Island biogeography theory views island species richness as an equilibrium of extinction rates and the immigration rates of novel species to an island. At equilibrium, MacArthur and Wilson’s model predicts that species composition will change over time, but species richness will remain relatively stable. In addition, large islands with low extinction rates and high immigration rates will tend to support more species than will small islands. Geographic ecologists also want to understand why particular species or groups of species have a particular geographic distribution. The theories of continental drift and plate tectonics have helped to resolve these questions. More recently, developments in molecular technology have allowed biogeographers to answer numerous questions about species distributions. Landscape ecology explores how variation in landscape structure, such as configuration or scale, influences the distribution and abundance of species. Conservation ecologists are particularly concerned that industrial, agricultural, and urban development have led to increased fragmentation of habitat that is suitable for sustainable wildlife populations. Applying the lessons of island biogeography, ecologists recommend erecting immigration corridors to increase immigration rates of novel species into nature preserves, thereby increasing species richness.

I am not aware of any other book that has shed so much light on species diversity patterns and generalities across time and space as has M. L. Rosenzweig’s (1995) Species diversity in space and time. Rosenzweig compared the study of species diversity patterns with a dinosaur that has come alive and is challenging us. He then listed 10 major challenges that we as ecologists and biogeographers have to address. Some of these are focused on arguably the most general pattern, and definitely one of the oldest known patterns, in nature, i.e. the species–area relationship (SAR). Rosenzweig, 25 years ago, was signifying that, regardless of the vast number of studies on SARs, we were still lacking, at his time of writing, a complete understanding of the pattern. All of the preceding chapters in this volume highlight the amount of progress that has been made since Rosenzweig’s book, the range of new methods and patterns that have been brought to light and the many new and insightful questions that have been asked; some have been answered, others still challenge us. Herein, I discuss issues related to the SAR that still require our attention, some of which have been noted in the preceding chapters.

Biological invasions by alien species (in this context, species transported by human actions to areas in which they do not naturally occur) represent one of the primary ways in which people are changing global biodiversity. Native species richness is a positive function of geographic area – the well-known species–area relationship. An interesting question is whether alien species recapitulate this pattern, broadly and/or in detail. Here, we review the increasing body of research exploring alien species richness in the context of geographic area. We assess both the similarities and differences between the species–area relationships of alien and native species groups and how adding alien species to areas affects the overall species–area relationship. Then, we assess how analysis of data for alien species informs our understanding of the mechanisms controlling species–area relationships more generally. We finish with some broad conclusions on the basis of the previous sections.

The search for the mechanisms that drive the species–area relationship (SAR) has been complicated by a number of factors. First, the different proposed mechanisms have generally been considered to be mutually exclusive. Second, due to the misinterpretation of curve shapes after (log) transformation of one or both of the axes. Third, due to confusion about different types of SAR, such as isolate and sample area SARs. These two SAR types are underpinned, at least partly, by different factors (or drivers), which act in combination. The different patterns and processes that drive the SAR can be organized according to a hierarchy: from underlying environmental patterns at the bottom, through the processes driving species diversity patterns, up to the research and sampling design. Environmental patterns include both biological and geographical patterns, while processes may be stochastic, evolutionary or ecological. The resultant species diversity patterns include species range patterns, species densities, species abundances and the spatial distribution of individuals of a species. Although the individuals of a species are rarely randomly distributed in space, the random placement model provides a useful null model that can be used to partition the effects of species abundances and the spatial distributions of individuals on SARs.

Hotspot identification is a crucial strategy for setting conservation priorities. Since both the total number of species and the number of endemic species tend to increase with area, prioritizing sites according to their overall species richness or endemic species richness can produce rankings that simply mirror the sizes of the sites. Thus, it is important to control for the dependence of species number on site area. For this reason, some authors have proposed that the species–area relationship (SAR) and/or the endemics–area relationship (EAR) should be modelled and then the sites located above the fitted curve(s) (i.e. those having positive residuals) designated as hotspots. However, (1) there may be large uncertainties about which model provides the best fit to the SARs/EARs, (2) the use of residuals may lead to sites being identified as hotspots when they only have very few species and (3) there is no guarantee that the sites selected as hotspots by the SAR really include a large fraction of the overall diversity. Thus, it is important to evaluate the ability of the hotspots designated by these procedures to really conserve total and endemic species diversity; the best strategy may in fact be to use a combination of approaches.

The species–area relationship (SAR) has been documented for a wide range of organisms, ecosystems and spatial scales. In contrast, little is known about the spatial scaling of functional and phylogenetic diversity, two other important facets of biodiversity. Describing and understanding how functional and phylogenetic diversity scale with area represents a promising research programme to unravel community assembly mechanisms across spatial scales, and to predict the loss of functional and phylogenetic diversity from habitat loss. In this review, our aim is to provide (1) practical recommendations to measure functional and phylogenetic diversity and to construct functional and phylogenetic diversity–area relationships, (2) a theoretical background on how to interpret the shape of phylogenetic diversity–area relationships and (3) an overview of the empirical phylogenetic diversity–area relationships published to date. We conclude by proposing a series of recommendations for future work.

Ecologists generally hold out hope that a unified understanding of ecosystems is possible because, in Darwin’s words, they are governed by 'laws acting around us'. But at the same time, ecologists take delight in the idiosyncrasies of nature, in the features that are unique to an organism or an ecosystem, in the phenomena that resist general theory. Sometimes this duality leads particularists to condemn the search for laws and universal theory and theorists to denigrate natural history as stamp collecting. Such conflicts are foolish. Here I demonstrate that the search to understand the species–area relationship (SAR) and the other patterns studied by macroecologists as well, exemplify how a well-defined boundary can be drawn between two legitimate domains: the phenomena that are unified by theory and those that are idiosyncratic.

