Can incomplete knowledge of species’ physiology facilitate ecological niche modelling? A case study with virtual species
Abstract
Aim
Ecological niche modelling (ENM) is widely used in biogeography and conservation studies. The performance of ENM is influenced by the quality of species’ presence and absence datasets. Presences may include marginal localities, and absences are usually difficult to collect. We evaluated the use of species’ physiological limits to improve selection of presences and absences for ENM in a virtual species framework with defined response functions as surrogates for physiological knowledge.
Location
The lower 48 states in USA.
Methods
We generated physiologically informed absences based on either complete or incomplete knowledge of species’ physiology. With the same physiological knowledge, we reduced noise (incorrect or marginal locations) from presence datasets, completely or incompletely. We compared (i) models based on physiologically informed absences and random background points, (ii) models based on presences with and without noise and (iii) models obtained with and without incorporating physiological knowledge in absence and presence datasets.
Results
Only absences based on complete physiological information produced better performing models than random background points. Model improvement was positively correlated with the percentage of noise being removed from the presence data, and best-performing models were obtained with true presences (all noise removed). Manipulating both absences and presences led to better models than manipulating only presences when all or majority of physiological limits were known.
Main conclusions
The benefit of incorporating physiological information into ENM datasets largely depends on completeness of physiological knowledge, but in reality incomplete understanding of species’ physiology is the norm. We found that applying incomplete physiological knowledge to absences may bias ENM, and thus, use of random background points is recommended; on the other hand, removing noise from species’ presence datasets based on incomplete physiological limits increases model performance, thus this approach could potentially improve the effectiveness of ENM applications in conservation planning and invasive species management.
1 INTRODUCTION
Ecological niche modelling (ENM) is a tool widely used in biogeography, conservation biology, and ecology to study species’ ecological niche and distribution through space and time (Elith & Leathwick, 2009; Franklin & Miller, 2009; Peterson et al., 2011). The theoretical basis of ENM is the concept of fundamental niche, defined by Hutchinson (1957) as the set of environmental conditions permitting indefinite existence of species. Generally, the environmental conditions considered in ENM are abiotic in nature (or scenopoetic; Soberón, 2007); thus, the niche being estimated is the abiotic niche (Soberón & Peterson, 2005). The niche estimated in environmental space is used to predict the species’ distribution in geographic space (Peterson et al., 2011).
Without considering species’ dispersal abilities and biotic interactions, we expect that the environmental conditions of species’ presences are part of the fundamental niche, whereas conditions of species’ absences are not (Araújo & Pearson, 2005; Soberón & Peterson, 2005), but usually in reality this is not the case. Species occurrence data, digitalized and stored in publicly accessible databases (e.g., www.gbif.org; www.bison.usgs.ornl.gov), have quality issues that warrant our attention (Beck, Böller, Erhardt, & Schwanghart, 2014; Feeley & Silman, 2010). Presence data can include occasional observations in unsuitable areas (noise), where species cannot persist, for example sink populations (Pulliam, 2000) or marginal occurrences (Feng & Papeş, 2015). Such noise in presence data can blur the modelling goal and bias the model prediction (e.g., towards broader potential distribution; Soley-Guardia, Radosavljevic, Rivera, & Anderson, 2014), but the issue has not drawn much attention, probably because of the difficulty or subjectivity in delineating noise from true presence.
Additionally, true absences are rare (Mackenzie, 2005), because gathering absences is not usually the goal of field surveys and the observed absence may be an artefact of species’ detection or limited dispersal ability rather than environmental unsuitability. In lieu of absence data, pseudo-absences are simulated for ENM algorithms (Engler, Guisan, & Rechsteiner, 2004; Hirzel, Helfer, & Metral, 2001). Frequently, random background points are used (e.g., the default method in MaxEnt; Phillips, Anderson, & Schapire, 2006), a mathematically feasible approach but difficult to interpret because it could mix true presences and true absences. Other methods simulate pseudo-absences from environmentally or/and geographically stratified areas (Barbet-Massin, Jiguet, Albert, & Thuiller, 2012; Iturbide et al., 2015; Senay, Worner, & Ikeda, 2013), but the best method depends on the modelling algorithm (Barbet-Massin et al., 2012). Phillips et al. (2009) used presences of related species as absences for the focal species, but this method requires more data and may not be broadly applicable. Without reliable data inputs (i.e., presences and absences), potential distribution maps obtained with ENM warrant our attention, particularly when used in conservation or invasive species management (Bond, Thomson, & Reich, 2014; Kulhanek, Leung, & Ricciardi, 2011).
