Comparative phylogeography in Fijian coral reef fishes: a multi-taxa approach towards marine reserve design

Connectivity modelling identifies sources and sinks of coral recruitment within reef clusters

Connectivity aids the recovery of populations following disturbances, such as coral bleaching and tropical cyclones. Coral larval connectivity is a function of physical connectivity and larval behaviour. In this study, we used OceanParcels, a particle tracking simulator, with 2D and 3D velocity outputs from a high resolution hydrodynamic-biogeochemical marine model (RECOM) to simulate the dispersal and settlement of larvae from broadcast spawning Acropora corals in the Moore Reef cluster, northern Great Barrier Reef, following the annual spawning events in 2015, 2016 and 2017. 3D velocity simulations showed 19.40-68.80% more links and sinks than those of 2D simulations. Although the patterns of connectivity among sites vary over days and years, coral larvae consistently dispersed from east to west in the cluster domain, with some sites consistently acting as sources or sinks for local larval recruitment. Results can inform coral reef intervention plans for climate change, such as the design of marine protected areas and the deployment of proposed interventions within reef clusters. For example, the wider benefits of interventions (e.g., deployment of heat adapted corals) may be optimised when deployed at locations that are a source of larvae to others within comparable habitats across the reef cluster.

The role of the Sunda shelf biogeographic barrier in the cryptic differentiation of Conus litteratus (Gastropoda: Conidae) across the Indo-Pacific region

Geographical and oceanographic processes have influenced the speciation of marine organisms. Cone snails are marine mollusks that show high levels of endemism and a wide distributional range across the Indian and Pacific Oceans. Discontinuities in distributions caused by biogeographic barriers can affect genetic connectivity. Here we analysed the connectivity within Conus litteratus using samples from the Lakshadweep archipelago (Arabian Sea, Indian Ocean) and from the Pacific Ocean. Maximum likelihood analyses based on the mitochondrial cytochrome C oxidase subunit I (COI) and on the non-coding 16S ribosomal RNA (16S rRNA) genes revealed cryptic diversity within C. literatus occupying distinct oceanographic regions. The intraspecific genetic distances between the two distinct clades of C. literatus from the Arabian Sea and the Pacific Ocean ranged from 7.4% to 7.6% for COI and from 2.4% to 2.8% for 16S rRNA genes, which is larger than the threshold limit for interspecific differentiation. The haplotype network analysis also corroborated the existence of two different lineages within C. litteratus. The detected genetic discontinuities reflect the effect of the Sunda shelf biogeographic barrier on the allopatric divergence of C. litteratus.

Biophysical models resolution affects coral connectivity estimates

Estimating connectivity between coral reefs is essential to inform reef conservation and restoration. Given the vastness of coral reef ecosystems, connectivity can only be simulated with biophysical models whose spatial resolution is often coarser than the reef scale. Here, we assess the impact of biophysical models resolution on connectivity estimates by comparing the outputs of five different setups of the same model with resolutions ranging from 250 m to 4 km. We show that increasing the model resolution around reefs yields more complex and less directional dispersal patterns. With a fine-resolution model, connectivity graphs have more connections but of weaker strength. The resulting community structure therefore shows larger clusters of well-connected reefs. Virtual larvae also tend to stay longer close to their source reef with a fine-resolution model, leading to an increased local retention and self-recruitment for species with a short pre-competency period. Overall, only about half of the reefs with the largest connectivity indicator values are similar for the finest and coarsest resolution models. Our results suggest that reef management recommendations should only be made at scales coarser than the model resolution. Reef-scale recommendations can hence only be made with models not exceeding about 500 m resolution.

Range-Wide Population Structure of 3 Deepwater Eteline Snappers Across the Indo-Pacific Basin

