, Table 2). For example, there were positive correlations for most species between observed and predicted abundances, and the error of average abundance estimation was relatively low. Specifically, median D_Spearman was 0.48 (0.14–0.72) and 0.43 (0.17–0.72) for bird and fish surveys, respectively, and median A_mae was 0.62 (0.43–0.97) and 0.69 (0.46–1.34), respectively. Some measures of model performance were poor, leading to a biased relationship between observed and predicted abundances and a poor estimation of abundance variation. Specifically, D_slope was 0.25 (0.02–0.68) and 0.20 (0.01–0.99) for bird and fish surveys, and P_dispersion was 0.51 (0.12–1.27) and 0.44 (0.05–1.67), respectively.

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Predictions of abundance from optimal models had a high correspondence with observed abundances, on average across all species, in both fish and birds (Fig. 4). However, as indicated by the evaluation metrics, the overall relationship was biased to be shallower than a 1:1 correspondence between observed and predicted abundance by models consistently overestimating low abundance and underestimating high abundances (Fig. 4; see the Supporting information for breakdown across individual optimal models). Applying a rescaling correction (rescaling‐predicted abundances to the observed abundance range) for each species helped to correct this systematic bias. Model performance improved as indicated by D_slope (before correction = 0.20–0.25 to after correction = 0.50–0.56) and P_dispersion (0.44–0.51 to 1.10); however, performance decreased when indicated by D_intercept (1.7–2.2 to 5.6–5.9) and A_mae (0.64–0.69 to 0.88–0.94; see full results in the Supporting information).

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Model transferability to novel conditions (i.e. out‐of‐sample)

Transferring models to novel conditions, the best‐performing algorithm for each species in terms of discrimination (precision, accuracy) shifted to GLMs being the best for 33% species (27%, 39%), RF for 29% (40%, 20%), GAMs for 19% (19%, 17%) and GBM for 19% (15%, 24%) of the species (Fig. 2, Supporting information). Building models using abundance–absence data remained the best‐performing treatment of response data in terms of discrimination (precision, accuracy) for 60% (33%, 35%) of species, with 21% (41%, 38%) of species having best models when using only species abundances and 20% (26%, 27%) using a two‐step approach (Fig. 2).

Transferring models to novel conditions reduced model performance for most metrics across both birds and fishes (Table 2, Fig. 3). The general discrimination of high and low abundances remained (median D_Spearman was 0.34 for birds and 0.34 for fishes). D_slope declined by more than half compared to within‐sample cross‐validations (median D_slope was 0.10 for birds and 0.06 for fishes). Accuracy also decreased compared to within‐sample cross‐validations, with a median of 0.78 and 0.83 in birds and fishes, respectively.

Predicted abundance still corresponded with observed abundances on average across all species, in both fishes and birds (Fig. 4), despite the poorer model performance. However, similar issues with a biased intercept and slope exist in the out‐of‐sample cross‐validations as for the within‐sample cross‐validations and were similarly corrected for by the rescaling procedure (Fig. 4; see the Supporting information for breakdown across individual optimal models and for comparisons with rescaling).

Species and data characteristics

The variation in model performance explained by species and data characteristics varied among performance metrics and was higher in general for within‐sample (R² = 0.04–0.44) compared to out‐of‐sample cross‐validations (R² = 0.01–0.33; Supporting information). All six evaluation metrics were affected by species or data characteristics in both birds and fishes (Supporting information). P_intercept had the most variation explained by species and data characteristics in both birds and fishes (R² of 0.42–0.44).

We present the example metric D_Spearman, which had an R² between 0.16 and 0.33. The effects of species and data characteristics on D_Spearman were highly consistent across within‐ and out‐of‐sample predictions and across both datasets (Fig. 5, Supporting information). More observations decreased the D_Spearman. Higher frequency of occurrence increased D_Spearman but only if species also had high number of observations. Species with higher abundance had higher D_Spearman only if species had high frequency too. This last effect was not evident for fish species in out‐of‐sample predictions. Phylogenetic signal (Pagel's λ) in the residuals was very weak ranging from 0 to 0.17.

