1.1 The Many Types of Species–Area Relationship

At this stage it is necessary to define what exactly is meant by the term ‘species–area relationship’. While the SAR may appear to be a relatively uncomplicated concept, its application within the ecological literature is often somewhat ambiguous. Most of this ambiguity concerns the fact that there is not a single type of SAR, but instead there is a suite of relationship types with more or less distinct data structures. While the search for an agreed classification and terminology has generated much debate (e.g. Scheiner, Reference Scheiner2003; Gray et al., Reference Gray, Ugland and Lambshead2004; Dengler, Reference Dengler2009), there are only two variables involved in each case: area and species number, and so the problem can be quickly described. First, the areal units analysed may be geographically separated or contiguous, permitting their analysis either as separate entities or as a nested sequence. Second, each species can be counted once as area is accumulated (whether from a nested sequence of contiguous areas or not) or separately in each (sub-)area. Third, for the accumulation curve structure, the value of richness entered for a given size of area can represent a single data point or the average richness value of multiple samples of that size (Dengler et al., Reference Dengler, Matthews, Steinbauer, Wolfrum, Boch, Chiarucci, Conradi, Dembicz, Marcenò, García‐Mijangos, Nowak, Storch, Ulrich, Campos, Cancellieri, Carboni, Ciaschetti, De Frenne, Dolezal, Dolnik, Essl, Fantinato, Filibeck, Grytnes, Guarino, Güler, Janišová, Klichowska, Kozub, Kuzemko, Manthey, Mimet, Naqinezhad, Pedersen, Peet, Pellissier, Pielech, Potenza, Rosati, Terzi, Valkó, Vynokurov, White, Winkler and Biurrun2020).

The upshot is that several forms of species accumulation curve (SAC) can be identified as types of species−area relationship (Type I−III curves in Scheiner’s Reference Scheiner2003 typology) but just one type of data structure of ‘isolate’ area versus species number per isolate (Gray et al., Reference Gray, Ugland and Lambshead2004), which some term island species–area relationships (ISARs; Type IV SARs in Scheiner, Reference Scheiner2003) (e.g. Triantis et al., Reference Triantis, Guilhaumon and Whittaker2012; Matthews et al., Reference Matthews, Guilhaumon, Triantis, Borregaard and Whittaker2016a, b). Further, SACs are often constructed using non-area-based measures of sampling effort (e.g. trap hours) and so sample area-based SACs can be distinguished as a subset of SACs.

At its most basic, SACs are constrained by their mode of construction to display a monotonic increase in species richness. A SAC must either remain constant or increase with each increment in area (Figure 1.2), such that the total richness of the study system is described by the final data point. By contrast, sometimes a larger island can have fewer species than a smaller one and, in certain rare circumstances, there can even be a negative overall ISAR or the relationship may be negative over a limited span of the area range of a study system (Figure 1.2).

Figure 1.2 Two hypothetical species−area relationships. To the left, an island (isolate) species−area relationship (ISAR) in which there is scatter around the mean trend, to the extent that some islands are less rich than one or more smaller island; to the right, a species accumulation curve (SAC). The SAC is constructed by adding the new species encountered per each extension of area, such that the SAC is constrained never to decrease. As each island may contain different subsets of species, the ISAR only crudely constrains the possible overall system richness, whereas the final data point for the SAC describes the overall system richness.

The lack of a generally agreed terminology distinguishing SAR types has presented a real hindrance to the development of a shared understanding. Studies comparing SARs often combine ISARs and SACs without acknowledging that that the two types have different properties (but see e.g. Drakare et al., Reference Drakare, Lennon and Hillebrand2006; Matthews et al., Reference Matthews, Triantis, Rigal, Borregaard, Guilhaumon and Whittaker2016b). For example, the seminal SAR figure of Wilson (Reference Wilson1961) for ponerine and cerapachyine ants in Melanesia compares an ISAR (island data) with a SAC (‘mainland’ New Guinea), a feature that is often neglected in work citing or reproducing it (see Figure 1.1B). Indeed, some have argued that, to fairly compare SARs from different systems, the whole sampling design must be identical, including range of area, type of SAR (SAC or ISAR) and if SACs are the focus of study, the accumulation order, sampling intensity, plot shape, use of continuous or discontinuous plots and, if the latter, the locations of the discontinuous plots within the study extent (see Chapter 7; see Figure 1.1C for some examples of SAR construction approaches).