Knowledge of species’ physiology has been fundamental in developing biophysical models to estimate potential distributions (Mathewson et al.,2016; Porter, Munger, Stewart, Budaraju, & Jaeger, 1994); however, these are data-intensive approaches requiring detailed information about the organism's energy budget and exchange with the environment and thus are unfeasible for most species (Peterson, Papeş, & Soberón, 2015). In contrast, basic knowledge of conditions that allow species’ survival (physiological limits; e.g., thermal tolerance) may be available for many species (Araújo et al., 2013; Hoffmann, Chown, & Clusella-Trullas, 2013). Here, we focus on integrating species’ physiological limits into ENM to address the issues of (1) noise in presence data and (2) relevance of pseudo-absence data. We assume that species’ physiological tolerance to abiotic conditions reasonably approximates the fundamental niche (Feng & Papeş, 2017; Martínez, Arenas, Trilla, Viejo, & Carreño, 2015). With inferences of what is physiologically tolerable by a species, we can eliminate noise from species’ presence dataset based on biologically meaningful information. Similarly, we can reasonably infer what is physiologically intolerable for a species, thus select biologically meaningful absences, independent of our ability to observe absences.
We tested integration of physiological limits into ENM through a virtual species framework, commonly used in developing and assessing ENM methodologies (Hirzel et al., 2001; Qiao et al., 2016; Zurell et al., 2010). Virtual species are simulated ecological niches, defined by abiotic variables in the environmental space. A simulated ecological niche is usually composed of multiple mathematical functions, each one describing a species’ response to one abiotic condition. The product (e.g., additive or multiplicative) of all mathematical functions determines the focal species’ response to the environment (e.g., suitability or probability of presence on the landscape), which is usually transformed into binary format (presences and absences). The advantage of using virtual species instead of real species is that the distribution of the species is defined and known; thus, the methodological evaluation is mathematically robust (Qiao, Soberón, & Peterson, 2015). We defined the fundamental niche with suitability functions in the virtual species framework and used the functions to determine the species’ physiological limits. However, in real world we seldom have complete knowledge of a species’ fundamental niche or physiological tolerance, so we simulated scenarios of incomplete physiological knowledge.
We designed three experiments to investigate techniques of integrating physiological limits into ENM. In Experiment 1, we simulated absences as (i) random background points, (ii) physiologically informed absences based on incomplete knowledge of species’ physiology and (iii) based on complete knowledge. In Experiment 2, we simulated (i) presences with noise, (ii) presences with noise reduced based on incomplete knowledge of species’ physiology and (iii) based on complete knowledge. In Experiment 3, we combined the design of Experiments 1 and 2. We hypothesized that physiologically informed absences will produce better performing models than random background points because the former are biologically relevant; the presences with reduced noise will produce better performing models than presences with noise because the noise could bias the models; and finally, the integration of physiologically informed absences and presences with reduced noise will lead to highest performing models because of the combined positive effects from both data inputs.
2 METHODS
2.1 Defining virtual species
We simulated ecological niches of virtual species using four bioclimatic variables in a real landscape, the contiguous USA (or lower 48 states). The four bioclimatic variables were annual mean temperature, temperature seasonality, annual precipitation, and precipitation seasonality, downloaded at the resolution of 2.5 arc min from WorldClim (Hijmans, Cameron, Parra, Jones, & Jarvis, 2005). We chose the four variables because they reflected broad climatic patterns (mean and variation of temperature and precipitation) and the correlation among these variables within the study area was moderate (|r| < .52), thus the influence of collinearity was reduced (Dormann et al., 2013). We chose the resolution of 2.5 arc min to guarantee the needed sample sizes for experimental simulations, while minimizing the computation time.
