Introduction

The threats to biodiversity, agriculture and human health from climate change (IPCC 2007) and invasive species (Mooney and Hobbs 2000) are creating a burgeoning demand for tools to estimate changes in potential species’ ranges (Holt and Keitt 2005). This demand is increased by the ongoing translocation of biological control agents (Sutherst 2003). Multivariate statistics and rule-based approaches, with environmental variables sourced from meteorological stations, ground observations or satellite imagery, have been used widely (e.g. Rogers 1995; Austin and Meyers 1996; Rogers et al. 1996; Estrada-Pena 2001; Pearson et al. 2002; Peterson 2003; Guisan and Thuiller 2007). The models are being used to make projections of the potential geographical distribution of species under current or future climates (Rogers and Randolph 1993; Beaumont and Hughes 2002; Midgley et al. 2002; Estrada-Pena et al. 2006). Such results and many others have been used to inform policy (Thomas et al. 2004), despite large differences between different models when projecting changes in ranges of the same species in response to environmental changes (Kriticos and Randall 2001; Robertson et al. 2003; Thuiller 2003; Elith et al. 2006; Zeman and Lynen 2006). Rigorous validation against independent data has been lacking (Sutherst 1998) partly because opportunities for such tests with endemic species do not exist (Sutherst and Maywald 2005). On the other hand invasive species provide many such opportunities as we now demonstrate.

One invasion that allows independent validation is provided by the pan-tropical bovine tick, Rhipicephalus (Boophilus) microplus (Canestrini) (Acari:Ixoididae), which has been expanding its range in Africa over a period of decades. We compare a priori estimates of the areas at risk of further invasion in Africa based on a multivariate logistic regression model (Cumming 1999a, b; Cumming 2002) and the inference-based, climatic response model, CLIMEX, (Sutherst and Maywald 1985; Sutherst et al. 1995; Sutherst 2003).

Historical geographical distribution of R. B. microplus

R. B. microplus is a bovine tick of Asian origin that is now widespread in tropical and sub-tropical Central and South America, Australia and the east coast of Africa (Wharton 1974; Cumming 1999a, b). It has been in south-east Africa for over a century (Theiler 1949), during which time its distribution has waxed and waned in southern Africa prior to 1999 as cited by Lynen et al. (2008). Theiler (1943) foresaw future extensions of the localised foci in southern Africa. The prior occupation of much of the continent by the very similar endemic species, B. decoloratus, which mates with R. B. microplus to produce sterile hybrid zones (Sutherst 1987a) has been a barrier to the latter’s spread. Modelling suggested that it was possible for R. B. microplus to colonise the occupied territory in much of sub-Saharan Africa under certain conditions of climate, host suitability and propagule pressure. As such this exotic tick, which transmits Babesia bovis, a more pathogenic bovine parasite than the endemic B. bigemina, is a potential threat to bovines in other parts of Africa.

Recently R. B. microplus expanded its range slightly into marginal country at the northernmost tip of South Africa during a period of above average rainfall (Tønnesen et al. 2004) and northern Tanzania (Lynen et al. 2008). Most recently the tick has been recorded for the first time from a ‘dense humid forest’ habitat 50 km north of Abidjan in Ivory Coast, West Africa (Madder et al. 2007), as shown with stars in Figs. 1b and 2. These invasions provide an excellent opportunity to compare model predictions using truly independent observations.

Fig. 1
figure 1

(a) Observed and (b) estimated potential geographical distribution of the bovine tick, R. B. microplus in Africa, using logistic regression fitted to the observed African distribution. The stars show the areas in Venda, north-western Tanzania and Ivory Coast in West Africa from where the tick has recently been recorded

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Fig. 2
figure 2

The potential geographical distribution of the bovine tick, R. B. microplus in Africa, estimated using the CLIMEX model and the Australian geographical distribution. The stars show the areas in Venda, north-western Tanzania and Ivory Coast in West Africa from where the tick has recently been recorded

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Model comparison

A regression model with up to 49 predictor variables (mean monthly rainfall, maximum and minimum temperatures, normalized difference vegetation index (NDVI) and elevation) was built for 73 species of ticks to describe Pan-African distributions of species richness (Cumming 1999a, b; Cumming 2002). The climatic data used were restricted to the southern hemisphere. A number of studies were cited (Cumming 1999a, b) that used multivariate analyses to estimate the likely range of particular species, and to infer the role of different environmental variables in determining species’ distributions. Some of the limitations of descriptive methods were pointed out but these caveats have not been taken into account by later users of regression and other statistical methods.