In this volume, we have encouraged authors to make explicit reference to the type(s) of SAR (e.g. ISAR, SAC or both) that their chapter is focused on. However, and as with most things in science and life in general, different people have different opinions on the correct terminology to use and we have not imposed a standard usage. For instance, in certain chapters SACs are referred to as nested SARs, and the term saSAR is used in some chapters to refer to sample-area based SACs. We acknowledge that our own use of the term ‘island SAR’ (or Isolate SAR) may not be the best solution as ISARs might be constructed using data not from isolates but for other irregularly sized geographical units of varying degrees of geographical isolation (e.g. countries or biogeographic provinces).

1.2 A Flexible Biogeographical Law

Our work has generally focused on the ISAR, whether that be for true islands (e.g. Triantis et al., Reference Triantis, Guilhaumon and Whittaker2012) or habitat islands (Matthews et al., Reference Matthews, Guilhaumon, Triantis, Borregaard and Whittaker2016a). What has struck us during this work (and in reading the work of many others) is that the idea that the ISAR is universal is only really true in the sense that larger areas tend to have more species than smaller areas. Beyond that, many characteristics of ISARs have been found to differ (often quite considerably) between datasets. Lomolino (Reference Lomolino2000; see also Whittaker & Triantis, Reference Whittaker and Triantis2012) recognized this when he described the ISAR as ‘protean’. The adjective ‘protean’, meaning ‘versatile’, ‘flexible’ and ‘able to change easily’, is derived from the Ancient Greek God ‘Proteus’. According to Greek mythology, Proteus was an early prophetic sea-god who had the ability to foresee the future, but would frequently change his shape to avoid those who asked him to share his prophetic knowledge. The name Proteus suggests the ‘first’, and the ISAR is considered to be one of the first discussed general patterns related to the diversity of life. One other obvious way that the ISAR can be considered a protean pattern is the fact that the mathematical form of the relationship often varies between datasets (Triantis et al., Reference Triantis, Guilhaumon and Whittaker2012; Matthews et al., Reference Matthews, Guilhaumon, Triantis, Borregaard and Whittaker2016a; Leveau et al., Reference Leveau, Ruggiero, Matthews and Bellocq2019). In practice, we can often fit multiple models successfully to the same dataset. We then have the challenge of trying to work out which is the best model, that is, the closest approximation to the true form of the relationship. This may be attempted as a statistical exercise, that is, as a black box type of approach. Alternatively, we may regard the process of model fitting rather differently, as an exercise in hypothesis testing, that is, we may have theoretical grounds for predicting a particular form or a particular set of alternative forms that are linked to distinct mechanisms or processes. The step of model fitting is then used to determine the plausibility of the initial hypothesis or of selecting from a set of multiple-working hypotheses those which remain standing and then, of these, which has the greatest verisimilitude. Hence, SARs have what we might think of as phenomenological flexibility, as we are describing a suite of slightly different aspects of how diversity and area are related and then, for these different phenomena, there are advocates for particular mathematical models to represent the SAR. Indeed, over thirty different functions have been proposed (Chapter 7).