We simulated a pool of random virtual species using the R package virtualspecies (Leroy, Meynard, Bellard, & Courchamp, 2016). We defined each species using four different Gaussian functions, each corresponding to a bioclimatic variable (representing knowledge of one physiological limit) and used the product of the four functions as the final suitability function of each species. The parameters of the Gaussian functions varied across the virtual species and thus produced distinct final suitability maps. To simulate virtual species with realistic distributions, we enabled the realistic option in the R package virtualspecies (Leroy et al., 2016), which ensured a latter function was restricted to areas with higher suitability values defined by the former function or functions, instead of independently generating four Gaussian functions. This option prevents generating unrealistic species and suitability maps (e.g., a species present in both extremely hot and cold areas), because contradictions among suitability functions are avoided (Leroy et al., 2016). We transformed the suitability maps into distribution maps (presences and absences) using a threshold method: pixels with suitability values ≥0.5 were classified as presences and those with values <0.5 as absences. We calculated the species’ prevalence by dividing the number of presence pixels by that of total pixels. Because of the potential influence of species’ prevalence on modelling performance (Manel, Williams, & Ormerod, 2002; Santika, 2011), we randomly selected six virtual species along a gradient of prevalence values (from 0.06 to 0.57; see Fig. S1 in Supporting Information) and evaluated the consistency of our results over this gradient.
2.2 Experimental design
2.2.1 Experiment 1—simulating absences
To explore the idea of simulating absences outside the species’ physiological limits, we generated five different sets of absences (Fig. S2). For set0 (control group), we randomly selected 10,000 points (random background points) from the study area, the predominant method in current ENM studies (Barbet-Massin et al., 2012). For the remaining sets (1, 2, 3 and 4; experimental groups), we simulated equal-size absence datasets using incomplete physiological knowledge (from one to three niche dimensions) for set1 to set3 and complete knowledge (from all four niche dimensions) for set4. Thus, the absences in set4 were true absences. We used the following specific steps for set1: we classified the pixels into presences or absences (i.e., physiologically tolerant or intolerant for the species, respectively) using the suitability function of one bioclimatic variable; then, we randomly selected absences for set1 based on this classification. The product of the functions of two bioclimatic variables was used for set2, three variables for set3 and all four variables for set4. We used the same procedure and threshold (0.5 suitability) explained above to transform suitability maps to presence–absence maps. We included all possible combinations of bioclimatic variables for set1, set2 and set3. To explore the influence of the amount of training presences as well as presence/absence ratio (Barbet-Massin et al., 2012), we randomly selected 100, 300 or 1,000 presences from the distribution map. Coupled with the variation in absence simulations (set0 to set4), we trained models using 15 different combinations of training presences and absences for each virtual species and algorithm (see below, Section 2.3).
2.2.2 Experiment 2—simulating presences
To investigate the effect of reducing noise in the presence datasets with species’ physiological tolerance information, we designed a second experiment with five different sets of presences (Fig. S3). In set0 (control group), we simulated 1,000 presences composed of 80% true presences and 20% noise from less suitable areas (suitability values from 0.3 to 0.5), similar to occasional observations in species’ presence datasets in real situations. In set1 to set4 (experimental groups), we kept the same number of true presences as in control group, but we removed noise using known species’ physiological tolerance, either incompletely, from one to three niche dimensions for set1 to set3, or completely, from all niche dimensions, for set4. As all noise was removed from set4, this represented true presences of virtual species. For set1, we classified the study area pixels into species’ presences (physiologically tolerant) or absences (physiologically intolerant) based on the suitability function of one bioclimatic variable and eliminated the noise using this classification. Similarly, we used the product of the functions of two bioclimatic variables for set2, three variables for set3, and all variables for set4. We included all possible combinations of variables for set1, set2, and set3. The same procedure and threshold (0.5 suitability) as explained above were used to transform suitability maps to presence–absence maps. The number of the presences in the five sets ranged from 1,000, when no noise was removed, to 800, when all noise was removed. To explore the influence of the number of presences on model performance, we repeated the same procedure but started with 100 and 300 training presences with noise, for the five sets (set0 to set4). In all, we trained models with 15 variations of presence sets and a sample of 10,000 random background points, for each virtual species and algorithm (see below, Section 2.3).
