A framework for disentangling ecological mechanisms underlying the island species-area relationship

The relationship between an island’s size and the number of species on that island—the island species-area relationship (ISAR)—is one of the most well-known patterns in biogeography, and forms the basis for understanding biodiversity loss in response to habitat loss and fragmentation. Nevertheless, there is contention about exactly how to estimate the ISAR, and the influence of the three primary ecological mechanisms—random sampling, disproportionate effects, and heterogeneity— that drive it. Key to this contention is that estimates of the ISAR are often confounded by sampling and estimates of measures (i.e., island-level species richness) that are not diagnostic of potential mechanisms. Here, we advocate a sampling-explicit approach for disentangling the possible ecological mechanisms underlying the ISAR using parameters derived from individual-based rarefaction curves estimated across spatial scales. If the parameters derived from rarefaction curves at each spatial scale show no relationship with island area, we cannot reject the hypothesis that ISARs result only from random sampling. However, if the derived metrics change with island area, we can reject random sampling as the only operating mechanism, and infer that effects beyond sampling (i.e., disproportionate effects and/or heterogeneity) are also operating. Finally, if parameters indicative of within-island spatial variation in species composition (i.e., β-diversity) increase with island area, we can conclude that intra-island compositional heterogeneity plays a role in driving the ISAR. We illustrate this approach using representative case studies, including oceanic islands, natural island-like patches, and habitat fragments from formerly continuous habitat, illustrating several combinations of underlying mechanisms. This approach will offer insight into the role of sampling and other processes that underpin the ISAR, providing a more complete understanding of how, and some indication of why, patterns of biodiversity respond to gradients in island area.

(1) Sampling effects. The simplest mechanism of the ISAR is that islands passively sample 79 individuals from a larger 'regional' pool of individuals of different species. Smaller islands will 80 sample fewer individuals in total than larger islands. And because the regional pool consists of 81 few common and many rare species (i.e., Preston 1960, May 1975, McGill et al. 2007), smaller 82 islands will have fewer species than larger islands. This will create a positive ISAR with more 83 rare species being present on larger islands, but only in proportion to their abundance in the total 84 pool (i.e., the relative proportions of species does not change from small to large islands). 85 (2) Area per se. This mechanism derives from theories that account for local and spatial 86 processes allowing for more species to persist in large areas relative to small areas. This can 87 include dispersal-enabled coexistence mechanisms such as those inherent to the theory of island 88 biogeography (e.g., Wilson 1963, 1967) and other mechanisms of spatial 89 coexistence via metacommunity dynamics (e.g., Tilman 1994, Hanski et al. 2013). Area per se 90 can also include population-level processes, such as Allee-effects or demographic stochasticity, 91 which are more likely to increase extinction or decrease establishment probabilities on smaller 92 islands (e.g., Levin 1974, Hanski and Gyllenberg 1993, Orrock and Wattling 2010. 93 (3) Heterogeneity. Heterogeneity leads to intraspecific aggregation (clumping), and larger 94 islands should have more opportunities for such aggregation. This can emerge from two distinct 95 sub-mechanisms: 96 (a) Habitat heterogeneity. Habitat heterogeneity leads to dissimilarities in species 97 composition via the 'species sorting' process inherent to niche theory (e.g., Whittaker 98 1970, Tilman 1982, Chase andLeibold 2003). As a mechanism for the ISAR, larger 99 islands are often assumed to have higher levels of habitat heterogeneity than smaller 100 islands (e.g., Williams 1964, Hortal et al. 2009). For example, larger oceanic islands 101 typically have multiple habitat types, including mountains, valleys, rivers, etcetera, 102 allowing for multiple types of species to specialize on these habitats, whereas smaller 103 islands only have a few habitat types. Likewise, in freshwater lakes, which can be 104 thought of as aquatic islands in a terrestrial 'sea', larger lakes typically have more habitat 105 heterogeneity (e.g., depth zonation) than smaller lakes. 106 (b) Compositional heterogeneity due to dispersal limitation. Dispersal limitation can also 107 lead to compositional heterogeneity through a variety of spatial mechanisms, including 108 ecological drift, colonization and competition tradeoffs, and the like (e.g., Condit et al. 2002, Leibold and Chase 2017). If dispersal limitation is more likely on larger islands, 110 we might expect greater within-island spatial coexistence via dispersal limitation, higher 111 compositional heterogeneity, and thus greater total species richness on larger than on 112 smaller islands. 113 Patterns of species compositional heterogeneity that emerge from these two distinct mechanisms 114 are difficult to distinguish without explicit information on the characteristics of habitat 115 heterogeneity itself (e.g., habitat maps, environmental data), and how species respond to that 116 heterogeneity. And thus, in the absence of information about environmental conditions, we 117 cannot disentangle these mechanisms. 118 While the above ecological mechanisms can independently determine the ISAR, it is also quite 119 possible that two or more of these mechanisms act in concert (e.g.., Chisholm et al. 2016 ISARs via the use of individual-based rarefaction curves (e.g., Heck et al. 1975, Gotelli and 130 Colwell 2001), and the metrics that can be derived from them, at multiple spatial scales.