We simulate habitat loss and derive species accumulation curves (SAC) and endemics–area relationship curves (EAR) in order to predict expected extinctions. The EAR may have a very different shape depending on the geometry of habitat loss. If area is lost in a spatially random way we may preserve more species than if area is lost in a clustered way, but with a larger extinction debt. If area is lost continuously inwards (‘inward EAR’) then the immediate loss of species can be much greater than if the same area is lost from the core towards its edge (‘outward EAR’). The main reason for these effects is the spatial autocorrelation of species distributions and the definition of endemics. Spatial autocorrelation means that sampling plots that are clustered are occupied by communities with more similar composition. If endemism is defined in relation to the study area, we can observe great species losses at the edge due to the large numbers of ranges that intersect the study area edge, but most of these species persist outside the study area. If instead we examine endemism on a global scale then the pattern of species losses is not influenced by the geometry of habitat loss.

We review trophic biogeography theory, a growing sub-discipline in ecology that seeks to merge food web ecology with the theory of island biogeography. We start by presenting a deliberately provocative theory, extending neutral community theory to multi-trophic systems, where one does not pay attention to the details of interactions across trophic levels, but rather emphasizes the consequences of traits associated with trophic rank, such as dispersal rates. Our results suggest that the effect of trophic rank on dispersal rates is a key driver of trophic rank effects on species–area relationships. We then examine effects of trophic specialization on species–area relationships, after which we turn to the implications of trophic generalization. An important arena of recent work is elucidating the impact of top down effects in food webs on species–area relationships. Lastly, we offer insights into key avenues for future research including the impact of cross-ecosystem subsidies in driving patterns of biodiversity in heterogeneous landscapes, the need to consider how species coexistence mechanisms may shift across islands or habitat patches varying in area and isolation, and assessing the evolutionary dimension of trophic influences on species–area relationships.

The discovery of the species-area relationship, or SAR, cannot be attributed to a single person or time. Rather, and as true of the description and analysis of many patterns in nature, the story started with the realization of a phenomenon which, over time, and through many individual contributions, evolved into a developed theory. The history of the SAR thus concerns both the origins and the different forms and uses of SARs. We describe how the discovery of the phenomenon eventually led to the first proposed mathematical models of the relationship in the early twentieth century. This initiated the ongoing debates on the shape of the species–area curve, the factors that underpin SARs and the most appropriate model(s) for fitting. Alongside these debates, we review the history of the uses of the SAR and the central role it has played in the development of various fields within biogeography, from island biogeography through to conservation biogeography.

Ecological neutral theory refers to a suite of neutral models that all assume the demographic properties of an individual are independent of its species identity. This is a strong assumption that precludes explicit ecological niches or trophic interactions. Nevertheless, neutral models have been historically successful in replicating classic ecological patterns and linking these to mechanisms in insightful ways. Here we review the species–area relationship (SAR) predicted by various neutral models in different contexts. We discuss ‘mainland SARs’ relevant to large swathes of uninterrupted habitat and show that neutral theory predicts a triphasic SAR shape across broad spatial scales. We discuss ‘island SARs’ relevant to isolated patches of habitat and show that neutral theory predicts no effect of area and a single species for small islands and potentially rich behaviour for larger islands which may harbour endemic species. We also discuss two more complex types of SAR corresponding to cases where the areas sampled and sometimes the habitat itself are distributed unevenly across space in a fragmented pattern. We conclude by demonstrating specific applications of neutral SARs, including calculating extinction debt as well as optimal design of sampling schemes and nature reserves.

It is widely acknowledged that we are in the midst of an extinction crisis and habitat loss is generally considered the primary driver. However, providing accurate estimates of extinction rates has proven to be problematic and a range of extinction estimates have been published. Arguably, the most commonly used method for predicting extinctions resulting from habitat loss has been application of the species–area relationship (SAR). The purpose of this chapter is to provide a review of the many ways in which the SAR has been used to predict the number of extinctions resulting from habitat loss. By doing so, we highlight the pitfalls of using the SAR in such a way and discuss how the SAR has been argued to both over-predict and under-predict extinctions. We also provide examples of the myriad ways in which studies have extended and built on standard SAR models and approaches to better model and predict extinctions. We conclude by arguing that there is a need to recognize that any approach based on a single variable (i.e. area), such as the SAR, is unlikely to provide a perfect extinction prediction, regardless of the specific details.

Although the species–area relationship (SAR) is commonly presumed to be either a power law or to follow the logarithmic relationship, a large number of other mathematical expressions have been proposed to describe the relationship. These models can be divided into four general categories, distinguishing between asymptotic and non-asymptotic, and between convex upward and sigmoid models (in arithmetic space). The choice of regression model should not be determined by best fit alone; rather, the choice should relate to the purpose of fitting mathematical models to SAR data: either descriptive, explicative or predictive. Therefore, we should choose models that are likely to result from expected ecological patterns. We argue that neither (accumulative) sample-area SARs (saSARs) nor island SARs (ISARs) have upper asymptotes and ISARs may be sigmoid if the smallest islands (finest scales) are included. Amongst the 30 different models we review here, few are non-asymptotic. Both the power model and logarithmic model return convex non-asymptotic curves, whereas the second persistence (P2) model and the quadratic logarithmic model consistently return sigmoid curves without asymptotes. We add the Tjørve-hybrid to this shortlist, as it can be useful when neither the power nor the logarithmic model provides a good fit to saSAR data.