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Successful aspects of species abundance models

A small number of good approaches for predicting species abundance emerged after exploring a large set of models. Correlation values from our optimal models were higher than ~0.3 for more than 75% of species and higher than ~0.6 for 25% of species (Table 2). Our finding that RF perform well at within‐sample prediction provides solid evidence that specific case studies reporting similar results, such as in Balearic shearwaters Puffinus mauretanicus (Oppel et al. 2012), apply more generally, at least across the 800 species of bird and fish tested here. The high discrimination, precision and accuracy of RF would improve confidence in assigning regions as important abundance‐priority areas for conservation.

A focus on linear functions relating environments to local abundances may have previously reduced predictive performance. More flexible response curves of machine‐learning approaches allow for what may often be highly nonlinear abundance niche shapes (Pearce and Ferrier 2001, Potts and Elith 2006, Renwick et al. 2012, Betts et al. 2019). Further optimised algorithms and deep learning approaches may better integrate abundance into biodiversity indicator frameworks, given the much better performance of machine‐learning approaches here (Jetz et al. 2019). If abundance has been perceived to be poorly explained by climate or other variables in the past, it could be falsely concluded that broad‐scale variables only weakly affect abundance and that abundance niches are more strongly constrained by factors other than species fundamental niches (but see Illan et al. 2014, Dallas and Santini 2020).

Accurate prediction of local abundances with abiotic variables supports the theoretical prediction that fitness optima along abiotic niche axes filters down to determine ecologically successful locations of high population growth rates (Maguire 1973). The prediction of abundance from abiotic niche axes has been questioned by recent empirical studies (Dallas and Hastings 2018, Santini et al. 2019, Sporbert et al. 2020). These studies determine environmental effects on abundance indirectly from habitat suitability or environmental centroids. Here, we directly relate abundance to environmental conditions which provides a more direct quantification of species abundance niche with fewer assumptions (Osorio‐Olvera et al. 2020).

Modelling abundance directly was better than an indirect approach (i.e. comparing our abundance–absence models to two‐stage models) for more than 80% of species. This finding indicates that spatial abundance and occurrence patterns are somewhat mismatched or at least not always congruent (although it is challenging to completely disentangle abundance from occurrence, and vice versa). Mismatches arise from different ecological controls of abundance and occurrence, such as different demographic rates controlling each to different extents (McGill 2012, Johnston et al. 2015, Acevedo et al. 2017, Bohner and Diez 2020, Dallas and Santini 2020, Schulz et al. 2020, Yancovitch Shalom et al. 2020). Understanding such mismatches offers an important avenue for better understanding range and abundance shifts under climate change (Geppert et al. 2020) and potentially guiding spatial management and conservation. For example, a focus on occurrence can miss critical patches of high abundance driven by a few isolated factors (Johnston et al. 2015, Suggitt et al. 2018). Such ‘strongholds' for species could be a common feature of ecological communities. Moving species distribution models beyond modelling occurrences, to help identify such areas, will require improving knowledge of species responses to environmental gradients using multiple performance metrics (i.e. occurrence, abundance, demographic rates) (Ehrlén and Morris 2015, Ashcroft et al. 2017, Bohner and Diez 2020).

Current limitations and challenges in species abundance models

We identify two important challenges in abundance models here. First, we systematically over‐predict low observed abundances and under‐predict high observed abundances (Pearce and Ferrier 2001, Fukaya et al. 2020, Ploton et al. 2020). Second, having more observations led to lower discrimination between high abundance sites and low abundance sites. These issues may jointly arise as we undoubtedly miss key biotic (e.g. ecological interactions) and microclimatic variables from our models (Lembrechts et al. 2019), leading to unexplained extreme local abundances.