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Testing ISAR Mechanisms with Individual-Based Rarefactions of Sample Data: 132 We show that it is possible to disentangle the three ecological mechanisms leading to the ISAR 133 -sampling, area per se, and heterogeneity-by measuring several parameters from the 134 individual-based rarefaction curves collected from larger and smaller scales (see Chase et al. to generate the curve. From this curve, we can visualize the total number of species on the island 145 (STotal), which can be derived from a extrapolation techniques or from independent data (i.e., 146 checklists). We can also visualize two other parameters of interest for dissecting the ISAR: (i) 147 the numbers of species expected from a given N, γSn (where the vertical dashlined line at n 148 intersects the solid curve) (ii) the probability of interspecific encounter (PIE), which when bias-149 corrected, represents the slope at the base of the rarefaction curve, γ PIE (solid grey arrow). The  First, we derive an individual-based rarefaction curve by combining all individuals from all 159 representative samples (e.g., transects, quadrats) measured on a given island and randomizing 160 individuals to generate the curve. Because this curve extends out to the regional extent of samples, we refer to it as the γ-rarefaction curve (solid line in Figure 1). This γ-rarefaction curve 162 allows us to estimate the first parameter of the ISAR: 163 1) The total number of species on a given island, Stotal. Because the γ-rarefaction curve 164 comes from samples, it is not a complete survey. Thus, the most straightforward way to 165 estimate Stotal is from independent information, such as checklists of species known to 166 occur on a given island. However, because this information is often unavailable, Stotal can 167 simply be the total number of species observed in the sampled plots (if sampling effort is 168 proportional to island size), or it can be estimated via techniques for predicting the 169 number of species in a given extent via sampling from within that extent (e.g., Colwell 2) The numbers of species expected from a rarefaction to a common number of individuals 180 (Sn). Because this value is calculated from the individual-based rarefaction curve from 181 the larger group of samples from across the island (i.e., the γ-rarefaction curve), we refer 182 to this as the rarefied number of species expected from the γ-rarefaction curve, γ Sn.  plots (or a defined subset of plots), which we call the α-rarefaction curve (dashed line in Figure   203 1). From the α-rarefaction curve, we can derive two more parameters, which are similar to those 204 described above but measured from within a given locality, rather than from across the entire 205 island.

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4) The numbers of species expected from a rarefaction to a common number of individuals 207 from individual plots, which we refer to as α Sn.

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5) The effective number of species from PIE as above, but calculated from the α-rarefaction 209 curve, which we refer to as α SPIE.

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These metrics from the -rarefaction curve can be taken from every replicate sample so that 211 these parameters have a mean and variance.

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Finally, we take the ratio of these parameters measured from the γand α-rarefaction curves to 213 derive two indices of β-diversity that provide an estimate of the amount of interspecific  more likely to persist on larger islands, so that Sn increases, but SPIE does not vary. D.

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Heterogeneity where both rare and common species are influenced. Depicted by a difference 249 between the -parameters, which do not vary with island area, and the -parameters, which do 250 differ. This also leads to significant effects on both -parameters (indicated in blue). E.

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Heterogeneity where only rare species are influenced. Depicted by a difference in Sn, but not 252 SPIE, from the to -levels, also leading to a difference in (indicated in blue). of these, hypotheses about how the metrics calculated from the γ-rarefaction curve and α-308 rarefaction curve will differ with island area and other variables will need to be modified. For     Table 1.

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Images are CC0 Creative Commons, with no attribution required.

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In this system, we find that Stotal increases with island area, as expected. Furthermore, both γ Sn 359 and γ SPIE increase with island area (Figure 3a). Thus, we can reject the null hypothesis that the Here, like the lizards above, we find that Stotal, γ Sn and γ SPIE increase with island area (Figure 3d), 380 and this pattern is reflected at the local scale ( Figure 3e). Thus, again, there is a clear signal for 381 an influence of area per se influencing both the number of species and their relative abundances.

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Unlike the lizards, however, here we found no effect of glade size on β-diversity between sweep 383 samples within a glade ( Figure 3F), suggesting that the ISAR did not likely result from increased 384 levels of heterogeneity in larger glades, but rather from spatial processes associated with area per 385 se effects. Synthesis of case studies-In the original studies, which primarily focused just on species 402 richness and not relative abundances, little more than describing the shape of the ISAR could be 403 discerned. However, from our more in depth analyses, we see consistent patterns in Stotal, but 404 distinct features in the metrics underlying this overall pattern, allowing us to delve deeper into 405 the possible mechanisms underlying these patterns. First, we can see that the ISARs of each 406 taxa/system result from more than just sampling effects. That is, for each system, larger 407 islands/patches have more species (indicated by a significant γ Sn relationship) than would have 408 been expected from a simple sampling process from the regional species pool. This effect 409 influenced both common and rare species for the island lizards and glade grasshoppers (indicated 410 by a significant γ SPIE relationship). Alternatively, only the rarer plant species were influenced by 411 fragment size in the terrestrial fragmented system in Israel (because there was no significant γ SPIE 412 relationship). Indeed, this may explain why the plot-level analyses by the authors failed to detect 413 any change in plot-level measures, and concluded that sampling effects were likely, even though 414 our analyses indicated that area per se played a role, at least for the rarer species.