While the variation in ISAR form between datasets has (so far) precluded the identification of a universal model that provides the best fit to all datasets, the discovery of generalities regarding how and why ISARs vary has improved our understanding of the processes shaping diversity patterns more generally (see the Foreword). We know for example that the factors that influence species richness vary across spatial scale (Shmida & Wilson, Reference Shmida and Wilson1985; Rosenzweig, Reference Rosenzweig1995; Whittaker et al., Reference Whittaker, Willis and Field2001; Turner & Tjørve, Reference Turner and Tjørve2005) and thus the ISAR should be scale-dependent (see Figure 1.3A). These different factors should also affect the nature of the relationship of species richness with area. Recent meta-analyses have shown that ISAR slope (z) increases from habitat, to continental shelf, to oceanic islands (Triantis et al., Reference Triantis, Guilhaumon and Whittaker2012; Matthews et al., Reference Matthews, Guilhaumon, Triantis, Borregaard and Whittaker2016a). The shallowest slopes and higher intercepts characterize systems with minimal isolation, in which island-extirpation events are typically rapidly reversed by recolonization (‘rescue effects’) and which therefore feature comparatively high richness even on the smaller islands. By contrast, remote oceanic islands receive such low rates of immigration that colonizing lineages can diversify in isolation. In these systems, in theory, the smallest islands have low species richness because their small, unreliable resource bases cannot sustain marginal populations of small size or permit the origin and persistence of newly formed endemics. In practice, as we argue in Chapter 3, the more remote oceanic archipelagos can be so isolated that the configuration of the archipelago itself exerts a strong influence on ISAR form, in part overriding the effect on slope and intercept exerted by distance from the mainland (and see Matthews et al., Reference Leveau, Ruggiero, Matthews and Bellocq2019).

Figure 1.3 Two contrasting models of ISAR form. (A) The theoretical relationship of species richness with area in arithmetic space according to Lomolino (Reference Lomolino2000). Starting at the left side, there is little change in species number until a critical threshold is reached, but beyond threshold t1, species number increases rapidly, as a function of the immigration/extinction dynamics of the equilibrium model of island biogeography. With islands larger than t2, species number shows a further increase, as it is afforced by in situ speciation. The ‘small-island effect’ is shown by many island datasets (see also Chapter 19), but the generality (and even existence) of the second threshold and the upward curve towards the right side of the plot is contested. (B) As archipelago isolation increases, the ISAR slope (z) generally increases. Rescue effect systems are the least isolated and hence species populations on smaller islands are continually rescued from extinction by supplementary immigration, resulting in high intercepts and low slopes. Islands of intermediate isolation experience higher rates of species turnover and therefore feature steeper slopes and lower intercepts. Speciation dominated systems refer to remote archipelagos in which larger islands gain species through in situ diversification, generating the steepest slopes and lowest intercepts. This panel is only approximated by analyses of empirical datasets (e.g. Matthews et al. Reference Matthews, Guilhaumon, Triantis, Borregaard and Whittaker2016a). (A) From Lomolino (Reference Lomolino2000; figure 6) under license from John Wiley and Sons; (B) from Whittaker et al. (Reference Whittaker, Fernández-Palacios, Matthews, Borregaard and Triantis2017; figure 4A) and reprinted with permission from AAAS

Thus, different processes are expected to result in different slopes; the difference is expected to be most pronounced when speciation-dominated systems are compared to systems where MacArthur−Wilson dynamics prevail and speciation has a secondary or no role (Figures 1.3 and 1.4). The cichlid species of the Great African Lakes provide an illustration of these differences, but also of a clear threshold effect where there appears to be no relationship between species and area until a minimum lake area has been reached. Above this threshold, those lakes in which in situ diversification has occurred demonstrate a clear positive relationship. The Anolis lizards of the Caribbean provide another pertinent example of a threshold in the speciation−area and species–area relationships (Losos & Parent, Reference Losos, Parent, Losos and Ricklefs2010; figures 15.3 and 15.5).