Missing inter‐ and intraspecific interactions has been a well‐recognised problem in predictive occurrence‐based species distribution modelling (Guisan and Thuiller 2005, Wisz et al. 2013, Mouquet et al. 2015, Pollock et al. 2020). For abundance‐based models, species interactions can drive population feedbacks that may be important for explaining extreme abundances, but are missing from models in general, leading to poor predictive performance. Recent theoretical work highlights how interaction feedbacks can modify abundance along environmental gradients, even if the fundamental niche shape is unimodal (Kéfi et al. 2016, Liautaud et al. 2019). In addition, behavioural aggregations from seasonal migrations or resource booms can lead to extreme abundances, challenging the identification of appropriate statistical response distributions (Lindén and Mäntyniemi 2011). These points emphasise the need to better understand how local environments, individual behaviour and species interactions together shape macroecological abundance patterns. Novel joint species distribution modelling approaches (Ovaskainen et al. 2017), or direct estimation of interaction strengths (Wootton and Emmerson 2005) are promising tools to help address such questions.

Abundance‐based species distribution models could be further improved by considering fine‐scale microclimatic data, a concept gaining traction for occurrence‐based species distribution models (Potter et al. 2013, Bennie et al. 2014, Lembrechts et al. 2019) and critical for better conservation planning in the face of climate change (Roslin et al. 2009, Isaak et al. 2017). Microclimate variation within grid cells can arise from variations in topography, aspect (Bennie et al. 2008, Graae et al. 2018) and land‐use features (Chen et al. 1999^, 2006, Zhao et al. 2014, Senior et al. 2017) that filter species locally, and affect abundances, depending on species physiological and climatic niches (Ashcroft et al. 2014, Nowakowski et al. 2018, Waldock et al. 2020). Including fine‐scale temporal variability of environmental predictors may also improve model performances by better representing the duration and timing of key life‐history events that influence population dynamics (Supporting information; Andrew and Fox 2020, Perez‐Navarro et al. 2021).

Incorporating environmental variation at the appropriate spatiotemporal scale for a given species is a critical area for model improvements (Roslin et al. 2009, Ashcroft et al. 2014, Rebaudo et al. 2016), especially for projections of future climate effects on species occurrence and abundance (Gillingham et al. 2012, Hannah et al. 2014, Maclean et al. 2015, Woods et al. 2015). Our sensitivity analysis indicates improved model fit with improved data resolution for some species, but not all, when using just one year of BBS data linked to a finer temporal resolution of climate data (Supporting information). This finding indicates species‐specific behaviour (migratory versus non‐migratory), mobility (sedentary or mobile, home‐range size), life‐cycle (hibernators versus year‐round activity) and environmental niche characteristics (breadth, plasticity) could contribute to the resolution and windows of microclimatic data required to accurately estimate local abundances and occurrence (Bennie et al. 2014, Lembrechts et al. 2019).

An additional problem, not present in occurrence‐based models, is that the probability of sampling a system in an extreme abundance state is higher with more samples, leading to outlier points (i.e. bright spots or dark spots). Perhaps these outliers could be an avenue to unveil important predictors of locations of hyper‐abundance or bright spots which in turn can comprise important targets for conservation (Cinner et al. 2016, Frei et al. 2018). Biased predictions and unexplained outliers have important consequences. For example, the shallower slope of predicted versus observed abundance will underestimate change in abundance when the environment changes. In contrast, the likelihood of persistence will be overestimated because abundance losses in the last stages of population decline are poorly captured by models such as ours (Bates et al. 2014). As such, separate models for occurrence and abundance patterns will need to be calibrated and outputs combined. For occurrence‐based models, more data generally leads to better models (Chefaoui et al. 2011), and we identify the opposite here with the consequence that for abundance‐based models, data‐poor species perhaps generate overconfident models, a caveat worth exploring further.