2.2.3 Experiment 3—simulating both presences and absences
We designed our last experiment with the goal of investigating the combined effect of using absences outside the species’ physiological limits and presences with reduced noise (Fig. S4). The control set-up was similar as for Experiment 1 and Experiment 2: 1,000 presences of which 20% represented noise (locations from less suitable areas) and 10,000 random background points. For the experimental groups (set1 to set4), we removed noise from presence datasets based on one to four physiological limits; these datasets were paired with physiologically informed absences, simulated using physiological limits in one (set1) to four (set4) environmental dimensions. Thus, Experiment 3 incorporated the approach for simulating absences from Experiment 1 and for refining presences from Experiment 2. We also varied the size of presence datasets by considering 100 or 300 presences. We trained models using 15 different combinations of training presences and training absences, for each algorithm (see below, Section 2.3) and virtual species.
2.3 Modelling algorithms
We used four modelling algorithms to evaluate the consistency of our framework and results: boosted regression tree (BRT; Friedman, Hastie, & Tibshirani, 2000; Leathwick, Elith, Francis, Hastie, & Taylor, 2006), generalized linear model (GLM; McCullagh, 1984; Wintle, Elith, & Potts, 2005), generalized additive model (GAM; Hastie & Tibshirani, 1990; Lehmann, Overton, & Leathwick, 2002) and maximum entropy (MaxEnt; Phillips et al., 2006). BRT is a machine-learning algorithm that uses a boosting method and simple regression tree models (Elith, Leathwick, & Hastie, 2008; Elith et al., 2006). GLM and GAM represent the traditional regression approach, with intermediate performance among ENM algorithms (Elith et al., 2006). MaxEnt is a good performing and widely used algorithm that makes inferences of the probability of species’ presence based on the maximum entropy principle (Phillips & Dudik, 2008).
As comparing performance of algorithms was not the goal of this study, we generally followed the parameter settings from previous studies that have shown reliable performance. We generated BRT models in R package dismo (Hijmans, Phillips, Leathwick, & Elith, 2013) using Bernoulli distribution and learning rate of 0.001, tree complexity of 5, step size of 50, and maximum trees size of 10,000, with fivefold cross-validation (Elith et al., 2008; Ridgeway, 2006). We trained GLM in R (R Core Team, 2014) using binomial with a logit link function and quadratic interaction and adopted the Akaike's information criterion stepwise selection (McCullagh & Nelder, 1989). We performed the GAM experiments in R package mgcv, using logit link with outer, newton optimizers and default degree of freedom (−1) that triggers an internal generalized cross-validation to optimize the actual effective degree of freedom (Wood, 2011). We assigned equal weights to training presences and absences (total weight of presences equals that of absences) for BRT, GLM, and GAM algorithms (Barbet-Massin et al., 2012). Finally, we ran MaxEnt in R package dismo (Hijmans et al., 2013), with default regularization multiplier and autofeatures option that determines the combination and transformation of variables (i.e., features) based on the number of training presences (Phillips & Dudik, 2008).
2.4 Evaluation indices of model performance
A total of 69,120 models were generated by repeating the three experiments 20 times for each virtual species, modelling algorithm and combination of training presences and absences. We used 10% of true presences and the same number of absences of each virtual species as testing data so that the ratio of testing presences and absences was one. We did not use the same pixel (presence or absence) at the same time for training and testing of models unless it was used as a random background point. We evaluated all models using three threshold-dependent indices, calculated with lowest training presence threshold (the lowest suitability value associated with training presences; Pearson, Raxworthy, Nakamura, & Peterson, 2007). Omission rate measures the percentage of presences predicted absent. Commission rate measures the percentage of absences predicted present. True skill statistic (TSS) accounts for both omission rate and commission rate and ranges from −1 to 1, with values above 0 indicating models better than random (Allouche, Tsoar, & Kadmon, 2006).