Figure 1.4 The effect of adaptive radiation on the ISAR (lighter points = lakes with speciation; darker points = lakes without speciation). The fit of two-slope ISAR models are shown (solid line = whole dataset; dashed line = lakes with speciation only). For the whole dataset model fit, the pre-breakpoint slope does not significantly differ from zero, the breakpoint occurs at 1,030 km² and the post‐breakpoint slope (1.29) is significant and positive. For the model fit to the lakes with speciation, the pre-breakpoint slope does not significantly differ from zero, the breakpoint occurs at 1,470 km² and the post‐breakpoint slope (0.99) is significant and positive. In both cases the two-slope model provides a better fit to the data than a one‐slope regression model according to AIC_c. The data are of cichlid fishes in forty-six African lakes. From Wagner et al. (Reference Wagner, Harmon and Seehausen2014; figure 3b) under license from John Wiley and Sons

Elements of the above arguments were codified in Rosenzweig’s (Reference Rosenzweig1995) seminal scale‐structured model of species–area relationships, which, however, included both ISARs and SACs (see Scheiner, Reference Scheiner2003; Whittaker & Fernández-Palacios, Reference Whittaker and Fernández-Palacios2007). His interprovincial curve represents an ISAR fitted between distinct biogeographical provinces, which he argued should exhibit a slope always >0.6 and generally close to unity (see Rosenzweig, Reference Rosenzweig1995, Reference Rosenzweig, McKinney and Drake1998, Reference Rosenzweig2001) (Figure 1.5A). SACs within continents, his intraprovincial curves, should be flatter and with higher intercepts than regular ISARs found within the province, which should display a range of values depending on their degree of isolation. Figure 1.5B was inspired by Rosenzweig’s model but differs in showing exclusively ISARs. Given the propensity for remote oceanic archipelagos to generate endemics in situ, the expectation is for the between-archipelago or archipelagic species–area relationship (ASAR) to provide a steep relationship, where the relevant within-archipelago ISAR only crudely predicts the archipelagic value and, again, there is variation in the overall richness of different archipelagos (Figure 1.5A and B) in perhaps widely different locations. This reasoning is supported by analyses showing that i) for oceanic archipelagos, inter-archipelago species–area relationships (ASARs) are systematically steeper than the constituent ISARs (e.g. Triantis et al., Reference Triantis, Economo, Guilhaumon and Ricklefs2015) and ii) ISARs estimated for endemic species are typically steeper with lower intercepts than those for non-endemic native species for the same archipelago (Figure 1.5C; Triantis et al., Reference Triantis, Mylonas and Whittaker2008). The final panel (Figure 1.5D) presents another generalization, which is that, for forest habitat island systems, ISARs calculated for generalist bird species are flatter and with higher intercepts than those for forest specialist bird species (Matthews et al., Reference Matthews, Cottee‐Jones and Whittaker2014). That i) specialist species, more reliant upon and restricted to the focal habitat, have the steeper slopes and ii) island endemic species have steeper slopes than non-endemic species (which may have populations on other islands or landmasses exchanging propagules with the islands in question) appears to be part of the same pattern, relating to the extent to which, as Rosenzweig put it, the islands in question are acting as sources or as sinks.

Figure 1.5 Generalized species–area relationships as a function of scale and isolation. (A) Rosenzweig’s scale‐structured model of species–area relationships, comprising a mix of SAC and ISAR types. (B) The archipelago species–area relationship (ASAR) and two of its constituent archipelago ISARs. Points A and B on the ASAR represent the archipelago diversity for archipelagos A and B, respectively. (C) ISARs constructed using endemic species and native non-endemic species. (D) Three ISARs for the same bird habitat island (seven islands) dataset: the bottom curve is for habitat specialist bird species, the middle curve is for habitat generalists and the top curve (and the crosses) for all bird species combined. The lines are the fit of the power (log–log) ISAR model. See text for further details. (A) From Rosenzweig (Reference Rosenzweig1995; figure 9.11; modified by Lomolino et al., Reference Lomolino, Riddle and Whittaker2017) and reprinted with permission from Cambridge University Press; (B) and (C) from Whittaker et al. (Reference Whittaker, Fernández-Palacios, Matthews, Borregaard and Triantis2017; figure 4c and figure 4b, respectively) and reprinted with permission from AAAS; and (D) from Matthews et al. (Reference Matthews, Cottee‐Jones and Whittaker2014; figure 1e) under license from John Wiley and Sons

