Biodiversity Informatics, 15, 2020, pp. 92-102 92 THE ABUNDANT NICHE-CENTROID HYPOTHESIS: KEY POINTS ABOUT UNFILLED NICHES AND THE POTENTIAL USE OF SUPRASPECFIC MODELING UNITS Carlos Yañez-Arenas1*, Gerardo Martín2, Luis Osorio-Olvera3,4, Jazmín Escobar-Luján1, Sandra Castaño-Quintero1, Xavier Chiappa-Carrara1 and Enrique Martínez-Meyer5 1Laboratorio de Ecología Geográfica, Unidad de Biología de la Conservación, Parque Científico y Tecnológico de Yucatán, Universidad Nacional Autónoma de México, Sierra Papacal, Yucatán 97302, México. 2 MRC Centre for Global Infectious Disease Analysis, Department of Infectious Disease Epidemiology, Imperial College London, UK. 3Biodiversity Institute, University of Kansas, Lawrence, 66045, USA. 4Instituto de Ecología, Universidad Nacional Autónoma de México, Ciudad Universitaria, Mexico City 04500, México 5Departmento de Zoología, Instituto de Biología, Universidad Nacional Autónoma de México, Ciudad Universitaria, Mexico City 04510, México. Abstract. Correlative estimates of fundamental niches are gaining momentum as an alternative to predict species’ abundances, particularly via the abundant niche-centroid hypothesis (an expected inverse relationship between species’ abundance variation across its range and the distance to the geometric centroid of its multidimensional ecological niche). The main goal of this review is to re- capitulate what has been done, where we are now, and where should we move towards in regards to this hypothesis. Despite evidence in support of the abundance-distance to niche centroid relationship, its usefulness has been highly debated, although with little consideration of the underlying theory re- garding the circumstances that might break down the relationship. We address some key points about the conditions needed to test the hypothesis in correlative studies, specifically in relation to niche characterization and configurations of the Biotic-Abiotic-Mobility (BAM) framework to illustrate the problem of unfilled niches. Using a created supraspecific modeling unit, we show that species for which only a portion of their fundamental niche is represented in their area of historical accessibility (M)—i.e., when the environmental equilibrium condition is violated—it is impossible to character- ize their true niche centroid. Therefore, we strongly recommend to analyze this assumption prior to assess the abundant niche-centroid hypothesis. Finally, we discuss the potential of using modeling units above the species level for cases in which environmental conditions associated with species’ occurrences may not be sufficient to fully characterize their fundamental niches. Key words: ecological niche modeling, niche centrality, abundant niche-centroid hypothesis, abundance, population density. Introduction Species Distribution Models (SDMs) and Eco- logical Niche Models (ENMs) represent a set of tools and techniques in which georeferenced records of presence (and sometimes absence) of species are statistically related with a set of environmental pre- dictors (e.g., temperature, precipitation, elevation) to infer their ecological requirements (i.e., their ecolog- ical niche), and project them onto the geography to estimate their potential distribution (Peterson et al. 2011). The estimated distributions can be used for different purposes: to discriminate areas with and without biological potential for the species of interest (Guisan et al. 2006), evaluate potential shifts in the geographic ranges of species as a consequence of en- vironmental changes (Thomas et al. 2004; Peterson 2006), identify regions where invasive species could * Corresponding author: lichoso@gmail.com Biodiversity Informatics, 15, 2020, pp. 92-102 93 establish (Peterson 2003; Thuiller et al. 2005), de- scribe biodiversity patterns and carry out macroeco- logical studies (Guisan and Rahbek 2011; Calabrese et al. 2014), among many others. However, for certain research goals and ques- tions, knowing the extent of occurrence is not suf- ficiently informative (Gaston and Rodrigues 2003; Hurlbert and Jetz 2007; Hooker et al. 2011). For instance, one of the criteria recommended in the design and establishment of natural protected areas is to maximize the area of high-quality habitat for a target species (Pearce and Ferrier 2001). In a dis- tribution map it is not possible to identify areas of high-quality habitat since all portions of the species’ distribution have the same weight. Furthermore, dis- tributional maps alone are useless to identify whether the protection of a fraction of the distribution (with- out associated information on demographic aspects) is sufficient to guarantee the viability of the species (Rodrigues et al. 2004). Population abundance or density are frequently good indicators of habitat quality (Johnson 2007), re- flecting factors such as reproductive rate, longevity, carrying capacity, and susceptibility of populations