# The Flea Analysis John Donne - Elite Skills

We first investigated whether population level factors, such as host density, influenced infection (*Bartonella*) or infestation (fleas) probabilities. The flea analysis considered data from spring 2002 onwards. We considered a range of covariates reflecting field vole density with different time-lags and at 2 spatial scales. For local quadrat density, we used the cumulative number of field voles caught on a quadrat during a survey and considered both current (Lag-0) density and density 6 months before (Lag-6). We also considered density at the clearcut scale, using Vole Sign Index (VSI) surveys, a calibrated method based on signs of feeding activity by field voles (), and we considered clearcut density estimates with a lag of 0, 6 and 12 months. We also included cumulative quadrat-level densities of bank voles and wood mice (Lag-0 and Lag-6). All density estimates were log transformed. The effect of season and interactions between season and all density estimates were also considered. We followed a step down procedure, because a model selection approach () is precluded by the absence of a selection criterion such as AIC in GLMMs. We eliminated interactions first, and retained only those variables significant at the 5% significance level. To guard against type 1 errors, at the end of the modelling process we confirmed the validity of including effects by comparing their coefficients and *P*-values to equivalent models without random effects.

## The Flea Poem Analysis - TES Resources

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We used Generalised Linear Mixed Models (GLMM) with a logit link, binomial errors and fitted using REML to investigate what factors influence the probability that an individual field vole was infested with fleas (using presence or absence of fleas as a binary response variable). Similar analyses were conducted for each of the *Bartonella* species. The large number of explanatory variables to be considered resulted in many potential models. Moreover, due to the study design, infection prevalences could be spatially correlated. Consequently, we conducted the analyses in several stages (detailed fully below). For the *Bartonella* analyses the investigation of fixed effects comprised 3 stages: the first investigated population level covariates that were shared by all individuals trapped in a clearcut during a single survey, the second investigated individual level covariates, and the third investigated the impact of fleas on infection probabilities. The flea analysis excluded the third stage. After modelling the fixed effects we examined whether the residual extra-binomial variation in the data exhibited spatial structuring. Care was taken to check the robustness of results with and without random effects. Three nested random effects were included in each analysis: survey, forest within a survey (forest*survey) and site within a survey (clearcut*survey). Prior to considering fixed effects, we determined what portion of the total variance each of the random effects explained, and whether each of the variance components was significantly different from zero using z-tests in the SAS GLIMMIX procedure ().

### The flea analysis excluded the third stage

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