Immature (larvae and nymph) tick burden on rodents is an important determinant of adult tick population size and understanding infectious disease dynamics. The objective of this research was to build a descriptive model for immature Dermacentor variabilis burden on Peromyscus leucopus. Mice were live-trapped on two permanent grids in an old field and an early successional forest every other month between April and October, 2006–2009. Negative binomial regression was used to examine the association between immature D. variabilis burden and the host related variables of host habitat, body mass, and/or sex. The model containing all three variables had the lowest Akaike's Information Criterion (AIC), corrected AIC (AICc), and greatest AICc weight. Immature D. variabilis burden was positively associated with mice with higher body mass, male mice, and those captured in the field habitat. These data are consistent with studies from other tick-rodent systems and suggest that single factor models do not describe host burden. Variables other than those that are related to the host may also be important in describing the tick burden on rodents. The next step is to examine variables that affect tick development rate and questing behavior.
Rodents are key hosts to the immature stages of many hard ticks. Immature burden on rodents is an important determinant of adult tick population size (Smart and Caccamise 1988). Therefore, identifying factors that affect individual mouse burden contributes to our understanding of infectious disease systems. Distribution of immature ticks on hosts has been observed to be clustered with a small portion of the host population carrying much of the burden (Kitron et al. 1991, Brunner and Ostfeld 2008, Kiffner et al. 2011). Host burden has been associated with a number of biotic and abiotic factors.
The objective of this study was to a build a model that describes immature (larval and nymphal) Dermacentor variabilis burden on Peromyscus leucopus, the primary host in northeast Missouri. Adult D. variabilis typically parasitize larger mammal hosts (Kollars 1996) and were not observed on P. leucopus in this study. As D. variabilis is heavily dependent on P. leucopus for feeding the early lifestages, the burden on this host will be important for the population dynamics of the tick and potential spread of Rickettsia rickettsii, the causitive agent of Rocky Mountain spotted fever. This study is the first to model burden in the D. variabilis-P. leucopus system. Tick burden has been modeled in six other tick-rodent systems (Brunner and Ostfeld 2008, Kiffner et al. 2011). These models suggest that there may not be a specific set of variables that predict burden in all tick-rodent systems. Our model will be based on the host variables body mass, sex, and habitat as there is a large body of field and experimental data suggesting that these are important determinants of host burden in rodents.
MATERIALS AND METHODS
Small mammal sampling was performed in two habitat types, an early successional forest and an old field dominated by non-native grasses, approximately 300 m apart in Adair County, MO. In each site, a 70 m × 120 m grid with 104 sampling points 10 m apart was established. A Sherman live trap (H. B. Sherman, Tallahassee, FL, U.S.A.) baited with a mixture of peanut butter and rolled oats was set at each sampling point. Trapping was performed concurrently on both grids in three or four night sessions in April, June, August, and October for three years (2006–2009) for a total of 298 P. leucopus captures. Ticks were observed on mice in all months examined in this study. Host body mass, sex, tail, and right hind foot length were recorded for all captures. Animals were marked via toe clipping to identify individuals and assure only first captures were considered in the present study. All animals were handled according to the Animal Care Guidelines of the American Society of Mammalogists (American Society of Mammalogists 1998). Ticks were removed and stored in ethanol for later identification to life stage and species.
The response variable, immature D. variabilis burden, was count data and strongly right-skewed (Figure 1). The current data suggest significant overdispersion (variance is much greater than the mean) based on the likelihood ratio test (F = 1782, p < 0.0001). In addition, the variation inflation factor (ĉ) (Burnham and Anderson 1998) was 10.76 fitting Poisson and 3.46 fitting negative binomial regression. This suggests that negative binomial regression (ĉ= 1 means no overdispersion present) with some degree of overdispersion is an appropriate model without fitting more complicated models (Crofton 1971).
Seven candidate binomial regression models were compared, including all possible combinations of host body mass, sex, and habitat of the host. In P. leucopus, sex and body mass are assumed to be independent variables as sexual size dimorphism is not expressed in the species (Dewsbury et al. 1980). Akaike's information criteria (AIC) (Akaike 1974) and corrected AIC (AICc) (Hurvich and Simonoff 1998) were calculated for each model. However, only corrected AIC values are reported as AIC converges to AICc with larger sample sizes. Smaller AICc values are considered closer to the “true” model. Δ AICc and AICc weights (Stauffer 2007) were also calculated for each candidate model to find the difference between AICc value and minimum AICc value and the probabilistic weight of each model relative to the true model given the model set and available data (Link and Barker 2006, Anderson 2008).
