Abstract: Extinction forecasting is one of the most important and challenging areas of conservation biology. Overestimates of extinction rates or the extinction risk of a particular species instigate accusations of hype and overblown conservation rhetoric. Conversely, underestimates may result in limited resources being allocated to other species/habitats perceived as being at greater risk. In this paper I review extinction models and identify the key sources of uncertainty for each. All reviewed methods which claim to estimate extinction probabilities have severe limitations, independent of if they are based on ecological theory or on rather subjective expert judgments.
Prediction is very difficult, especially about the futureNils Bohr, Nobel Prize winning physicist
Preventing the extinction of species is probably the most emblematic objective of the global conservation movement. To fulfill this aim effectively requires that decision makers and environmental managers are provided with accurate information on: (1) the identities of specific species/populations with a high probability of going extinct without further interventions; (2) the predicted rates of extinction among a range of taxa in different geographic areas and biomes under various ecological scenarios.
Armed with this information rational decisions can then be made on the allocation of resources to habitat or species protection measures with the aim of reducing the likelihood of a species going extinct or a reduction in the general rate of extinctions over a wider area.Although the rationale for accurate assessment of extinction risk for a species or a geographic area is clear, the best techniques for achieving these objectives have not been resolved. Indeed, extinction forecasting is one of the most problematic and controversial areas of conservation science where crude estimates (e.g., ) have been the subject of high profile criticism by environmental skeptics  or have become the subject of misleading newspaper headlines . The uncertainty surrounding extinction forecasting is understandable given the diversity of available methods, each of which is based on various assumptions and all of which use a wide variety of data or varying quality and completeness.
In this short review article I create a simple typology for defining different classes of extinction forecasting models and to identify the key assumptions and sources of uncertainty for each category of model. I will conclude with a discussion on the role of human agency in avoiding extinction and argue that, ultimately, it is the reaction of the global conservation movement to information on extinction risk that determines the probability of extinction for many taxa and that this should be factored into future extinction models. This review is aimed at conservation scientists, researchers and especially the growing numbers of interdisciplinary academics who are in the process of incorporating ideas from social science and practice into the standard natural science framework used in conservation.
Before presenting the typology of extinction models it is important to consider what is meant by extinction. Extinction has traditionally been viewed by conservation scientists as logical end point of the process of population decline—the point on the graph where the population size curve meets the x-axis and terminates abruptly and finally . The IUCN defines a species as extinct if ?there is no reasonable doubt that the last individual has died? , a definition that reveals one of the main stumbling blocks for measuring extinction: the difficulty of ascertaining the continued existence of a species that is certainly exceedingly rare, and which may also inhabit an isolated habitat that is difficult to effectively survey.Indeed, IUCN guidelines require that a species can be declared extinct only after exhaustive surveys fail to produce any observations over an appropriate time period and geographical range appropriate to its life cycle and life-form—an unfeasible task for most species . Butchart and his colleagues have recently introduced a new category of ?possibly extinct‘ to apply to those species that are, ?on the balance of evidence, likely to be extinct, but for which there is a small chance that they may be extant and thus should not be listed as Extinct until adequate surveys have failed to find the species and local or unconfirmed reports have been discounted .The above definitions are concerned with situations where a species is known to science and has been collected (on at least one occasion).
However, if science was to restrict extinction forecasts only to those species that have been formally identified there would be a danger of considerable underestimations in magnitude. Extinctions of undiscovered species inferred from estimates of species diversity for a given ecosystem or region and the species-area relationship have been termed Linnean extinctions  (after the Linnean shortfall in biogeography) or Centinelan extinctions  and probably outnumber documented extinctions many times over. Such unseen extinctions are highly dependent of estimates of species richness and are the source of most of the headline grabbing figures that periodically appear in the global press.
Moreover, the majority of such extinctions are in poorly described taxa and biomes such as arthropods in tropical forests.
2. A Typology of Extinction Forecasting
Extinction forecasting models are defined here as any model/method that indicates: (i) the likelihood that a species is already extinct, or will go extinct at some defined point in the future; (ii) the number of species that are likely to go extinct within a given geographic area within a given timeframe. In this respect extinction forecasting can answer 4 key questions for conservationists (Table 1):
- How many species are likely to go extinct in area x over time t?
- What are the identities of the species with a high probability of extinction in area x over time t?
- What is the probability of species y going extinct in habitat x over time t?
- What is the probability that species y is already extinct in habitat x?
Table 1. A use-based framework for classifying extinction forecasting models based on the four fundamental questions about extinction (see text for full explanation). Model choice is critically constrained by type of data available.
Specificity refers to taxonomic level (individual species versus extinctions within a defined area) and geographical focus.2.7.