2.5 Statistical tests
To assess the effect of number of physiological limits on model performance in each experiment, we ran one-way ANOVAs to compare model evaluation indices of the control and four experimental groups. We used Tukey's post hoc analysis for the paired comparison of any two groups (Zar, 2010). When the assumption of homogeneity of variances was violated, we used Welch test and Games–Howell post hoc analysis instead (Games & Howell, 1976; Welch, 1947). We performed the statistical tests for each possible combination of number of training presences, modelling algorithm, and virtual species, expecting to find consistency of patterns across these settings. To compare the differences of manipulating presences only (Experiment 2) versus manipulating presences and absences (Experiment 3), we used t tests on the model evaluation indices for each pair of sets (e.g., set1 vs. set1) or used Welch test when homogeneity of variances was violated (Welch, 1947; Zar, 2010). We ran analyses for each combination of number of training presences, modelling algorithm, and virtual species.
3 RESULTS
3.1 Experiment 1—simulating absences
TSS and omission rate of models increased and commission rate decreased (Figures 1 & S5) as more physiological limits were used to define the training absences (set1 to set4). Models based on absences with partial physiological information (set1 to set3) had significantly lower TSS (p < .05) than models obtained with control group (set0, random background points), in all or majority of combinations of algorithm, number of training presences, and virtual species (Table 1). In contrast, the absences based on complete physiological information (set4) produced models with highest TSS by maintaining relatively low omission and commission rates. Most of the set4 models (74%) had significantly higher TSS (p < .05) than the control group (set0). Overall, set1 models showed the lowest TSS and omission rate but highest commission rate and set4 models showed the highest TSS and omission rate but lowest commission rate. The evaluation indices of set0 models were between the two extremes, although more similar to indices of set4 models, with a few exceptions (omission rates of GAM and MaxEnt models trained with 100 presences; Table 1 & Figures 1 & S5).
| Experiment | Comparison | TSS (%) | Omission rate (%) | Commission rate (%) | ||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Lower | No difference | Higher | Lower | No difference | Higher | Lower | No difference | Higher | ||
| Experiment 1 | set1 vs. set0 | 100 | 0 | 0 | 65 | 35 | 0 | 0 | 0 | 100 |
| set2 vs. set0 | 97 | 0 | 3 | 36 | 56 | 8 | 0 | 0 | 100 | |
| set3 vs. set0 | 61 | 35 | 4 | 18 | 51 | 31 | 3 | 25 | 72 | |
| set4 vs. set0 | 1 | 25 | 74 | 8 | 46 | 46 | 88 | 13 | 0 | |
| Experiment 2 | set1 vs. set0 | 0 | 76 | 24 | 0 | 99 | 1 | 25 | 75 | 0 |
| set2 vs. set0 | 0 | 14 | 86 | 0 | 57 | 43 | 92 | 8 | 0 | |
| set3 vs. set0 | 3 | 3 | 94 | 0 | 11 | 89 | 100 | 0 | 0 | |
| set4 vs. set0 | 4 | 4 | 92 | 0 | 0 | 100 | 100 | 0 | 0 | |
| Experiment 3 | set1 vs. set0 | 100 | 0 | 0 | 15 | 68 | 17 | 0 | 0 | 100 |
| set2 vs. set0 | 47 | 28 | 25 | 6 | 33 | 61 | 26 | 24 | 50 | |
| set3 vs. set0 | 1 | 18 | 81 | 0 | 13 | 88 | 89 | 11 | 0 | |
| set4 vs. set0 | 1 | 3 | 96 | 0 | 0 | 100 | 100 | 0 | 0 | |
- Percentages may not total 100% because of rounding
3.2 Experiment 2—simulating presences
Comparable to results of Experiment 1, TSS and omission rate of models increased and commission rate decreased (Figures 2 & S6) with more physiological information used to refine the training presences (set1 to set4). With noise incompletely or completely removed (set2 to set4), most models (86%–94%) had significantly higher TSS (p < .05) than that models based on set0 (presences with noise) (Table 1). The percentage of models with significantly higher TSS increased from 24% to 94% as more physiological limits were included (set1 to set4). This pattern was mainly due to changes in the commission rate (Fig. S6), which were related to the percentage of noise being removed (Figures 3 & S7). This outcome was more notable for broadly distributed species. BRT and GAM models trained with 100 presences slightly deviated from the general trend of results, especially by showing high omission rates (Figures 2 & S6).