Deep-sea habitats may drive unique dispersal and demographic patterns for fishes, but population genetic analyses to address these questions have rarely been conducted for fishes in these environments. This study investigates the population structure of 3 tropical deepwater snappers of the genus Etelis that reside at 100-400 m depth, with broad and overlapping distributions in the Indo-Pacific. Previous studies showed little population structure within the Hawaiian Archipelago for 2 of these species: Etelis coruscans and E. carbunculus. Here we extend sampling to the entire geographic range of each species to resolve the population genetic architecture for these 2 species, as well as a recently exposed cryptic species (Etelis sp.). One goal was to determine whether deepwater snappers are more dispersive than shallow-water fishes. A second goal was to determine whether submesophotic fishes have older, more stable populations than shallow reef denizens that are subject to glacial sea-level fluctuations. Both goals are pertinent to the management of these valuable food fishes. A total of 1153 specimens of E. coruscans from 15 geographic regions were analyzed, along with 1064 specimens of E. carbunculus from 11 regions, and 590 specimens of E. sp. from 16 regions. The first 2 species were analyzed with mtDNA and 9-11 microsatellite loci, while E. sp. was analyzed with mtDNA only. Etelis coruscans had a non-significant microsatellite global FST, but significant global mtDNA Ф ST = 0.010 (P = 0.0007), with the isolation of Seychelles in the western Indian Ocean, and intermittent signals of isolation for the Hawaiian Archipelago. Etelis carbunculus had a non-significant microsatellite global FST, and significant global mtDNA Ф ST = 0.021 (P = 0.0001), with low but significant levels of isolation for Hawai'i, and divergence between Tonga and Fiji. Etelis sp. had mtDNA Ф ST = 0.018 (P = 0.0005), with a strong pattern of isolation for both Seychelles and Tonga. Overall, we observed low population structure, shallow mtDNA coalescence (similar to near-shore species), and isolation at the fringes of the Indo-Pacific basin in Hawai'i and the western Indian Ocean. While most shallow-water species have population structure on the scale of biogeographic provinces, deepwater snapper populations are structured on the wider scale of ocean basins, more similar to pelagic fishes than to shallow-water species. This population structure indicates the capacity for widespread dispersal throughout the Indo-Pacific region.

Comparative phylogeography of the ocean planet

Understanding how geography, oceanography, and climate have ultimately shaped marine biodiversity requires aligning the distributions of genetic diversity across multiple taxa. Here, we examine phylogeographic partitions in the sea against a backdrop of biogeographic provinces defined by taxonomy, endemism, and species composition. The taxonomic identities used to define biogeographic provinces are routinely accompanied by diagnostic genetic differences between sister species, indicating interspecific concordance between biogeography and phylogeography. In cases where individual species are distributed across two or more biogeographic provinces, shifts in genotype frequencies often align with biogeographic boundaries, providing intraspecific concordance between biogeography and phylogeography. Here, we provide examples of comparative phylogeography from (i) tropical seas that host the highest marine biodiversity, (ii) temperate seas with high productivity but volatile coastlines, (iii) migratory marine fauna, and (iv) plankton that are the most abundant eukaryotes on earth. Tropical and temperate zones both show impacts of glacial cycles, the former primarily through changing sea levels, and the latter through coastal habitat disruption. The general concordance between biogeography and phylogeography indicates that the population-level genetic divergences observed between provinces are a starting point for macroevolutionary divergences between species. However, isolation between provinces does not account for all marine biodiversity; the remainder arises through alternative pathways, such as ecological speciation and parapatric (semiisolated) divergences within provinces and biodiversity hotspots.

A multispecies approach reveals hot spots and cold spots of diversity and connectivity in invertebrate species with contrasting dispersal modes

Genetic diversity is crucial for species' maintenance and persistence, yet is often overlooked in conservation studies. Species diversity is more often reported due to practical constraints, but it is unknown if these measures of diversity are correlated. In marine invertebrates, adults are often sessile or sedentary and populations exchange genes via dispersal of gametes and larvae. Species with a larval period are expected to have more connected populations than those without larval dispersal. We assessed the relationship between measures of species and genetic diversity, and between dispersal ability and connectivity. We compiled data on genetic patterns and life history traits in nine species across five phyla. Sampling sites spanned 600 km in the northwest Mediterranean Sea and focused on a 50-km area near Marseilles, France. Comparative population genetic approaches yielded three main results. (i) Species without larvae showed higher levels of genetic structure than species with free-living larvae, but the role of larval type (lecithotrophic or planktotrophic) was negligible. (ii) A narrow area around Marseilles, subject to offshore advection, limited genetic connectivity in most species. (iii) We identified sites with significant positive contributions to overall genetic diversity across all species, corresponding with areas near low human population densities. In contrast, high levels of human activity corresponded with a negative contribution to overall genetic diversity. Genetic diversity within species was positively and significantly linearly related to local species diversity. Our study suggests that local contribution to overall genetic diversity should be taken into account for future conservation strategies.