to extinction. Therefore, modeling and mapping spe- cies’ abundance may be more informative for many researchers and stakeholders than just estimating geographic ranges (Hobbs and Hanley 1990). When abundance/density is available from several loca- tions, it is preferable to model it directly as a function of key environmental predictors (Boyce et al. 2001). However, obtaining abundance data is complicated and demanding, especially for rare and cryptic spe- cies (Johnston et al. 2015). Therefore, since SDMs/ ENMs became popular, researchers have been inter- ested in evaluating their capacity to infer species’ abundance (e.g., Pearce and Ferrier 2001; Pearce and Boyce 2006). Outputs of many algorithms used in SDMs/ ENMs are raster layers with continuous values that are usually interpreted as environmental suitability, that is: higher values should represent better envi- ronmental conditions for species. Yet, this interpreta- tion assumes the existence of a positive relationship between the estimated output of the algorithm and independent measures directly related to a species’ biological fitness, like abundance or population den- sity (Gil and Lobo 2017). First attempts to evaluate this relationship, via a SDM framework, failed to consistently provide strong abundance-suitability correlations (Pearce and Ferrier 2001; Pearce and Boyce 2006; Jiménez-Valverde et al. 2009). Prob- ably, these inconsistencies may be due to the inca- pacity of some modeling methods to account for environmental suitability (Jiménez-Valverde et al. 2009). Later, some studies found more promising re- sults when using correlative ENMs (VanDerWal et al. 2009; Yañez-Arenas et al. 2012; Martínez-Meyer et al. 2013; Weber et al. 2017). Among these works, the abundant niche-centroid hypothesis stands out as a key element to understand the abundance-environ- mental suitability relationship. The Abundant Niche-Centroid Hypothesis Niche theory suggests that reproduction and survival of individuals should be higher in locali- ties placed at optimal conditions of their ecological fundamental niche (NF); conceptualized as an n-di- mensional hypervolume where each dimension rep- resents a relevant variable that acts on the organism’s fitness (Hutchinson 1973; Peterson et al. 2011). This idea was initially suggested by Hutchinson (1957), but Maguire (1973) was the first one to explicitly propose that different regions of the NF space should correspond to different values of the species intrinsic population growth rate (r). If this is true and popula- tion abundance is an expression of fitness, then, spe- cies’ abundance should be explained by their position with respect to the centroid of their NF’s (i.e., greater abundance should be found in populations closer to the centroid and decreases towards the edges show- ing a negative correlation; Fig. 1; Martínez-Meyer et al. 2013). Initially the hypothesis accumulated some em- pirical support: 1) Yañez-Arenas et al. (2012) and Martínez-Meyer et al. (2013) observed negative cor- relations between population abundance/density and the distance to the niche centroid (estimated with correlative methods) of some vertebrates; 2) Man- they et al. (2015), Ureña-Aranda et al. (2015) and Martínez-Gutiérrez et al. (2018) noted that popula- tions tend to have positive growth rates closer to the niche center and negative at the margins. However, more recent comprehensive analyses have obtained contradicting results: Dallas et al. (2017) and Santini et al. (2019) found weak support to the niche-central- ity hypothesis when tested for different taxa; in con- trast Osorio-Olvera et al. (2020) observed that cor- relations between abundances and the distance to the niche centroid of North American birds were mostly Biodiversity Informatics, 15, 2020, pp. 92-102 94 negative. Differences between findings could be ex- plained by methodological artifacts and the quality of the abundance data used (Knouft 2018; Soberón et al. 2018). In any case, these studies tested the hypothesis in all possible species for which abundance data were available. However, we consider that it is necessary, in the first place, to assess some theoretical assump- tions and circumstances under which the abundant niche-centroid hypothesis may be able to explain the geographic patterns of species’ abundance. On the Problem of Unfilled Fundamental Niches Testing the abundant niche-centroid hypothesis requires an unbiased characterization of a species’ NF, which would allow the estimated centroid to truly rep- resent its environmental optimum (Osorio-Olvera et al. 2019). However, estimating the NF via correlative techniques is not an easy task (Peterson et al. 2011). Under many circumstances a species’ niche may be geographically unfilled (Strubbe et al. 2013; Ashby et al. 2017). The BAM diagram is a simple heuristic tool specifically designed to summarize the potential effects of biotic