The observed and estimated distributions of R. B. microplus in Africa (Cumming 1999a, b) are shown in Fig. 1a, b. The model provides a very credible description of the data. It also shows small areas at risk in Namibia and Angola. Zero or minimal risk is attributed to most of East and Central Africa. The results were reproduced in a series of high profile maps by a consortium supported by the UK Department for International Development’s (DFID) Animal Health Programme, Food and Agriculture Organization (FAO), International Livestock Research Institute (ILRI) and the Integrated Consortium on Ticks and Tick-borne Diseases (ICTTD), with tick and tick-borne disease interests in Africa (Minjauw et al. 2001).

We repeated Cumming’s analysis, using only climatic variables because Cumming stated that climate accounted for nearly all of the observed variation, due to the high correlation between the predictive variables. The presence of hosts and vegetation types had also been eliminated as limiting factors (Cumming 1999b, 2002). We ran the model using an interpolated climate surface (monthly maximum and minimum temperature, rainfall and relative humidity) with a resolution of 10′ (New et al. 2002). Our results were sufficiently similar to those of (Cumming 1999a, b) to ensure that a climate-based model comparison was valid for further comparisons. A question arose as to what weighting effect the different density of observational records had on the estimation of the model parameter values. The data are heavily biased towards northern Malawi and south-western Tanzania. This coincides with the area with greatest predicted habitat suitability. We tested the effect of the sampling bias, by aggregating clusters of data points, and found that it had little discernable effect on the predicted areas. A major effect on the range limits arose from the weighting given to absence records.

The potential geographical distribution of R. B. microplus in relation to climate had also been estimated for Africa (Sutherst and Maywald 1985; Sutherst 1987b), using the CLIMEX model. CLIMEX is a simplified simulation model that infers the responses of species to average maximum and minimum temperatures, rainfall and relative humidity from its geographical distribution and seasonal phenology. It incorporates a hydrological model and runs on a weekly time step. The model combines growth and stress parameters to produce a measure—the Ecoclimatic Index (EI)—of the overall suitability of the climate for the target species. The original CLIMEX model of R. B. microplus was parameterised using the distributions in Australia (Sutherst and Maywald 1985) and the south coast of South Africa because a quarantine boundary prevented southward spread beyond the Queensland, New South Wales border, so the cold-limited boundary could not be estimated precisely in Australia (Sutherst 1987a, b).

In order to make the model comparison fair and equal, we re-fitted the CLIMEX parameters using only the distribution records of Cumming (1999a, b) (Fig. 1) and the results are shown in Fig. 2. There was minimal difference between these results and those of Sutherst and Maywald (1985) and those differences related to the cold limits only which do not affect the current argument. CLIMEX was unable to include the observed records of occurrence without also including a large additional area beyond the northern limits of the data. The map depicts the suitability of the climate for the tick in the whole of Africa and hence the area predicted to be at risk of invasion in the absence of other constraints. It indicates that the highest risk areas in Africa have not yet been invaded, i.e. in East, Central Africa including most of Angola and West Africa.

Both models identified Venda as being moderately suitable. CLIMEX also identified north-western Tanzania and Ivory Coast in West Africa as being highly favourable for R. B. microplus. In addition, it flagged the high risk to much of the highlands of East and Central Africa, and the humid tropics of West Africa. Further, it revealed a western corridor of suitable habitat connecting southern and north-western Tanzania. The regression model classified northern Tanzania as unsuitable and it could not be applied to West Africa because it was parameterised with climatic data from the southern hemisphere.