Community assembly of coral reef fishes along the Melanesian biodiversity gradient

The Indo-Pacific is home to Earth’s most biodiverse coral reefs. Diversity on these reefs decreases from the Coral Triangle east through the islands of Melanesia. Despite this pattern having been identified during the early 20^th century, our knowledge about the interaction between pattern and process remains incomplete. To evaluate the structure of coral reef fish communities across Melanesia, we obtained distributional records for 396 reef fish species in five taxa across seven countries. We used hierarchical clustering, nestedness, and multiple linear regression analyses to evaluate the community structure. We also compiled data on life history traits (pelagic larval duration, body size and schooling behavior) to help elucidate the ecological mechanisms behind community structure. Species richness for these taxa along the gradient was significantly related to longitude but not habitat area. Communities are significantly nested, indicating that species-poor communities are largely composed of subsets of the species found on species rich reefs. These trends are robust across taxonomic groups except for the Pomacentridae, which exhibit an anti-nested pattern, perhaps due to a large number of endemic species. Correlations between life history traits and the number of reefs on which species occurred indicate that dispersal and survival ability contribute to determining community structure. We conclude that distance from the Coral Triangle dominates community structure in reef fish; however, conservation of the most species-rich areas will not be sufficient alone to conserve the vivid splendor of this region.

Contrasting Evolutionary Paths Among Indo-Pacific Pomacentrus Species Promoted by Extensive Pericentric Inversions and Genome Organization of Repetitive Sequences

Pomacentrus (damselfishes) is one of the most characteristic groups of fishes in the Indo-Pacific coral reef. Its 77 described species exhibit a complex taxonomy with cryptic lineages across their extensive distribution. Periods of evolutionary divergences between them are very variable, and the cytogenetic events that followed their evolutionary diversification are largely unknown. In this respect, analyses of chromosomal divergence, within a phylogenetic perspective, are particularly informative regarding karyoevolutionary trends. As such, we conducted conventional cytogenetic and cytogenomic analyses in four Pomacentrus species (Pomacentrus similis, Pomacentrus auriventris, Pomacentrus moluccensis, and Pomacentrus cuneatus), through the mapping of repetitive DNA classes and transposable elements, including 18S rDNA, 5S rDNA, (CA)₁₅, (GA)₁₅, (CAA)₁₀, Rex6, and U2 snDNA as markers. P. auriventris and P. similis, belonging to the Pomacentrus coelestis complex, have indistinguishable karyotypes (2n = 48; NF = 48), with a peculiar syntenic organization of ribosomal genes. On the other hand, P. moluccensis and P. cuneatus, belonging to another clade, exhibit very different karyotypes (2n = 48, NF = 86 and 92, respectively), with a large number of bi-armed chromosomes, where multiple pericentric inversions played a significant role in their karyotype organization. In this sense, different chromosomal pathways followed the phyletic diversification in the Pomacentrus genus, making possible the characterization of two well-contrasting species groups regarding their karyotype features. Despite this, pericentric inversions act as an effective postzygotic barrier in many organisms, which appear to be also the case for P. moluccensis and P. cuneatus; the extensive chromosomal similarities in the two species of P. coelestis complex suggest minor participation of chromosomal postzygotic barriers in the phyletic diversification of these species.

Population expansions dominate demographic histories of endemic and widespread Pacific reef fishes

Despite the unique nature of endemic species, their origin and population history remain poorly studied. We investigated the population history of 28 coral reef fish species, close related, from the Gambier and Marquesas Islands, from five families, with range size varying from widespread to small-range endemic. We analyzed both mitochondrial and nuclear sequence data using neutrality test and Bayesian analysis (EBSP and ABC). We found evidence for demographic expansions for most species (24 of 28), irrespective of range size, reproduction strategy or archipelago. The timing of the expansions varied greatly among species, from 8,000 to 2,000,000 years ago. The typical hypothesis for reef fish that links population expansions to the Last Glacial Maximum fit for 14 of the 24 demographic expansions. We propose two evolutionary processes that could lead to expansions older than the LGM: (a) we are retrieving the signature of an old colonization process for widespread, large-range endemic and paleoendemic species or (b) speciation; the expansion reflects the birth of the species for neoendemic species. We show for the first time that the demographic histories of endemic and widespread reef fish are not distinctly different and suggest that a number of processes drive endemism.