interactions (B), abiotic suitable con- ditions (A) and mobility characteristics (M) on a spe- cies’ distribution, and can be used to assess ex-ante whether it is possible to characterize the NF correla- tively or not (Soberón and Peterson 2005). Biological features of species and scales of analysis define rela- tive sizes and positions of the BAM components that lead to different configurations, some of which allow a better characterization of the NF (Saupe et al. 2012). We use the BAM components and configurations to exemplify situations in which distances to the niche centroid estimated from distributional data may and may not explain species abundances. The geographic expression of a species’ NF is termed the existing fundamental niche (NF*), which is equivalent to A in the BAM framework (Soberón and Peterson 2005; Soberón 2010). Relationships between these terms can vary among species and geographical scales. If a species’ NF = NF* = A ⸦ M, and B has no significant effects on constraining the occupied geography (Go, or the intersection of B, A and M in the traditional configuration), then niche centrality determined correlatively is likely to explain abundance patterns. Such BAM configura- tion is commonly called ‘the Hutchinson’s dream’ (Saupe et al. 2012) and it is the ideal scenario to test the abundant niche-centroid hypothesis (Fig. 2; up- per right panel). However, if NF* ⸦ NF, then there will be portions of the NF that do not exist in geogra- phy (G) and therefore cannot be characterized from species’ occurrences. Here, an adequate estimation of the niche centroid will depend on the magnitude of the difference between NF and NF*. For instance, thermal tolerance limits of some reptiles and am- phibians is roughly 10 oC above the optimum, which could constitute a general guideline for assessing the difference between NF and NF* (Soberón and Ar- Figure 1. The abundant niche-centroid hypothesis. Left panel: bi-dimensional environmental space in which a hypothetical niche, its centroid and internal structure are shown. Black circles represent localities with different population abundance (defined by the size of the circle). Right panel: expected relationship between abundance and the distance to the niche centroid. Biodiversity Informatics, 15, 2020, pp. 92-102 95 royo-Peña 2017). Alternatively, if only a portion of A exhibits bi- otic features suitable for the survival of a species, then Go = A ∩ B, and a reduction of the NF is also expected. Hutchinson (1957) was the first one to ex- plicitly describe the above relationships in environ- mental space when the concept of realized niche (NR) was introduced. Recent empirical data reveals that key interspecific interactions may have significant effects on species’ geographic ranges (e.g., Gaston 2003; Louthan et al. 2006; Gotelli et al. 2010; Ashby et al. 2017; Anderson 2017). Such cases would result in a major challenge to study abundance-centrality relationships, because it is almost axiomatic that es- timated NF will be reduced or biased. Therefore, re- search on niche centrality is highly dependent on the assumption of the so-called ‘Eltonian noise’ that is, when inter-specific interactions do not limit species’ ranges at coarse geographical scales (Soberón and Nakamura 2009; Soberón 2010). As described above, an important assumption to estimate a species’ NF via correlative modeling is that individuals can move freely across G and occur in all abiotic suitable locations, while being absent from all unsuitable ones, i.e., the environmental equilibrium assumption (Araújo and Pearson 2005). However, under many real-life situations, species are limited by geographical barriers and dispersal abilities (Soberón and Peterson 2005; Soberón 2010); hence, unfilled NF are expected under some BAM configurations in which M is included, such as ‘classic BAM’ (Go = B ∩ A ∩ M; Go = A ∩ M) (Fig. 2; upper left panel) and ‘Wallace’s dream’ (Go = M ⸦ B ∩ A; Go = M ⸦ A) (Fig. 2; lower left panel). Also, considering that M determines the set of regions and environments occupied by the species, the known set of presence records (G+) occur in geographic space (Go), so the associated environments η(G+) are already reduced by M. As a consequence, niche models that have been calibrated in an M region will frequently under-char- acterize the NF (Peterson and Soberón 2012), and the estimation of their centroid will be biased. An excep- tion may occur under the ‘Full overlap’ configuration since Go = M ≈ A and a complete characterization of the species NF is possible (Fig. 2; lower right panel). A Hypothetical Example of M Effects Using two virtual entities we show a simple ex- ample of how the correlation between abundance and distance to the niche centroid may be profoundly af- fected by an incomplete characterization of the NF under two different M configurations. Generating virtual entities We created two virtual entities