1.3 From Species–Area Relationships to Diversity–Area Relationships

Recently, and echoing the shift in macroecology and biogeography more generally, ISAR research has expanded to include other facets of diversity, such as functional (FD) and phylogenetic (PD) diversity (Whittaker et al., Reference Whittaker, Rigal, Borges, Cardoso, Terzopoulou, Casanoves, Pla, Guilhaumon, Ladle and Triantis2014; Mazel et al., Reference Mazel, Renaud, Guilhaumon, Mouillot, Gravel and Thuiller2015; Chapter 5). Figure 1.6 provides an example of an ISAR and the corresponding functional diversity–area and phylogenetic diversity–area relationships for a dataset of breeding birds in a lake island archipelago in China (Si et al., Reference Si, Cadotte, Zhao, Zhou, Zeng, Li, Jin, Ren, Wang, Ding and Tingley2018). As has been argued for community ecology in general (e.g. Webb et al., Reference Webb, Ackerly, McPeek and Donoghue2002; Kraft et al., Reference Kraft, Valencia and Ackerly2008), there is a hope that a focus on functional and phylogenetic diversity in SAR/diversity–area relationship studies may help us better understand the processes that underpin SARs/diversity–area relationships and ultimately the mechanisms that underpin community assembly. In addition, it enables us to better predict the impact of habitat loss on these other facets of biodiversity, which may have some value for developing models of ecosystem function (see Chapter 5). However, as many FD and PD metrics generally co-vary strongly with taxonomic diversity (TD), discerning the additional information provided by these metrics requires assessment of whether and how the trends diverge from null expectations (e.g. Whittaker et al., Reference Whittaker, Rigal, Borges, Cardoso, Terzopoulou, Casanoves, Pla, Guilhaumon, Ladle and Triantis2014). Going forward, the evaluation of other diversity–area relationships alongside SARs represents a challenging but promising avenue for future research in the field.

Figure 1.6 The relationship between island area and taxonomic diversity (top), functional diversity (middle) and phylogenetic diversity (bottom) for seventy-seven breeding bird species recorded on thirty-six islands in the Thousand Island Lake, China (surveyed between 2007 and 2016). The circles are observed diversity and the triangles diversity estimated using multi‐species occupancy models. The lines are linear regression model fits (with the 95 per cent confidence intervals around each point in the case of the occupancy models) to the two sets of data after accounting for island isolation. Functional diversity was measured using a dendrogram-based metric and phylogenetic diversity using Faith’s index. The grey bars represent 95 per cent Bayesian credible intervals of posterior mean estimates of TD, FD and PD. From Si et al. (Reference Si, Cadotte, Zhao, Zhou, Zeng, Li, Jin, Ren, Wang, Ding and Tingley2018; figures 1a, c and e) under license from John Wiley and Sons

1.4 The Present Volume

This book is loosely structured into five sections. The first section comprises the present chapter and a chapter on the history of the SAR (Chapter 2). The SAR has a long history; one that includes several early studies published by Scandinavian authors, which have been overlooked in the mainstream ecological literature until recently (Tjørve et al., Reference Tjørve, Tjørve, Šizlingová and Šizling2018). Chapter 2 provides an overview of these early studies, the development of mathematical SAR theory and the subsequent application of the SAR in a wide range of fields, such as island biogeography and conservation biogeography.