Understanding the Spatial Scale of Genetic Connectivity at Sea: Unique Insights from a Land Fish and a Meta-Analysis

Quantifying the spatial scale of population connectivity is important for understanding the evolutionary potential of ecologically divergent populations and for designing conservation strategies to preserve those populations. For marine organisms like fish, the spatial scale of connectivity is generally set by a pelagic larval phase. This has complicated past estimates of connectivity because detailed information on larval movements are difficult to obtain. Genetic approaches provide a tractable alternative and have the added benefit of estimating directly the reproductive isolation of populations. In this study, we leveraged empirical estimates of genetic differentiation among populations with simulations and a meta-analysis to provide a general estimate of the spatial scale of genetic connectivity in marine environments. We used neutral genetic markers to first quantify the genetic differentiation of ecologically-isolated adult populations of a land dwelling fish, the Pacific leaping blenny (Alticus arnoldorum), where marine larval dispersal is the only probable means of connectivity among populations. We then compared these estimates to simulations of a range of marine dispersal scenarios and to collated FST and distance data from the literature for marine fish across diverse spatial scales. We found genetic connectivity at sea was extensive among marine populations and in the case of A. arnoldorum, apparently little affected by the presence of ecological barriers. We estimated that ~5000 km (with broad confidence intervals ranging from 810-11,692 km) was the spatial scale at which evolutionarily meaningful barriers to gene flow start to occur at sea, although substantially shorter distances are also possible for some taxa. In general, however, such a large estimate of connectivity has important implications for the evolutionary and conservation potential of many marine fish communities.

Population Connectivity Measures of Fishery-Targeted Coral Reef Species to Inform Marine Reserve Network Design in Fiji

Coral reef fish serve as food sources to coastal communities worldwide, yet are vulnerable to mounting anthropogenic pressures like overfishing and climate change. Marine reserve networks have become important tools for mitigating these pressures, and one of the most critical factors in determining their spatial design is the degree of connectivity among different populations of species prioritized for protection. To help inform the spatial design of an expanded reserve network in Fiji, we used rapidly evolving mitochondrial genes to investigate connectivity patterns of three coral reef species targeted by fisheries in Fiji: Epinephelus merra (Serranidae), Halichoeres trimaculatus (Labridae), and Holothuria atra (Holothuriidae). The two fish species, E. merra and Ha. trimaculatus, exhibited low genetic structuring and high amounts of gene flow, whereas the sea cucumber Ho. atra displayed high genetic partitioning and predominantly westward gene flow. The idiosyncratic patterns observed among these species indicate that patterns of connectivity in Fiji are likely determined by a combination of oceanographic and ecological characteristics. Our data indicate that in the cases of species with high connectivity, other factors such as representation or political availability may dictate where reserves are placed. In low connectivity species, ensuring upstream and downstream connections is critical.

Simple rules for establishment of effective marine protected areas in an age-structured metapopulation

The implementation of effective protected areas is one of the central goals of modern conservation biology. In the context of fisheries management and marine ecosystem conservation, marine reserves often play a significant role to achieve sustainable fisheries management. Consequently, a substantial number of studies have been conducted to establish broad rules for the creation of MPAs, or to test the effects of MPAs in specific regions. However, there still exist many challenges for implementing MPAs that are effective at meeting their goals. Deducing theoretical conditions guaranteeing that the introduction of marine reserves will increase fisheries yields in age-structured population dynamics is one such challenge. To derive such conditions, a simple mathematical model is developed that follows an age-structured metapopulation dynamics of a sedentary species. The obtained results suggest that a sufficiently high fishing mortality rate and moderate recruitment success of an individual's eggs is a necessary for marine reserves to increase fisheries yields. The numerical calculations were conducted with the parameters of red abalone (Haliotis rufescens) to visualize and to check validity of the analytical results. They show good agreement with the analytical results, as well as the results obtained in the previous works.