Ecosystem or trophic cascade models of extinction are defined here as any model that predicts extinction on the basis of direct or indirect impacts of removing one or more species from a food-web. The loss of one species is most likely to cause the extinction of other species that depend on it (coextinction) in the case of mutualisms and parasitism, although the effects can cascade throughout the ecosystem. Paradoxically, although this is likely to be among the most common and most predictable type of extinctions there have been very few documented examples [reviewed in 31].Perhaps the simplest and best known example was described by Temple, who hypothesized that a coevolved obligate mutualism between the extinct dodo (Raphus cucullatus) and the very rare tambalacoque tree (Sideroxylon grandiflorum) had doomed the tree to extinction . The supposed mutualism was based on the notion that seeds of the tree needed to pass through the dodo‘s gut before they could germinate and supported by the fact that no seeds had germinated since the dodo‘s demise more than three hundred years ago. Sadly, neither line of evidence turned out to be correct. Tambalacoque seeds germinate in low numbers without abrasion and there are several of these rare trees of less than 300 years old .This type of extinction model is not restricted to simple pair-wise species interactions but also encompasses the hypothesized loss of entire functional groups.
For example, da Silva and Tabarelli Diversity 2009, 1 143 describe how the loss of large-gap birds and frugivorous mammals in the remaining fragments of Brazil‘s Atlantic forest are predicted to cause the regional extinction of about 33.9% of trees that need these species to disperse their seeds . Such simple deterministic models are arguably unable to sufficiently capture the complexities of multispecies interactions to provide precise estimates of future extinctions although they clearly have considerable heuristic value.More recently, sophisticated simulations have suggested that increased robustness and decreased levels of food web collapse are associated with higher diversity systems that have high levels of complexity, as measured by connectivity . However, the development of truly predictive and robust food web models that can accurately predict the number and identity of ?knock-on‘ extinctions after the loss of one of more species remains a significant challenge.
2.8. Changes in Extinction Risk Categorization
The IUCN Red List of Threatened Species  is regarded as the most authoritative list of globally threatened species.
At the heart of this system are a set of simple quantitative criteria based on population sizes and population decline rates, and range areas and range declines which are used to allocate species to one of several categories of extinction risk (e.g., endangered, critically endangered, extinct in the wild, etc.
). It should be noted that the list employs different methods of assessing extinction risk depending on the available data and that the criteria used to assess species status are in themselves methods (e.g., PVA).
In this sense it may be better to consider Red Lists as a framework for standardising and communicating extinction risk. Nevertheless, transitions between categories, on whatever basis they may have been allocated, have been used as an indicator of increasing extinction probability at a variety of spatial scales.The key transition for extinction forecasting is between ?endangered‘ where a population has a ?very high risk of extinction in the wild? to ?critically endangered‘ where the species is considered as having an ?extremely high risk of extinction in the wild? . The criteria for inclusion in the latter category include very small populations and geographic ranges and a strong trend of population decline. The final category (as do all categories) includes the potential for integration of results from population viability analysis: ?Quantitative analysis showing the probability of extinction in the wild is at least 50% within 10 years or three generations, whichever is the longer (up to a maximum of 100 years)? .Critically endangered can thus be cautiously used as a surrogate for imminent extinction. Brooke et al. tested this proposition by comparing the historical transition of bird species into the critically endangered with verified extinctions at both a global level and within Australia .
They concluded that species were actually going extinct at a rate 2 (Australia) to 10 (globally) times lower than predicted. The potential cause of this discrepancy was identified as the effectiveness of the global conservation community at rescuing bird species on the brink of extinction (see Section 2.9 below).A potentially more serious issue with the IUCN Red Lists is whether the extinction risk criteria have been correctly applied. In 1997, the eminent Canadian zoologist and sea turtle expert, Nicholas Mrosovsky, accused the IUCN‘s Marine Turtle Specialist Group of upgrading the listing of the Hawksbill sea turtle (Eretmochelys imbricata) without making available the scientific evidence for this change in status, and then using this to influence proposals for sustainable use of the species . Thus, it is possible that unconscious or conscious biases in the information accepted and used by specialist groups might influence the categorization of species and, hence, provide an unduly pessimistic prognosis of their future survival.Recently, the Red Lists have been used in combination with the results of bioclimatic envelope models (shifts and reductions in species‘ ranges) to estimate extinction rates. A good example is the study of Bomhard et al.
, who computed the current and future Red List status of endemic Proteaceae in the Cape region of South Africa assuming a number of different land-use and climate change scenarios for the year 2020 . The impacts of climate change were estimated using standard niche-based species distribution models (see above).They concluded that up to a third of species become more threatened (are ?upgraded‘ to a higher Red List category) under future scenarios and that under the most severe scenario the proportion of Critically Endangered taxa increases from approximately 1% to 7% and almost 2% of the 227 species will become globally Extinct. This general approach has been heavily criticised by Akçakaya et al., who argue that where such combined approaches have been adopted the Red List criteria were frequently misapplied due to arbitrary changes to spatial and temporal scales, confusion surrounding the use of spatial variables, and a widespread assumption of a linear relationship between abundance and range area .