3.3 Experiment 3—simulating both presences and absences
Overall, the results obtained with Experiment 3 were similar to those obtained with Experiments 1 and 2: as more physiological information was used to manipulate training presences and absences (set1 to set4), the models achieved higher TSS and omission rate and lower commission rate (Figures 4 & S8). Compared with models based on control group (set0, random background points and presences with noise), all models obtained with set1 (considering one physiological limit) had significantly lower TSS (p < .05). The patterns were less clear for models obtained with set2 (two physiological limits), which had a mix of significantly higher or lower relationships with set0 models, or non-significant differences (Table 1). Models based on set3 and set4 (three and four physiological limits, respectively) had significantly higher TSS (p < .05) than set0 models in most cases (81% for set3 models and 96% for set4 models). Similarities between the results of Experiment 3 and Experiment 1 included lowest TSS and omission rate and highest commission rate of models obtained with set1 and highest TSS and omission rate and lowest commission rate for models based on set4 (Figures 4 & S8); also similar to Experiment 1 results, in Experiment 3, the evaluation indices of set0 models were between the two extremes (set1 models and set4 models); but in contrast to Experiment 1, evaluation indices of set0 models approximated set2 models, instead of set4 models. BRT models trained with 100 presences slightly deviated from the general trend of results, especially showing high omission rates (Figures 4 & S8).
3.4 Comparison between Experiment 2 and Experiment 3
Using a single physiological limit to select absences and reduce noise from presences (set1 in Experiment 3), we obtained models with significantly lower TSS (p < .05) and higher commission rate than using physiological limits only to reduce noise from presence datasets (set1 in Experiment 2), in all cases (Table 2 & Figures 5 & S9). In most cases (>82%), two physiological limits applied to both presence and absence simulations (set2 of Experiment 3) produced models with significantly lower TSS and higher commission rate (p < .05) than using two physiological limits to simulate presences (set2 in Experiment 2). The pattern was reversed when using three or four physiological limits (set3 and set4): in more cases, the models of Experiment 3 had significantly higher TSS and lower commission rate (p < .05) than models of Experiment 2. This reversed pattern was more obvious for species with higher prevalence (Figures 5 & S9). The differences in the omission rate were generally less pronounced between the models of the two experiments (Table 2).
| Experiment 2 (exp2) vs. Experiment 3 (exp3) | TSS (%) | Omission rate (%) | Commission rate (%) | ||||||
|---|---|---|---|---|---|---|---|---|---|
| Higher in exp2 | No difference | Higher in exp3 | Higher in exp2 | No difference | Higher in exp3 | Higher in exp2 | No difference | Higher in exp3 | |
| set0 vs. set0 | 0 | 100 | 0 | 0 | 100 | 0 | 0 | 100 | 0 |
| set1 vs. set1 | 100 | 0 | 0 | 35 | 44 | 21 | 0 | 0 | 100 |
| set2 vs. set2 | 82 | 11 | 7 | 24 | 25 | 51 | 7 | 10 | 83 |
| set3 vs. set3 | 29 | 31 | 40 | 13 | 31 | 57 | 39 | 31 | 31 |
| set4 vs. set4 | 3 | 14 | 83 | 13 | 39 | 49 | 93 | 7 | 0 |
- Percentages may not total 100% because of rounding.
4 DISCUSSION
We studied three methods of integrating physiological information into ENM by optimizing selection of training presences and absences. The first method, selecting physiologically informed absences, did not produce better performing models than random background points, unless complete knowledge of the species physiology was used (in our study, intolerance to four abiotic conditions). The second method, selecting presences that met physiological limits, produced better performing models and model improvement (measured with commission rate) was positively correlated with percentage of noise being removed from presence dataset. Our findings with these two methods generally held across all combinations of virtual species, algorithm and number of training presences. Our third method, integrating physiologically informed absences and presences with reduced noise, did not produce better performing models than adjusting presence datasets only, unless all or majority (three of four) of physiological limits were known; the improvement in model performance when adjusting both presences and absences was more obvious for species with broader distributions. The patterns we found were rather consistent for all algorithms, although with a few exceptions when fewer presences were used.
