In this study, we developed an algorithm for predicting the occurrence of I. scapularis populations in Canada. The algorithm predicted with reasonable accuracy the occurrence of the small number of I. scapularis populations that were known in Canada prior to this study. A warming climate was considered to cause changes in the speed of bird migration and distances of dispersion of ticks by migrating birds, and changes in the geographic range of territory with a climate warm enough for the ticks to complete their lifecycle and establish populations. With this information, the algorithm was then used as a simple model to predict the progression of I. scapularis as it spreads across Canada as the climate warms, given two scenarios for the current potential occurrence of I. scapularis populations in Canada.
There were of course many assumptions in this process. These include i) the assumptions of the I. scapularis population model , which have more effect on the gradient of the relationship between tick abundance and DD > 0°C than on the intercept with the x-axis ; ii) assumptions of the climate models and the emissions scenario; iii) assumptions that the interpolation of temperature data from meteorological stations and, in particular, output from the climate model, which have a crude 400 km spatial scale, have a negligible effect; iv) assumption that the distribution of I. scapularis-endemic areas in the USA described by Dennis et al.  represents the true distribution, and that the distribution of known I. scapularis populations in Canada represents the true distribution; v) assumption that the speed at which birds migrate is equal across Canada irrespective of water bodies or other hazards for the birds (which is possibly relevant to the Atlantic provinces but unlikely to impact dispersion elsewhere in Canada); and vi) assumption that there are no other determinants of I. scapularis establishment (e.g. host densities) that are more limiting than temperature and rates of dispersion by hosts. The latter is relevant to Prince Edward Island and Newfoundland and Labrador where there are no white-tailed deer, which are thought to be key hosts for adult I. scapularis .
Our validation of the index of nymphal tick immigration suggests that the distribution of I. scapularis-endemic sites in Dennis et al  combined with the estimate of bird dispersion ranges from these and Canadian endemic areas provides a workable model of the spatial dispersion of I. scapularis across Canada. Furthermore, the field study in southern Quebec suggested that the risk algorithm predicts the occurrence of I. scapularis surprisingly well in an area where, prior to our study, reproducing I. scapularis populations were not thought to exist. The selected risk algorithm performed better at predicting the occurrence of potential I. scapularis populations than either of its two component parts individually (model-derived relationships between temperature conditions and tick abundance, and an index for predicted numbers of immigrating ticks), i.e. there appeared to be synergy between these values. This field validation, combined with validation of the index of nymphal tick immigration, gives confidence that the maps may give us insight into the possible range of I. scapularis at present, that temperature is a likely limiting factor on I. scapularis distribution, and that climate change could drive changes to the geographic footprint of this tick and possibly Lyme disease risk in the coming decades. The prevalence of I. scapularis positive sites in both high risk and moderate risk zones were lower than the highest estimates for prevalence of positive CSDs predicted by algorithm cut-off values. This difference could be expected as absence of I. scapularis from one site per CSD does not confirm complete absence of I. scapularis from that CSD, and because at the edge of range expansion it would be expected that not all I. scapularis-suitable niches are filled by I. scapularis populations.
Clearly, the further we project into the future the distributions of I. scapularis populations, the less certain we are of them because of uncertainties in emissions scenarios, climate model outputs and rates of tick dispersion. However the risk maps as presented represent both an architecture and a starting point for decision making on policies on, and targeting of, surveillance activities. Surveillance data should then be used to continue validation of the risk maps and drive refinements due to changes in the algorithm used here, or by addition of additional information as described in the following.
Our field studies suggest that the rate of I. scapularis establishment may be somewhere between the 'fast' and 'slow' scenarios, i.e. it is likely that not all CSDs identified as having 'moderate risk' for I. scapularis populations actually contain them, but some possibly do. The rate at which I. scapularis populations establish in climatically suitable areas, given a particular rate of tick immigration needs further field study to enhance our power to predict tick establishment. Increasing knowledge of the location of I. scapularis populations in Canada will also allow us to refine the relationships between climatic suitability and tick immigration rates by more formal spatial regression analyses. Furthermore, we need to investigate to what extent land mammals such as deer  may become more important than migratory birds in dispersing I. scapularis once the ticks become more widely established in south eastern Canada. Dispersion by land mammals would introduce more biologically explicit spatial autocorrelation amongst location-specific probabilities of I. scapularis population establishment.
Habitat, as described by percentage forest cover of CSDs was not a factor that improved prediction of current I. scapularis populations even though there is a priori evidence that habitat is an important factor for I. scapularis survival, and a determinant of the density of the mammalian and avian hosts of the tick . It is likely that sufficient suitable habitat exists in all CSDs even if the percent coverage is small. Indeed, investigations not described here suggest that percentage forest cover could have a non-linear relationship with tick population occurrence: a high percentage of cover could mean a lot of incoming migratory birds and a lot of habitat suitable for tick survival, but small percentages of forest cover may mean that migratory birds are concentrated into finite areas with correspondingly high densities of bird-borne ticks. However, the estimates of forest cover are crude because a number of averaging steps were used, including averaging of remote-sensed AVHRR data into land cover maps and averaging of land cover maps per CSD. Therefore the forest cover estimates are likely to be crude indices of habitat suitability for I. scapularis, its hosts and the numbers of migratory passerines such habitats may attract.
Further studies are required to expand our current knowledge of the suitability of habitat for I. scapularis in Canada. Habitat may be a more useful predictor of the occurrence of I. scapularis at a finer spatial scale than that used here . Further studies are under way in southern Quebec and elsewhere in Canada to investigate the rates at which the agent of Lyme disease, B. burgdorferi becomes established in newly-established I. scapularis populations, to determine at what rate the risk of a tick bite becomes the risk of an infected tick bite. The rate of B. burgdorferi establishment may depend on factors that are not explicitly considered in our algorithms at present, such as reservoir host densities, although in the initial expansion zone in southeastern Canada, the densities of reservoir hosts and adult tick hosts such as deer are not considered limiting factors .
Habitat may have another effect on predictions. If off-host tick mortality is higher or lower than that set in the I. scapularis population model, then the model can slightly over- or under-estimate (respectively) tick abundance [10, 19]. The model was parameterised in woodland habitats of central/eastern Canada, and greater tick survival in woodland habitats of Manitoba is a possible explanation for the survival of the I. scapularis at the Manitoba site when the model predicted population die-out. In other studies, ROC analysis of the predictions of logistic regression models has been used to identify geographic variation in the predictive power of regression models . Here our method identified possible regional variations in the predictive power of the risk maps, although we cannot, without field studies, rule out the possibility that the microclimate at the Manitoba site is in fact suitable for tick survival as the model predicts.
For simplicity we have only used one emissions scenario and the output from one global climate model in our study. More detailed studies await i) output from the third version of the Canadian Coupled Global Climate Model (CGCM3, which is almost ready for use by the scientific community), ii) new emissions scenarios from the fourth assessment of the Intergovernmental Panel on Climate Change (IPCC), and iii) projected climate at a much finer geographic scale courtesy of regional climate models for North America . If and when I. scapularis becomes established in the more northern regions of risk identified by the risk maps, then a different unit of spatial scale than CSD will be needed as CSDs, which partly reflect population densities, become vary large in northern Canada.