Discussion

Comparison of the results from the two models (Figs. 1b, 2) could not provide a more stark contrast in prediction of invasive risk. The regression described the observed distribution records of R. B. microplus in southern Africa accurately but excluded the main range extensions. On the other hand the CLIMEX results included the observed distribution but also included large areas outside the range of the observations, which included the observed range extensions. The reasons for these differences go to the heart of modelling non-equilibrium populations.

Firstly, the regression algorithm and parameter fitting process treat each data point as a presence or absence record. This has the unavoidable effect of categorising those areas that the species has not yet colonized as unsuitable. Such a model is therefore inherently unsuitable for anticipating range extensions of invasive species that have not yet reached equilibrium in their new environment. With CLIMEX, absence data—in areas that are estimated to be suitable from the climatic conditions associated with presence data—prevent the model from restricting its parameter values to simulating only the presence records. Such absence records are attributed ‘unknown’ status in such conditions. They stimulate a search for other explanations.

Secondly, the regression fitting process is limited to using truncated or selective independent variables. In the current application, despite the use of numerous climatic variables, the model is unable to take account of the different seasonal patterns across latitudes and longitudes. While southern Africa has mostly a summer rainfall pattern, further north the rainfall seasonality is quite different. The pattern-matching algorithm categorises different combinations of climatic variables as having low suitability because they do not correspond well with the patterns associated with the observations.

The inability of statistical models to accommodate different patterns of environmental variables has been noted previously (Kriticos and Randall 2001). This failure can be partly overcome by choosing variables that are more independent of the structure of seasonal cycles of temperature and rainfall. Annual average temperatures and rainfall (Rogers and Randolph 2000) or derived variables like annual degree-days or moisture indices based on ratios of rainfall to evaporation (Austin and Meyers 1996; Lindsay et al. 1998) have been used. However they do not take account of the needs of species to have concurrent combinations of suitable temperature and moisture (Sutherst and Maywald 2005). They also only estimate conditions suitable for growth and do not take account of the limiting effects of extreme conditions of different durations. The result is risk assessments with vast scope for bias and error from ignoring both seasonality and interactions between temperature and moisture variables.

In discussing the major differences between the original CLIMEX model predictions of the area at risk in Africa and the historical observed distribution, the authors stated that ‘Clearly areas such as western Kenya have a high risk from R. B. microplus if that species should be introduced there’. They also stated that ‘discrepancies between observed and predicted distributions can be just as useful as agreements in identifying limiting factors’ (Sutherst and Maywald 1985). In the case of R. B. microplus this discrepancy contributed to identifying the hybrid zone phenomenon involving this tick and B. decoloratus in Africa (Sutherst 1987a, b).

In fact, the reported distribution of R. B. microplus in southern Africa includes almost all of the range of temperature and moisture values that define the tick’s climatic domain. The tick has a preference for a warm, humid climate as found in tropical Asia and also in East, Central and West Africa. The unsuitable rating from the regression model was produced even though the most basic consideration of the temperature and moisture requirements of the tick indicates that the climates are highly favourable. Indeed other similar Boophilus species occupy large parts of sub-Saharan Africa (Hoogstraal 1956; Cumming 1999a, b).

The major differences between the results from using regression compared with CLIMEX arise in part from the different objectives of the different methods. Firstly, statistical models often used in conjunction with geographical information systems (GIS) are powerful tools for interpolating between sample data to fill in missing values. They are not appropriate for extrapolating beyond the data sets as is necessary with species invasions or climate change scenarios. They can describe geographical distributions precisely (Rogers and Randolph 1993) but the dangerous assumption is often made that the models therefore enable valid extrapolation to other regions or global change scenarios. The better the fit to the data the more successful the model is considered to be. The inappropriateness of using such models to describe species distributions of tsetse fly (Glossina spp.) (Rogers and Packer 1993; Rogers 1995; Robinson et al. 1997), ticks (Rogers and Randolph 1993) and malaria (Rogers and Randolph 2000) has been alluded to previously (Sutherst 1998, 2004). Many claims of high accuracy of statistical and simulation models in describing species’ potential distributions arise from comparison of highly correlated subsets of data obtained by splitting datasets for training and validation exercises. This inappropriate practice is widespread and may have arisen from a misunderstanding of the recommendation to split data sets in order to obtain unbiased estimates of parameter values after selecting models using the original subset (Miller 2002).