Genetic structure of Scomber japonicus (Perciformes: Scombridae) along the coast of China revealed by complete mitochondrial cytochrome b sequences

The phylogeography history and contemporary agents of selection for many marine fisheries, characterized by widespread species distributions in the face of significant harvest, remains poorly understood. Chub mackerel (Scomber japonicus) are a widespread species in the Indo-Pacific and represent one of the top five commercially fished species in the world, yet their phylogeographic history remains unknown. We characterized the genetic diversity, structure and demographic history of S. japonicus throughout adjacent Chinese seas (from the Yellow Sea to the South China Sea). Using 220 individuals from 11 sites, we inferred 55 distinct haplotypes from complete mitochondrial cytochrome b gene sequences. Haplotype diversity ranged from 0.505 to 0.967 and nucleotide diversity ranged from 0.00056 to 0.01042. Genetic differentiation (F_st) statistics suggested that the highest level of differentiation existed between the SanYa and SanSha localities (F_st = 0.86977), while the lowest levels of differentiation occurred between the DongGang and ShiDao localities (F_st∼ 0). Kimura's genetic distances ranged from 0.001 to 0.011 within and from 0.001 to 0.018 between populations. Hierarchical analysis of molecular variance, Neighbor-joining and median-joining network analyses identified significant phylogeographic structure with two localities (SanYa, Hainan of the South China Sea and LianYunGang, Jiangsu of the East China Sea) explaining most of the genetic variation observed, while the remaining populations were poorly differentiated.

Detecting concerted demographic response across community assemblages using hierarchical approximate Bayesian computation

Methods that integrate population-level sampling from multiple taxa into a single community-level analysis are an essential addition to the comparative phylogeographic toolkit. Detecting how species within communities have demographically tracked each other in space and time is important for understanding the effects of future climate and landscape changes and the resulting acceleration of extinctions, biological invasions, and potential surges in adaptive evolution. Here, we present a statistical framework for such an analysis based on hierarchical approximate Bayesian computation (hABC) with the goal of detecting concerted demographic histories across an ecological assemblage. Our method combines population genetic data sets from multiple taxa into a single analysis to estimate: 1) the proportion of a community sample that demographically expanded in a temporally clustered pulse and 2) when the pulse occurred. To validate the accuracy and utility of this new approach, we use simulation cross-validation experiments and subsequently analyze an empirical data set of 32 avian populations from Australia that are hypothesized to have expanded from smaller refugia populations in the late Pleistocene. The method can accommodate data set heterogeneity such as variability in effective population size, mutation rates, and sample sizes across species and exploits the statistical strength from the simultaneous analysis of multiple species. This hABC framework used in a multitaxa demographic context can increase our understanding of the impact of historical climate change by determining what proportion of the community responded in concert or independently and can be used with a wide variety of comparative phylogeographic data sets as biota-wide DNA barcoding data sets accumulate.

Genetic structuring across marine biogeographic boundaries in rocky shore invertebrates

Biogeography investigates spatial patterns of species distribution. Discontinuities in species distribution are identified as boundaries between biogeographic areas. Do these boundaries affect genetic connectivity? To address this question, a multifactorial hierarchical sampling design, across three of the major marine biogeographic boundaries in the central Mediterranean Sea (Ligurian-Tyrrhenian, Tyrrhenian-Ionian and Ionian-Adriatic) was carried out. Mitochondrial COI sequence polymorphism of seven species of Mediterranean benthic invertebrates was analysed. Two species showed significant genetic structure across the Tyrrhenian-Ionian boundary, as well as two other species across the Ionian Sea, a previously unknown phylogeographic barrier. The hypothesized barrier in the Ligurian-Tyrrhenian cannot be detected in the genetic structure of the investigated species. Connectivity patterns across species at distances up to 800 km apart confirmed that estimates of pelagic larval dispersal were poor predictors of the genetic structure. The detected genetic discontinuities seem more related to the effect of past historical events, though maintained by present day oceanographic processes. Multivariate statistical tools were used to test the consistency of the patterns across species, providing a conceptual framework for across-species barrier locations and strengths. Additional sequences retrieved from public databases supported our findings. Heterogeneity of phylogeographic patterns shown by the 7 investigated species is relevant to the understanding of the genetic diversity, and carry implications for conservation biology.