We identify that the transferability of species abundance models to novel environmental conditions is presently limited. This shortcoming also applies to occurrence‐based species distribution models (Sequeira et al. 2018a, Yates et al. 2018) and models of family‐level abundances (Sequeira et al. 2018b) but may be exacerbated when considering species abundance. Models with perfect discrimination of presence–absence can still have poor predictive power of abundance values because more mechanisms underlie abundance variation, and errors in capturing each mechanism using statistical response functions will accumulate (Bahn and McGill 2013, Johnston et al. 2015). We demonstrate model performance also declines when predicting outside the bounds of even a single covariate (rather than a spatial block (Ploton et al. 2020)), with strong consequences for future climatic predictions.

Novel climatic conditions are fast emerging (Williams and Jackson 2007) and hence solutions that improve model transferability are urgently needed (Radeloff et al. 2015, Harris et al. 2018). Whilst mechanistic models offer accurate predictions at coarse spatial scales (Fernandes et al. 2013^, 2020), further integration with correlative frameworks may enable prediction at fine scales and in novel environments (Cheung et al. 2008, Fernandes et al. 2020, Gamliel et al. 2020).

Which species to target for abundance‐based species distribution modelling?

Our consideration of strengths and limitations of species abundance models can help guide their application for predicting the spatial distribution of species abundance for systematic conservation planning (Margules and Pressey 2000, Pinsky et al. 2020, Pollock et al. 2020). Importantly, from a conservation perspective, we outline how model performance relates to rarity and thus extinction risk. Our results suggest that species with low frequency of occurrence and low mean abundance will be more challenging to predict. Perhaps such species are only weakly constrained by physiological niche limits and more strongly constrained by meta‐population dispersal, microclimate effects and availability of resources, hosts or prey items (Selig et al. 2014, Venter et al. 2014, Mouillot et al. 2016, Suggitt et al. 2018). In contrast, common and abundant species that mostly contribute to ecosystem functions and services may be good targets for species abundance modelling (Winfree et al. 2015, Mouillot et al. 2016). We also highlight how the treatment of abundance data can modify how well models perform in accuracy, discrimination and precision, which could have important consequences depending on the target application. Here, consideration of species abundances as well as changes in occurrence should greatly assist understanding how biodiversity change affects ecosystem functioning and human well‐being (Johnston et al. 2015, Kissling et al. 2018, Pinsky et al. 2020).

Conclusions

Species abundances in localised field surveys can be predicted for a large number of species on the basis of broad‐scale environmental and human factors, such as climate, land cover and habitat area. Species abundance models showed surprisingly similar performance for species from two very different taxonomic groups and ecological contexts. Transferring models to novel conditions was very challenging, however. Models fitted better for more frequently encountered and abundant species, highlighting that abundance models may be most applicable to questions relating to ecosystem function and service provision rather than in modelling rare or endemic species under extinction threats. When common species are to be prioritised (Pinsky et al. 2020), species abundance models could be used in many ways, providing spatial maps of species abundance, landscape scale estimates of ecological processes and services (Gilby et al. 2020) or helping to identify regions with large, stable, viable populations that can act as sources and facilitate reserve spillover and ecosystem stability (Halpern et al. 2010, Rondinini and Chiozza 2010, Timus et al. 2017, Cabral et al. 2020; Table 1). We argue that spatial abundance models can provide critical biodiversity information with the potential to improve the ecological relevance and species conservation applications of species distribution models.

Author contributions

Conor Waldock: Conceptualization (lead); Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Software (lead); Validation (lead); Visualization (lead); Writing – original draft (lead); Writing – review and editing (lead). Rick D. Stuart‐Smith: Data curation (equal); Writing – review and editing (equal). Camille Albouy: Funding acquisition (equal); Writing – review and editing (equal). William W. L. Cheung: Writing – review and editing (equal). Graham J. Edgar: Data curation (equal); Writing – review and editing (equal). David Mouillot: Funding acquisition (equal); Writing – review and editing (equal). Jerry Tjiputra: Data curation (equal); Writing – review and editing (equal). Loic Pellissier: Funding acquisition (equal); Supervision (equal); Writing – review and editing (equal).

Transparent Peer Review

The peer review history for this article is available at <https://publons.com/publon/10.1111/ecog.05694>.