Models were validated with test data gathered in 2010 from the same field site using the same methodology (n = 69). For the seven candidate negative binomial regression models, mean squared error (MSE) values were calculated using
where Yi is an observed and Ŷi is an expected value calculated from each candidate model of the response variable. MSE values were used to access the fit of each candidate model to the test data. The model corresponding to the lowest MSE value for the test data (data not used to build the negative binomial regression models) corresponds to the “best” fit model.
The full parameter model containing host body mass, sex, and habitat has the lowest values of AICc (Table 1) indicating that this is the closest model to the “true” model. Akaike weight, representing the strength of evidence for a particular model, was 0.73 for the full parameter model. The model with host body mass and sex has the second largest AICc weight of 0.261. All other models have AICc weights of less than 0.05. The fitted negative binomial regression model with host body mass (X1), host sex (X2) (1=male; 0=female), and habitat (X3) (1=field; 0=forest) can be written as
Table 1. Negative binomial regression models examining the association between immature D. variabilis burdens and all possible combinations of P. leucopus body mass (Mass), sex (Sex), and habitat (Habitat). Model selection is based on AICc and AICc weights (wi). Δ AICc is the difference between a given model and the model with the lowest AICc value.
Mass Sex Habitat
where is the estimated conditional expectation of the response variable given the independent variables.
The expected log count D. variabilis for a one-unit increase in host body mass increased by 0.067, meaning that an increase of one gram of host body mass would cause the expected immature D. variabilis burden to increase by a factor of e0.067= 1.07 for the same host sex in the same habitat. Likewise, male hosts will have 1.6 more D. variabilis on the average for the same host body mass in the same habitat. Mice in the field habitat will have 1.34 more D. variabilis than forest habitat host on the average for the same host body mass and the same host sex.
MSE values of each candidate model for the test data are given in Table 2. The model containing host body mass, sex, and habitat (given in Equation 1) has the smallest MSE value, implying the lowest degree of error, thus “best” fit model. This heuristic, combined with the smallest AICc values, provide evidence that the model containing host body mass, sex, and habitat is the closest to the “true” model given the model set and available data.
Table 2. Mean Squared Error values for each candidate negative binomial regression model.
P. leucopus is typically found in wooded areas and ecotones between woods and fields (Brown 1964). As the preferred habitat of D. variabilis is old field or wood/field ecotones (Campbell and MacKay 1979), mice crossing the wood/field ecotone with greater frequency are more likely to encounter ticks. Home range size of Peromyscus differs among individuals (Metzgar 1971) is generally larger in males (Sonenshine and Stout 1968) and varies temporally (Stickel 1960). Differences in the portion of the habitat used by individual mice and the size of the home ranges likely impact the likelihood of encounter with ticks. In addition to males having a greater probability of encountering ticks due to home range size differences, laboratory studies (Hughes and Randolph 2001) suggest they are more susceptible to tick infestation.
Although host-related variables are important in describing tick burden, the burden of immature D. variablis on P. leucopus is likely influenced by additional biotic and abiotic variables. Models of other tick-rodent systems (Brunner and Ostfeld 2008, Kiffner et al. 2011) demonstrated that multiple variables predict tick burdens on rodents and suggest that each tick-rodent system may have a different suite of predictive variables. The next step in the D. variablis- P. leucopus system is to develop a model that considers variables that influence development rate and questing behavior of immature ticks, including environmental and seasonal factors. In addition, other statistical models can be considered to improve model fit.
We appreciate the numerous student labtechnicians for their diligent fieldwork along with Mary Peng, Margaret Bassi, Jake Henderson, and Georgia Mueller for help with early drafts of the manuscript. Additional thanks go out to Dr. Boris Krasnov, Derek Zelmer, and several anonymous reviewers for their critiques on this manuscript. Partial funding support was provided through the National Science Foundation under Grant No. 0431664 and No. 0436348 and a Love of Learning grant to Tad Dallas from Phi Kappa Phi.