Phylogeography of the California sheephead, Semicossyphus pulcher: the role of deep reefs as stepping stones and pathways to antitropicality

In the past decade, the study of dispersal of marine organisms has shifted from focusing predominantly on the larval stage to a recent interest in adult movement. Antitropical distributions provide a unique system to assess vagility and dispersal. In this study, we have focused on an antitropical wrasse genus, Semicossyphus, which includes the California sheephead, S. pulcher, and Darwin's sheephead, S. darwini. Using a phylogenetic approach based on mitochondrial and nuclear markers, and a population genetic approach based on mitochondrial control region sequences and 10 microsatellite loci, we compared the phylogenetic relationships of these two species, as well as the population genetic characteristics within S. pulcher. While S. pulcher and S. darwini are found in the temperate eastern Pacific regions of the northern and southern hemispheres, respectively, their genetic divergence was very small (estimated to have occurred between 200 and 600 kya). Within S. pulcher, genetic structuring was generally weak, especially along mainland California, but showed weak differentiation between Sea of Cortez and California, and between mainland California and Channel Islands. We highlight the congruence of weak genetic differentiation both within and between species and discuss possible causes for maintenance of high gene flow. In particular, we argue that deep and cooler water refugia are used as stepping stones to connect distant populations, resulting in low levels of genetic differentiation.

Speciation in fishes

The field of speciation has seen much renewed interest in the past few years, with theoretical and empirical advances that have moved it from a descriptive field to a predictive and testable one. The goal of this review is to provide a general background on research on speciation as it pertains to fishes. Three major components to the question are first discussed: the spatial, ecological and sexual factors that influence speciation mechanisms. We then move to the latest developments in the field of speciation genomics. Affordable and rapidly available, massively parallel sequencing data allow speciation studies to converge into a single comprehensive line of investigation, where the focus has shifted to the search for speciation genes and genomic islands of speciation. We argue that fish present a very diverse array of scenarios, making them an ideal model to study speciation processes.

Vicariance across major marine biogeographic barriers: temporal concordance and the relative intensity of hard versus soft barriers

The marine tropics contain five major biogeographic regions (East Pacific, Atlantic, Indian Ocean, Indo-Australian Archipelago (IAA) and Central Pacific). These regions are separated by both hard and soft barriers. Reconstructing ancestral vicariance, we evaluate the extent of temporal concordance in vicariance events across three major barriers (Terminal Tethyan Event (TTE), Isthmus of Panama (IOP), East Pacific Barrier, EPB) and two incomplete barriers (either side of the IAA) for the Labridae, Pomacentridae and Chaetodontidae. We found a marked lack of temporal congruence within and among the three fish families in vicariance events associated with the EPB, TTE and IOP. Vicariance across hard barriers separating the Atlantic and Indo-Pacific (TTE, IOP) is temporally diffuse, with many vicariance events preceding barrier formation. In marked contrast, soft barriers either side of the IAA hotspot support tightly concordant vicariance events (2.5 Myr on Indian Ocean side; 6 Myr on Central Pacific side). Temporal concordance in vicariance points to large-scale temporally restricted gene flow during the Late Miocene and Pliocene. Despite different and often complex histories, both hard and soft barriers have comparably strong effects on the evolution of coral reef taxa.

Functional endemism: population connectivity, shifting baselines, and the scale of human experience

Quantifying population connectivity is important for visualizing the spatial and temporal scales that conservation measures act upon. Traditionally, migration based on genetic data has been reported in migrants per generation. However, the temporal scales over which this migration may occur do not necessarily accommodate the scales over which human perturbations occur, leaving the potential for a disconnect between population genetic data and conservation action based on those data. Here, we present a new metric called the "Rule of Memory", which helps conservation practitioners to interpret "migrants per generation" in the context both of human modified ecosystems and the cultural memory of those doing the modification. Our rule states that clades should be considered functionally endemic regardless of their actual taxonomic designation if the migration between locations is insufficient to maintain a viable population over the timescales of one human generation (20 years). Since larger animals are more likely to be remembered, we quantify the relationship between migrants per human (N) and body mass of the organism in question (M) with the formula N = 10M(-1). We then use the coral reef fish Pomacentrus moluccensis to demonstrate the taxonomic and spatial scales over which this rule can be applied. Going beyond minimum viable population literature, this metric assesses the probability that a clade's existence will be forgotten by people throughout its range during a period of extirpation. Because conservation plans are predicated on having well-established baselines, a loss of a species over the range of one human generation evokes the likelihood of that species no longer being recognized as a member of an ecosystem, and thus being excluded in restoration or conservation prioritization. [Correction added on 26 December 2012, after first online publication: this formula has been corrected to N=10M(-1)].