4.1 Physiologically informed absences
Although physiologically informed absences could be true absences because the environmental conditions are unsuitable for the species, the approach of simulating physiologically informed absences did not improve overall performance of models (i.e., TSS) unless most or all physiological limits were known. Our interpretation of this outcome is that incomplete information of species’ physiological limits provides a biased understanding of conditions associated with species’ absence, thus misguiding ENM towards a broader estimate of the fundamental niche. Martínez et al. (2015) obtained a broader species’ potential distribution based on one type of physiological tolerance (i.e., thermal) than based on an ecological niche model. The broader estimation should be signalled by higher commission rate, similar to what we observed with absences with partial physiological information. The disagreement between physiological prediction and ENM prediction may be attributed to the effect of overlooking biotic interactions (Martínez et al., 2015); another plausible explanation is that only one type of physiological tolerance amounts to insufficient understanding of the species’ fundamental niche.
In theory, incorporating more dimensions of physiological tolerance should improve identification of true absences, thus reduce overestimation of the fundamental niche; our results supported this expectation. We also found that models of broadly distributed species benefited most from use of physiologically informed absences incorporating all or majority of physiological limits. This outcome is probably due to the fact that such physiologically informed absences approximated the complete information of absence, the positive effect of which outweighed the negative effect of noise in presences. However, optimistic interpretations of this result should be avoided because in reality we rarely have a complete understanding of a species’ physiology. Therefore, the use of physiologically informed absences should be avoided when knowledge of a species’ physiology is scarce. Instead, we recommend the use of random background points because our experiments show a minimal effect of true absences on model optimization. However, we note that our method of selecting random background points may not be ideal in other, diverse situations (Barbet-Massin et al., 2012; Iturbide et al., 2015; Lobo & Tognelli, 2011; Phillips et al., 2009).
4.2 Removing noise from presence datasets
In contrast with the patterns observed for simulated physiologically informed absences, the technique of removing physiologically intolerant presences increased the overall model accuracy. Our interpretation is that removing noise from presence datasets reduces the commission rate, thus avoiding overestimation of species’ fundamental niche or potential distribution. Other studies have used different methods to eliminate noise from occurrence datasets in the context of ENM. For example, a thresholded model based on omission rate (e.g., 10%) may deliberately omit areas of lower suitability probability from the predicted potential distribution (Peterson et al., 2011), corresponding to a narrower estimate of the niche; however, threshold selection depends on researcher’ judgement on the quality of the occurrences, which can be subjective. Soley-Guardia et al. (2014) implemented a two-step approach to detect marginally suitable occurrences, by first building a preliminary niche model and locating occurrences with lower predicted suitability, then using habitat information from collectors’ field notes and literature to determine marginal occurrences; this approach can be objective although may be limited by the role of habitat or availability of such information (Soley-Guardia et al., 2014). Another approach is monitoring population dynamics (Pulliam, 2000; Soberón, 2007) to understand status of species (temporal vs. indefinite existence or sink vs. source population), but logistics and time constraints do not make this approach widely applicable.
Our proposed approach provides a biologically meaningful avenue for handling noise in species’ presence datasets. Physiological limits are species’ responses to abiotic conditions and should provide a reasonable approximation of the fundamental niche (Feng & Papeş, 2017; Martínez et al., 2015). A focal species’ distribution can be better understood through application of physiological limits to the presence dataset (Feng & Papeş, 2017), and the noise-reduced presence dataset can lead to better performing ENM, in our study evidenced by higher TSS and lower commission rate. A lower commission rate generally means a narrower but more precise prediction in geographic space. Such model improvement can increase the effectiveness of ENM conservation applications, for example in rare species surveys or invasive species management (Bond et al., 2014; Kulhanek et al., 2011), because limited effort and resources can be focused on a smaller, targeted area. However, the effect of physiological filters is dependent on their importance on a species’ distribution; best case scenarios are when the known physiological limits are dominant factors shaping species’ distribution and the noise is well expressed along the environmental axes being considered. We also note that models obtained with BRT and GAM trained with 100 presences showed relatively poor performance, characterized by high omission rates; therefore, we recommend avoiding these situations.