that are based on the biology and real data of two mussels; Mytilus edulis and M. galloprovincialis. We chose these spe- cies because they are distributed in two geographical regions separated by mainland Europe which have different environmental conditions. Both species are closely related, therefore for some niche axes they may have similar environmental tolerances (Lee et Figure 2. BAM configurations in which we show, in each letter (a – h), the potential scenarios regarding the distribution of the niche centroid conditions (red dots) in geographic space. In all cases we have omitted B to match the components accounted for in the analyses. Abiotic suitable conditions = red circles (A component of BAM); historically accessible area = blue circles (M component of BAM); Go = occupied geography. Upper left panel (a - c) = Classic BAM; lower left panel (e – g) = Wallace’s dream; upper right panel (d) = Hutchinson’s dream; lower right panel (h) = Full overlap. Biodiversity Informatics, 15, 2020, pp. 92-102 96 al. 2019). The former is native to northern Europe, and the latter occur in the Mediterranean Sea (Won- ham 2004). Based on the assumption of phylogenetic niche conservatism (Harvey and Pagel 1991), we hy- pothesized that both mussel species could have largely similar NF. Therefore the BAM configuration of our example is Go = A ∩ M (the classic BAM without B). Inputs for generating the niche models We obtained presence records of M. edulis (here- after “Northern entity”) and M. galloprovincialis (“Southern entity”) from GBIF (https://www.gbif. org). All data points which were evidently miss-geo- referenced (outside its known range or placed on land) were eliminated. Data were filtered for dupli- cate points with the “clean_dup” function of the “nt- box” R package (Osorio-Olvera et al. 2020), using a distance threshold equal to the resolution of the envi- ronmental data (below). Finally, we randomly select- ed 150 occurrence records of each species to remove from the dataset used to characterize NF. Hence, we obtained for each modeling entity two spatially-inde- pendent datasets of presence points called “d_pres” (full database without the 150 removed points) and “d_abun” (the 150 records removed from the original filtered database). We also obtained 12 marine vari- ables from the Bio-Oracle database v2.0 (Assis et al. 2018; http://www.bio-oracle.org), at a spatial resolu- tion of 10’ (~20 km). These surfaces describe annual trends of sea surface temperature and salinity for the period 2000–2014: average, range, average maxi- mum, average minimum, maximum, and minimum. We used a principal components analysis (PCA) to reduce multicollinearity applying the ‘PCARaster’ function of the ‘ENMGadgets’ package (Barve and Barve 2013) in R (R Core Team 2018), and retained the first three components that explained 93% of the overall variance for further analyses. Niche models First, we merged the “d_pres” datasets of oc- currence records of both virtual entities to create the “Coupled unit”. Then, using a minimum volume ellip- soid (MVE, Van Aelst and Rosseeuw 2009) we gen- erated a hypothetical NF that included 97.5% of the occurrence records (leaving out the presence records from atypical environmental conditions that might represent sink populations or undetected errors in the original data cleaning process; Fig. 3; green ellipsoid). The assumption is that NF are convex, as suggested by abundant observational and physiological experimen- tal data (Maguire 1973; Hooper et al. 2008; Angilletta 2009; Soberón and Nakamura 2009), and theoretical arguments (Drake 2015). The MVE was generated with the function “cov.rob” of the MASS package in R (R Core Team 2019), and graphed with “rgl” (Adler et al. 2019). Using the “cov_center” function of pack- age “ntbox” (Osorio-Olvera et al. 2020), we calcu- lated the volume and its centroid. Then we projected the Mahalanobis distance to the MVE centroid with the “mahalnobis” function of R to project the niche in geographic space (G) and obtained a continuous map of environmental suitability. The inputs to the “ma- halanobis” function were the covariance matrix of the environmental variables and the vector of the centroid coordinates. Finally, we built the MVEs using the same described methods with the sets of presences for the Northern and Southern entities separately (Fig. 3; blue and red ellipsoids, respectively). Abundance data As abundance data we used the maximum num- ber of individuals reported for either species in an area equal to the size of the grid cells. Then, we matched abundance data with the distance to the cen- troid of the MVE of the Coupled unit. The result was Figure 3. Minimum volume ellipsoids defined by three marine variables (Sea Surface Mean Temperature, Sea Surface Tempera- ture Range, Sea Surface Salinity). Green ellipsoid: hypothetical fundamental niche built with presence records of both species (“Northern” and “Southern”). Blue ellipsoid: niche characterized only from occurrences of the Northern species. Red ellipsoid: niche characterized only from occurrences of the Southern spe- cies. The estimated centroid is also presented for each entity. Biodiversity Informatics, 15, 2020, pp. 92-102 97 that the maximum observed abundance (12,500 vir- tual individuals) was perfectly, negatively correlat- ed with the distance to the niche centroid (Fig. 4). Using this approach of virtual entities we eliminated the effects of biotic interactions, dispersion, human impact, and variability of physiological tolerances among populations. Statistical analyses We performed Spearman correlation tests with the “cor_test” R function between abundance and distance to the centroid of the Northern and Southern entities. The two real species (and their virtual entities) have geographically disjoint distributions, separated by mainland Europe, which represents the main barrier to dispersal (M) and impedes their sympatry. Simul- taneously, Europe interrupts the spatial continuity of the environmental conditions to which these species have historically developed physiological tolerance. Therefore, these tests are equivalent to an assessment of the effect of a niche characterization limited by M. Results The resulting environmental suitability from each MVE had a distinct geographic pattern. In the Cou- pled unit model, the highest environmental suitabil- ity occurred throughout most of the Cantabric Sea, a portion of the Northern Sea and a small region in the southern coast of France, in the Mediterranean Sea. In the Northern entity model, the highest environ- mental suitability almost exclusively occurred in the Northern Sea, while in the Southern entity there are high suitability values (small distances to the niche centroid) across the three southern European seas: Adriatic, Aegean and Tyrrhenian. Given that hypo- thetical abundance was derived from environmental suitability of the Coupled unit model, the correlation between this and abundance was ρ = 0.99. The cor- relation between abundance and the environmental suitability estimated for the other models were ρ = 0.27 and ρ = 0.16, for the Northern and Southern en- tities, respectively (Fig. 5). Conclusion As expected, the correlation between abundance and environmental suitability characterized from oc- cupied niches reduced and biased by M was signifi- cantly lower. This example shows that accessibility has a crucial effect on the characterization of the NF and the resulting environmental centroids. Under BAM configurations in which there is a previous sus- picion that there is a strong effect of M over Go, the abundant niche-centroid hypothesis has low expec- tations to explain the geographic patterns of abun- dance. Then, the following questions arise from these problems: 1) should species with unfilled fundamen- tal niches be completely avoided when measuring the centrality-abundance relationship? 2) What options exist to reconstruct the NF of species in which this problem exists? The Potential Use of Supraspecific Modeling Units Mechanistic modeling is a good alternative to es- timate and map species’ NF truncated by geography. These techniques are based on data from controlled experiments for measuring the physiological effects of different manipulated variables to estimate their tolerance limits (Kearney and Porter 2004; 2009). Building these models, however, requires complex and long experimental processes and equipment (Gallien et al. 2010). For these reasons, mechanistic models are usually built only with one or two envi- ronmental variables, and are unlikely to capture all the biologically relevant environmental factors for a species (Aragón et al. 2010). In addition their ap- plication is limited to species in which physiological experiments are feasible (Larson et al. 2014). Figure 4. Distribution of the 300 locations with a hypothetical abundance value. Blue circles represent abundance data of the Northern species within its M (pink polygon) and red circles represent abundance data of the Southern species within its M (yellow polygon). Biodiversity Informatics, 15, 2020, pp. 92-102 98 On the other hand, characterizing the NF from presence data and using correlative methods is limit- ed under many BAM scenarios, as we have shown in the previous sections. Nevertheless, modeling with supraspecific entities (i.e., modeling units above spe- cies level), may represent an alternative to overcome the problem of “unfilled niches” (Qiao et al. 2017; Smith et al. 2018; Castaño et al. in press). This ap- proach is valid under the assumption of phylogenetic niche conservatism, which states that evolutionary patterns of species with common ancestors share a substantial portion of their biological and physiolog- ical characteristics that determine their NF. In other words, ancestral adaptations to a set of environmental