More recently, the last ten to fifteen years have seen i) the publication of several meta-analyses that have aimed to draw out general SAR patterns (e.g. Triantis et al., Reference Triantis, Guilhaumon and Whittaker2012; Matthews et al., Reference Leveau, Ruggiero, Matthews and Bellocq2019) and ii) the expansion of SAR theory to other types of diversity (e.g. Mazel et al., Reference Mazel, Renaud, Guilhaumon, Mouillot, Gravel and Thuiller2015) as well as non-traditional species assemblages (e.g. alien species; Baiser & Li, Reference Baiser and Li2018). The second section of the book covers these ideas, including, in regard to the former, an expansion of a recently published global model of ISARs that aims to explain variation in parameters of the power ISAR model between datasets (Chapter 3) and a more general discussion of the determinants of SAR shape, including the idea that SAR drivers can be organized as a hierarchy of different processes and factors (Chapter 4). In regard to the latter, reviews of functional diversity and phylogenetic diversity–area relationships (Chapter 5) and alien species–area relationships (Chapter 6) provide comprehensive accounts of these topics.

Due in part to increases in computer power, increased mathematical training in ecology and biology courses and the now wide range of available software packages for ecological data analysis, the last twenty years has seen a resurgence in theoretical SAR research: both in terms of pure SAR research questions and in the development of (macro) ecological theories in which the SAR is a fundamental component. The third section of the book, focused on theoretical advances in SAR research, includes chapters dedicated to both of these types of theoretical developments, including topics such as the search for mathematical SAR functions (Chapter 7), the scaling and geometric properties of SARs (Chapter 8), extreme value theory and the SAC (Chapter 9), trophic SARs (Chapter 12) and the role of SARs in two recently proposed unified macroecological and biogeographical theories: the maximum entropy theory of ecology (Chapter 10) and the unified neutral theory (Chapter 11).

The fields of conservation biology and conservation biogeography are concerned with impacts of environmental change on biodiversity and on generating useful applied information that can be used in conservation and sustainable biodiversity management. As a general rule, conservation biology is focused more on local scale questions, whilst conservation biogeography is the subset of that broader field that revolves around issues operating at coarser spatial (and often temporal) scales. However, the SAR is a fundamental tool in both disciplines and has been used, amongst other things, to estimate the number of species likely to become extinct as a result of habitat loss and climate change (e.g. Ladle, Reference Ladle2009; Triantis et al., Reference Triantis, Borges, Ladle, Hortal, Cardoso, Gaspar, Dinis, Mendonça, Silveira, Gabriel, Melo, Santos, Amorim, Ribeiro, Serrano, Quartau and Whittaker2010) and to identify potential biodiversity hotspots and protected areas in both the terrestrial and marine realms (e.g. Neigel, Reference Neigel2003; Guilhaumon et al., Reference Guilhaumon, Gimenez, Gaston and Mouillot2008). The fourth section of the book focuses on the applied uses of the SAR, including reviews of the aforementioned applications (hotspot identification – Chapter 13; extinction predictions – Chapter 14), as well as novel contributions such as the use of network theory in island biogeography research and the importance of intra-archipelago configuration (which is of both pure and applied interest) (Chapter 15), the importance of geometry in habitat loss research and extinction predictions (Chapter 16) and the introduction of the concept of relict species–area relationships to estimate the conservation value of reservoir islands in flooded forest landscapes (Chapter 17). The section concludes with a chapter on the application of SARs in the marine realm, with a particular focus on the issues involved in interpreting marine SARs at large spatial scales (Chapter 18).

The final section of the book, consisting of a single chapter (Chapter 19), is based around a metaphor M. L. Rosenzweig used in the preface of his 1995 book, comparing the study of species diversity patterns with a dinosaur that has come alive and is challenging us. This final chapter also brings together some of the general findings of the previous chapters and identifies outstanding research questions and areas where further work is needed; we hope providing a catalyst for future ISAR-based research.

Ultimately, our aim in this volume has been to bring together a diverse array of leading researchers on SAR issues in order to: i) generate a comprehensive treatment that is relevant to a wide range of fields, ii) provide a useful general resource for students and researchers interested in the SAR and iii) provide a substantial novel contribution to the literature. We hope that it may serve to increase interest in the SAR as a pattern (or set of patterns) and to stimulate further developments in the field.