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Going a step further, by deriving β-diversity measures to capture within-island aggregation, we 416 see that lizards on islands and plants in fragments appeared to show higher levels of within-417 island aggregation on larger islands, at least among the rarer species (i.e., significant 418 results). This suggests that at least some amount of the ISAR in these two systems was 419 influenced by compositional heterogeneity. Without additional environmental data, however, we 420 cannot tell if that heterogeneity is due to dispersal limitation or environmental variation.

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Grasshoppers in glades, however, do not appear to show any divergent β-diversity patterns 422 across different sized glades, suggesting that variation in heterogeneity among different sized 423 glades was not a primary driver of the ISAR, but that area per se effects were primarily 424 operating. Unfortunately, however, without further information, we cannot say exactly what 425 sorts of area per se mechanisms allowed more species of grasshoppers to persist in larger glades 426 than expected from sampling. 427 We used the selected case studies to demonstrate the utility of our framework to provide insight 428 for the possible ecological mechanisms that underpin ISARs. A more complete exploration of 429 the generality of the different patterns and potential mechanisms leading to the ISAR will require 430 a much more thorough analysis of natural islands and patchy landscapes, as well as habitat 431 islands that are created by habitat loss and fragmentation. Such analyses will allow us to achieve 432 a more general synthesis of the patterns and possible processes creating ISARs in natural and 433 fragmented landscapes, but will also require more data (i.e., spatially explicit data of total and  found that fern species richness in standardized plots did not increase with island area when 477 measured at small spatial grains (i.e., 400m 2 -2400m 2 ), but that the slope became significantly 478 increasing at the largest sampling grain (6400 m 2 ). Second, it is possible that S measured in 479 standardized plots may not vary with island size, but that habitat heterogeneity leads to different 480 species present in different habitat types, creating the ISAR. For example, Sfenthourakis and 481 Panitsa (2012) found that plant species richness on Greek islands measured at local (100m 2 ) 482 scales did not change with island area, but that there were high levels of β-diversity on islands 483 that were larger, likely due to increased heterogeneity. In both of these studies, simply 484 measuring standardized species richness in small plots across islands of different spatial grains 485 may have led to the faulty conclusion that sampling effects predominated (i.e., no relationship of 486 S with island area). This is because area per se and/or habitat heterogeneity can generate 487 patterns that are largely indistinguishable from sampling effects when sampling grain, and 488 habitat heterogeneity are not considered. However, our approach, which explicitly considers 489 these scaling effects, provides a more definitive way to test amongst these alternative  In an approach similar to our own to disentangle the role of sampling effects from ISAR studies, they interpreted to indicate that sampling was primarily responsible for differences in S among 501 habitat fragments. While this approach was quite similar to ours in spirit, the use of Fisher's α as 502 a measure of diversity is predicated on the implicit assumption that the distribution of 503 commonness and rarity follows a log-series distribution; when it does not, the metric can give 504 highly suspect results (e.g., Jost 2007). Thus, we prefer the use of PIE and its conversion to an 505 effective number of species SPIE, for capturing differences in the relative abundances of species, 506 which makes no such assumptions, can be more directly compared to changes in S along the Hill 507 number continuum, and can be more meaningfully compared across spatial scales (e.g., Jost  Despite its advantages, it is important to note that our approach is purely observational and 510 dissects the island-wide ISAR into metrics that capture different elements of how biodiversity 511 scales with sampling. As such, it cannot definitively discern process from these patterns, 512 although it can provide deeper insights into the likely mechanisms that influence the ISAR than 513 previous observational approaches. To more definitively test the primary ISAR mechanisms 514 described here (e.g., sampling, area per se, and heterogeneity; see Connor and McCoy 1979), we 515 would need to go a step or two further. This could include, for example, observational studies that took advantage of natural experiments such as islands that varied semi-orthogonally in both 517 area and heterogeneity (Nilsson et al. 1988, Ricklefs and Lovette 1999, Kallimanis et al. 2008, 518 Hannus and Von Numers 2008), but also dissecting patterns of species richness in a more 519 explicit way as we have outlined here. Or it could include manipulative experiments that directly 520 alter island size and/or heterogeneity (e.g., Simberloff 1976, Matias et al. 2010), or disrupt the 521 processes occurring within islands (e.g., altering patterns of within-island dispersal and/or 522 extinction).

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Finally, we note that the approach that we advocate here is only one step towards creating a 524 deeper understanding of patterns of diversity on islands and island-like habitats. We have only 525 focused on the simplest pattern of diversity on islands, the ISAR. We hope that new analyses 526 and meta-analyses will emerge along the lines of what we have presented above in the 'case 527 studies' section, so that we might start to see some generalities emerge. However, there are 528 many other features of islands that vary in addition to and in conjunction with island area (and  This work emerged from discussions among the co-authors in many contexts over many years, 538 and was also improved by discussions with many other colleagues, including S. Blowes, T.