4.3 Completeness and effectiveness of physiological limits in ENM
Our study showed that complete knowledge of physiological limits applied to selecting absences will lead to better models than random background points. Better performing models are also obtained if at least half of the physiological limits are known and are applied to selecting both absences and presences, or if any physiological limit is known and is applied to reducing noise in presence data. Therefore, the effectiveness of the three techniques tested here largely depends on our knowledge of species’ physiology. For studies of real species, scholars commonly gain knowledge of physiological limits through reviewing literature (Araújo et al., 2013; Feng & Papeş, 2017; Hoffmann et al., 2013), but this knowledge could also be gained through field surveys (Churchill, 2013; White, Hamilton, & Sarnelle, 2015) and laboratory experiments (Claudi et al., 2013; McMahon, 1996). We expect that species’ physiological information is substantial in the literature, because physiology is one of earliest scientific disciplines in biology (Scheer, 1963). Thermal tolerance is one of the major foci of physiological research, a key determinant of species’ geographic distribution (Gaston, 2003; Kearney & Porter, 2009; Wiens & Donoghue, 2004) and frequently studied in relation to climate change and extinction risk (Sinervo et al., 2010) and invasive species management (Morse, 2009). Precipitation (Byrne, McMahon, & Dietz, 1988), pH (Claudi et al., 2013), salinity (Morton & Tong, 1985), and calcium concentration (Cairns & Yan, 2009) have also been studied for various purposes. Information on physiological limits has been accumulating in the literature, but taxonomic or trait biases could be common (Feng & Papeş, 2017). A complete understanding of species’ physiology seems unattainable for most species, as well as assessing the completeness of physiological knowledge. However, we argue that completeness does not necessarily mean effectiveness. Species’ ecological niche can be defined with a large number of variables (Hutchinson, 1957), but in a real landscape not all variables are playing a crucial role and those that do may not have equal roles. For example, air oxygen concentration must be a crucial factor in defining the niche of nine-banded armadillo, and possibly of many other terrestrial species, but is not expected to limit the species’ geographic range; on other hand, temperature and precipitation are important for shaping the distribution of nine-banded armadillo in North America (Feng & Papeş, 2015). As we have shown in Experiment 2, model improvement was positively associated with the percentage of noise being removed from presence datasets (Figure 3); from this perspective, we argue that, although complete physiological knowledge is rare, identifying one effective variable is more beneficial than considering several noninformative variables in the context of improving ENM.
4.4 Looking forward
Current ENM algorithms (typically correlative) are useful for identifying relationships between species’ presence or absence and the environment, which is an estimate in between the fundamental niche and realized niche (Soberón & Nakamura, 2009), but are generally weak in extrapolations to novel conditions (Peterson et al., 2011). Physiological information mechanistically relates species’ presence and absence with the environment, and these relationships are transferrable to novel conditions (e.g., climate change; Martínez et al., 2015). The drawback is lack of complete understanding of every biological aspect of a species. Future studies may consider different ways of defining physiologically intolerant locations or develop new ENM algorithms that can directly handle information from the perspective of species’ physiology. For example, new algorithms could use biologically meaningful information [e.g., physiological tolerance in Feng and Papeş (2017); expert range map in Domisch, Wilson, and Jetz (2016)] as prior understanding of species’ response to environmental conditions, and update the response functions based on occurrence data in a Bayesian framework (e.g., Brewer, O'Hara, Anderson, & Ohlemüller, 2016).
ACKNOWLEDGEMENTS
The computing for this project was performed at the High Performance Computing Center at Oklahoma State University supported in part through the NSF-OCI 1126330. We thank three anonymous referees for constructive comments on an earlier draft of this manuscript.
BIOSKETCHES
Xiao Feng is a Ph.D. candidate at Oklahoma State University. His research focuses on applications of ecological niche modelling (ENM) on biogeography questions and methodological and conceptual issues in ENM, with special interest in the integration of ENM and physiological information.
Monica Papeş is an assistant professor at University of Tennessee. Her research focuses on species’ geographic distributions and in particular on remote sensing applications to mapping biodiversity, seasonal variation of species’ distributions and predicting areas at risk of invasive species.