These findings show that using regression, and by implication any descriptive pattern-matching approach, is not appropriate when predicting potential range changes under global change or invasion scenarios. The failure of such models to make provision for non-equilibrium ranges, as shown with this example of R. B. microplus in Africa demonstrates their weaknesses wherever extrapolations are required. This has led to the misguided practice of using ensembles of statistical models (Thuiller 2003) in an attempt to reduce the errors. That does not address the underlying problem of inappropriate model structures and optimisation methods. CLIMEX on the other hand aims to infer the species climatic response relationships from the known geographical distribution and then to project likely responses to climates in different places and climate change scenarios. Rather than trying to achieve a precise description of the distribution, the emphasis is on interrogating the data to shed light on the climatic conditions that support growth or limit the survival of the species. The need to ensure internal consistency in the results is paramount and the aim is to include all known positive locality records. Inconsistencies, like those above, warn that climate alone is not responsible for limiting the geographical distribution, or that the species has not reached its equilibrium distribution, rather than indicating model failure.

Most native species have spread to their maximum potential ranges and so do not provide the opportunity for an a priori assessment of areas suitable for further spread. An exception was the invasion of the highlands of Zimbabwe by two African species of ticks, Amblyomma variegatum and Amblyomma hebraeum (Bruce and Wilson 1998). This occurred after a warning of such a risk was given a decade earlier based on a CLIMEX analysis (Sutherst and Maywald 1985). Such apparent discontinuities or inconsistencies in geographical distributions may also arise from incomplete distribution records and CLIMEX can help to identify such gaps (Hall and Wall 1995; Sutherst 2003; Sutherst and Maywald 2005). R. B. microplus can be expected to continue its spread through the continent and occupy those habitats to which it is better adapted than the resident Boophilus species. The continuing spread will provide further opportunities for model validation.

We repeat the appeal (Sutherst and Maywald 2005) for less concern with precision of model fits to species geographical distributions (Cumming 2000a, b; Anderson and Lew 2003; Elith et al. 2006), which are usually of poor quality and more emphasis on avoiding the systemic errors that arise from faulty model structures. Such errors are not revealed by statistical measures of goodness of fit. We now add the issue of inappropriate selection of predictive environmental variables and weighting given to absence records. Derived measures of climatic suitability may improve the performance of statistical models but will not enable them to match the performance of dynamic simulation models. The mechanistic CLIMEX simulation model performed reliably using such derived variables and provides more insight into the role of specific growth and limiting conditions across all global climates. As such, it is a useful first step in an ecological study of any species (Sutherst et al. 2007). Being mechanistic, each parameterised function constitutes a testable hypothesis on the role that the climatic factor has in supporting population growth or limiting a species range (Sutherst et al. 1995). The relationships can inform policy and guide further process-based studies.

As ecologists we need to go back to the basics of our discipline and consider the needs of species from first principles (‘to look at the world through the eyes of the species we are studying’) instead of applying descriptive models to multiple species using a black-box ‘plug-and-play’ approach as done for many studies such as those cited by (Thomas et al. 2004). Risk assessments for biodiversity under global change will be better served by selecting species with ranges that are representative of their compatriots and understanding them thoroughly as a basis for extrapolation to the other species with similar ranges. Progress in understanding the factors limiting species’ geographical distributions will only come from applying mechanistic, hypothesis-based approaches to the analyses. This, after all, is the fundamental distinguishing characteristic of science and it leaves little room for descriptive methods.