9. Expert Judgement
Extinction predictions that incorporate multiple environmental drivers may also be derived from the reasoned judgement of experts. These sorts of forecasts have undoubtedly been the most problematic for conservation science because of a clear tendency on the part of many senior scientists to make pronouncements that appear to over-exaggerate the extinction crisis. Possibly the most famous of these pronouncements, and one that subsequently appeared in numerous intergovernmental reports, was Norman Myers ?prediction‘ in 1979 that 1 million species would be extinct by the year 2000 at a rate of 40,000 a year . A year after the publication of Myers‘ book Thomas Lovejoy forecast that fifteen to twenty percent of the world‘s species would be extinct by the turn of the century (cited in ).Such misplaced predictions of imminent demise have also been attached to a number of rare taxa. For example, Johns and Ayres proposed that an Amazonian primate, the southern bearded saki (Chiropotes satanas satanas) was already ?beyond the brink‘ in eastern Amazonia due to deforestation, hunting, its sensitivity to habitat disturbance and a dependence on many tree species valued for their timber, and would be extinct by the end of the Century .
Subsequent studies in the late 1990s demonstrated that the monkeys were still relatively abundant in some forest fragments where hunting was absent . Of course, dire forecasts of mass extinction or of the disappearance of a specific species may influence the allocation of resources reducing the likelihood of the prediction being realized—and this is clearly often the aim.It is this blurring between science and advocacy that makes expert predictions about extinction so difficult to assess, and possibly why so few genuine experts can be drawn into a public pronouncements. One possible solution that might reduce uncertainty and personal biases is forecasts based on the opinions of several experts filtered through a standard protocol such as the Delphi Diversity 2009, 1 145 technique which uses a series of iterative questionnaires and controlled feedback from experts .
Such forecasts might be able to better ?factor-in‘ cultural elements such as future funding flows and the potential impacts of interventions (see 2.10 below) into the results of standard extinction models.
The direct role of humans in the extinction process through exploitation for food and/or trade has long been recognized as an important, if difficult to predict, component of extinction forecasting. The traditional view, derived from economic theory, was that a species would be exploited until its density fell to a level that was no longer economically viable to exploit. This view was recently challenged by Courchamp et al. who coined the term anthropogenic Allee effect to refer to the situation where the abstract value that people attach to global rarity means that the higher costs of exploiting a rare species are offset by the higher prices that ?collectors‘ or connoisseurs are willing to pay .However, although there is strong evidence that the general public values rarity , it is equally clear that not all rare species are equally collectable. Moreover, there have been few comparative studies of the attitudes and behaviors of bird-keepers or reptile enthusiasts that drive this trade (see  for a rare exception]. More generally, by the same argument placing a ?collectable‘ endangered species on the IUCN Red List or on a CITES appendix could also increase the economic value of a rare species in addition to acting as a global advert alerting interested parties to this fact.Figure 2.
Schematic of proposed protocol for a phased implementation of an applied biocultural theory of avoided extinction to improve prioritization procedures (redrawn from ).3. Conclusions
Several general conclusions can be drawn from the above brief review of contemporary extinction forecasting methods:
- There is a great range of models available to conservationists that vary in their scope and precision.
The models use different types of data, have a wide range of uncertainties and assumptions and generate predictions that can be used for different purposes. Choice of model should thus critically depend on end purpose. What will this information be used for and what level of uncertainty is acceptable? There has been a strong tendency among conservation organizations to widely disseminate extinction rate predictions made over large geographic areas based on species-area or species distribution models. Unfortunately, these models also have very high levels of uncertainty associated with their predictions leading to widespread media misrepresentation .
- There is no systematic application of different models or, more significantly, combinations of models. There is great scope for developing consensus modelling approaches which area being successfully developed in other areas of ecology  and may reduce some of the uncertainties. Moreover, advances are also being made in combining models.
For example, Keith et al. recently successfully integrated a species distribution (habitat suitability) model with a stochastic (meta-) population model to explore the vulnerability to extinction of plants in the South African fynbos .
- The importance of the global conservation movement in avoiding extinction is acknowledged to reduce the precision of extinction forecasts , but there have been few attempts to incorporate this into extinction forecasting frameworks . Moreover, it is clear that different types of extinction have different amounts of agency within conservation. Thus, even though the processes leading to local extinction are identical to those that cause the global extinction of a species, the reaction of the conservation community will likely be very different.
Whereas an imminent local extinction may promote some local action, an imminent global extinction may result in considerable investment of conservation resources and an emergency response from the global conservation movement. Equally, the degradation of a species rich habitat with no endemics will be far less likely to be the focus of conservation action than an equivalent area rich in endemics. Social values will thus have a significant influence of the future geography and intensity of extinction events .
- There is a strong qualitative signal from all the models—species are currently going extinct in unusual numbers . Predicting their identities and focusing attention on geographic areas that are expected to suffer very high rates of extinction remains the key challenge for the global conservation movement.
- Finally, it is important to note that although all the described methods have their limitations, they still provide important information upon which rational decisions can be made about the protection of species and environment.
Indeed, while a species that is predicted to become extinct still persists (an extinction debt), there is still time for conservation to intervene and possibly reverse the situation . Scientists should therefore be encouraged to continue refining and developing extinction forecasting methods , even with the associated risks of being overly optimistic or pessimistic.
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