conditions tend to be preserved by descendant spe- cies (Harvey and Pagel 1991). Niche conservatism tends to break down over time, although there is vast evidence showing that at timescales comparable with speciation events, the most common pattern is that of little ecological divergence of NF (climatic pref- erences of species tend to be phylogenetically pre- served; Peterson 2011; Pavoine and Bonsall 2011). Therefore, it is possible to assume that sister species have similar NF despite having natural geographical distributions with different climatic characteristics. Under this scenario, each species would inhabit dif- ferent portions and combinations of the entire envi- ronmental space, but complementary regarding their NF. This strategy of combining presence records of sister species is known as “lumping” (Smith et al. 2018). Recent analyses of invasive species have demonstrated that lumping allows better characteri- zation of NF when it has been reduced in Go by M or B (Castaño et al. in press). Lumping, therefore, appears to be a good strat- egy to improve predictability of biological inva- sions or estimating NF for evaluating the abundant niche-centroid hypothesis. The assumption is that when BAM configurations produce unfilled niches, lumping would allow a better approximation to es- Figure 5. Top panels: environmental suitability estimated from the distances to the niche characterized by different MVEs (the gradient goes from highest to lowest suitability = from light blue to dark blue). Panels below: correlations between hypothetical abundance and environmental suitability estimated by each modeling entity. Biodiversity Informatics, 15, 2020, pp. 92-102 99 timate the NF and its centroid, hence improving the chances that abundance is explained by the abundant niche-centroid hypothesis. A third possibility is that of modeling subspecific units (e.g., subspecies, populations, environmental units) when local adaptation plays an important role in determining local abundance. Under this scenario, the single centroid would not represent the species’ optimum, instead, several subspecific units would have individual optima. This may occur in species with very extensive geographic distributions and wide ecological niches (Yañez-Arenas et al. 2012). Concluding Remarks The abundant niche-centroid hypothesis is cur- rently a hot topic in biogeography, macroecology and distributional ecology. To-date, at least three studies have evaluated the generality of the idea, one of them finding strong support for the hypothesis (Osorio-Ol- vera et al. 2020), and the other two showing contrast- ing results (Dallas et al. 2017; Santini et al. 2019). Some of the factors that may affect the expected neg- ative correlation between species’ abundance and the distance to their niche centroid are related to meth- odological issues, such as the effect of sample size and bias in occurrences used to build niche models (Yañez-Arenas et al. 2014), the quality of abundance/ density data (Soberón et al. 2018, Knouft 2018), and decisions regarding the metrics used to compute en- vironmental distances (Soberón et al. 2018). Others are inherent to the system of study. For instance, biotic interactions (e.g., high levels of competition, predation, herbivory, or parasitism), metapopulation dynamics (e.g., stochastic processes of individuals dispersal among populations, Allee effects) and hu- man impact (e.g., direct exploitation of species, hab- itat destruction/modification) can decrease species’ population abundances in localities that are environ- mentally near the centroid of the niche (Osorio-Olve- ra et al. 2016; Weber et al. 2017; Osorio-Olvera et al. 2019). Also, adaptation of populations to local envi- ronments would result in higher abundance in those localities (Leimu and Fischer 2008), some of which may be distributed at the edges of the niche where selection pressures are stronger (Aguirre-Liguori et al. 2017). In such cases, splitting lineages into sub- especific units (e.g., environmentally similar units) and estimate niche models for each unit may be a good strategy to describe environmental relation- ships (Yañez-Arenas et al. 2012; Smith et al. 2018). Some of the mentioned factors are impossible to identify prior to test the abundant niche-centroid hy- pothesis. However, here we demonstrate that thinking about assumptions related to the problem of unfilled niches and analyzing the potential BAM configura- tion could be used to decide ex-ante in which cases it is worth testing the hypothesis. We showed that M is important in limiting the NF of species and the ex- planatory power of the niche structure towards abun- dance within its distribution. Thus, species in which environmental conditions within their M do not rep- resent a subset of their NF are the best candidates to study abundance-niche relationships. 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