A dynamic population model to investigate effects of climate on geographic range and seasonality of the tick Ixodes scapularis
Introduction
Ixodes scapularis Say (1821) is an important ixodid tick vector of tick-borne zoonoses (Lyme borreliosis, Human Granulocytic Ehrlichiosis and Human Babesiasis: Thompson et al., 2001) in North America. Northwards spread of I. scapularis, into Canadian habitats where it has not previously occurred, may be predicted in parallel with distributions of other terrestrial arthropods in response climate change (Root et al., 2003). There is evidence that climate change, particularly warming, has already occurred over the last decade (Parmesan and Yohe, 2003). During this period, the number of foci in Canada where I. scapularis is known to be resident has risen from one to seven (Barker and Lindsay, 2000; Lindsay, L.R., unpublished results).
The existence of endemic populations of the tick vector, and the establishment of new populations, is constrained by biotic factors (host densities and habitat) and abiotic factors such as climate (Gray, 2002). Each of these factors affect tick survival rates, influencing the densities of endemic tick populations, and the threshold number of immigrating ticks needed to establish a tick population in a new focus. Climate impacts tick survival mostly during non-parasitic periods of the life cycle: outside certain ranges of temperature and rainfall tick populations cannot survive, because these conditions directly kill the ticks (Ogden et al., 2004) or inhibit host-seeking activity (Randolph, 1997). Within these limits, temperature may also determine intersstadial development rates (Peavey and Lane, 1996, Ogden et al., 2004). Assuming that developing and host-seeking ticks suffer mortality at a more or less constant rate in nature (Vail et al., 1994), then the lower the temperature, the longer is the development and the higher is tick mortality. The geographic variability of such effects may be limited, however, by the influence of temperature-independent diapause on development rates (Belozerov and Naumov, 2002, Ogden et al., 2004). Yuval and Spielman (1990) suggested that the most sensitive point of the ticks' life cycle is the production of larvae from engorged adult females: adult females must lay eggs, eggs must hatch into larvae and the larvae must feed all within 2 years because unfed larvae cannot survive over two winters. Climate also affects rates that ticks find hosts because temperature and relative humidity influence tick activity (Vail and Smith, 1998). It has been hypothesised that a northern latitude threshold for I. scapularis persistence may exist, this being the point north of which winter temperatures arrive too soon each year for larval development to occur and eggs exhaust their stored energy resources (Lindsay et al., 1995).
The potential geographic ranges of tick species may be modified on a local scale by the community structure that gives rise to variations in (i) the leaf litter layer and understorey microhabitats and microclimates in which the non-parasitic ticks exist; (ii) the species range and densities of tick hosts. The former influences the survival of ticks during non-parasitic phases of the life cycle (Lindsay et al., 1998), the latter influences tick survival by affecting host-finding success, on-host tick mortality rates and density-dependent regulation of the tick populations (Randolph, 1994, LoGiudice et al., 2003, Shaw et al., 2003). In some cases, statistical models are useful to predict geographic variations in the densities of parasites (including I. scapularis) where (for example) indices of local climate and habitat correlate with variations in parasite survival on and off the host (Guerra et al., 2002). Process-based dynamic models of parasite populations may be more useful, however, for investigating the potential for spread of parasites into geographic regions and/or habitats (such as much of Canada for I. scapularis) where the parasites do not occur at present (Corson et al., 2004), where extensive empirical studies are lacking or impractical (Randolph and Rogers, 1997), and if we wish to investigate scenarios of future climate or habitat change (White et al., 2003). Dynamic population models have the added advantage that they can be used to predict the seasonality of different tick instars, which is crucial to understanding temporal and spatial risk of tick-borne pathogens (Randolph and Rogers, 1997).
Models of specific aspects of I. scapularis population biology have been used to ask specific questions about endemic cycles of Borrelia burgdorferi (Porco, 1999, Schauber and Ostfeld, 2002) and endemic cycles under discrete conditions (Sandberg et al., 1992). To date, the only detailed population model of I. scapularis underpins LYMESIM (Mount et al., 1997), a model of B. burgdorferi s.l. transmission that aims to predict seasonal risk periods for human Lyme borreliosis in different geographic areas of the USA. All of these are matrix models that use weekly time steps to capture the effects of seasonally variable climate on tick development and activity that are important in the dynamics of tick-borne pathogens. As such they cannot be readily used to compare environmental conditions that may result in die out of tick populations by either a deterministic approach to zero, or by stochastic extinction.
We developed a process-based dynamic population model of I. scapularis with three objectives: (i) to review the availability and robustness of the data required for such a model; (ii) to develop a model capable of simulating effects of intra-annual temperature variations on the seasonality of different tick instars; (iii) to investigate whether the model can be used to identify limits for the potential northward spread of I. scapularis, that may be imposed by effects of temperature on tick survival. To achieve this we have created a model that incorporates intra-annual, temperature-dependent variations in the development rates of different tick instars to investigate the effects of temperature data from different geographic locations, on tick mortality.
Section snippets
Model development
The model, created in STELLA 7.0.3 for Windows software (High Performance Systems, Inc., NH) is a discrete, deterministic differential and difference equation model comprised of 12 mutually exclusive states (illustrated as compartments—Fig. 1). Each state represents a specific point in the life of the tick: eggs, questing larvae, nymphs and adults, feeding and engorged larvae, nymphs and adult females, and egg-laying adult females. An additional state (hardening larvae) comprised hatched larvae
Empirical validation
Using the starting values, the model came to a steady, cyclical equilibrium after approximately 10 years. At equilibrium, peak values for the numbers of ticks were the same for each run using the same temperature data. The model closely predicted the seasonal activity pattern observed in Ontario for all three instars in as much as the start and finish of activity periods were almost identical, and in most cases detected peaks of activity were the same too (Fig. 4). The model predicted the
Discussion
In this study, we have created a dynamic population model of I. scapularis, which achieves one of two possible equilibria, die out or a cyclical equilibrium, depending on the entered temperature data. The model is robust to multiple starting conditions. The simulated seasonality of the different instars was similar to that observed in field sites in Ontario (albeit a source of data used in model calibration) and Maryland (albeit using data combined from 2 years) when simulations incorporated
Acknowledgements
This study was funded by the Climate Change Action Fund of Natural Resources Canada.
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