Statistical analysis
To investigate the number of L3 entering the host and the total number
of nematodes established in the lungs (dependent variables in separate
analyses), we used generalized linear mixed models (GLMM) with a
negative binomial response distribution using the R package lme4 (Bateset al. 2015) to correct for a non-normal distribution of the
count data (O’hara & Kotze 2010). To analyze the proportion of L3
entering the lungs (number of parasites in the lungs in relation to the
number that entered the host, dependent variable), we used a GLMM with a
binomial response distribution using the R package lme4 (Bates et
al. 2015). For all three analyses we initially ran a full model,
including the initial SUL of the toads, toad origin, L3 origin, and
treatment as fixed effects and clutch ID as random intercept (Table 1,
S1). Moreover, we divided the analyses into two data sets, one for
range-core toads and one for invasion-front toads to avoid higher order
interactions (i.e. toad origin x L3 origin x treatment). For these six
analyses (Table S1), we included the initial SUL of the toads, L3
origin, treatment, and the interaction of L3 origin x treatment (to test
if the reduction of skin secretion had different effects on the
infectiveness of L3 from different origin) as fixed effects and clutch
ID as random intercept. Finally, we analyzed the size of the nematodes
that we had obtained from the toad lungs (dependent variable), using a
LMM with a Gaussian link. We included toad SUL, L3 origin, toad origin,
and the interaction of treatment x L3 origin as fixed effects and toad
ID nested within clutch as random intercept (Table 1, S1).
To investigate differences in L3 survival depending on L3 origin, we
used a Kaplan Maier survival analysis in the R package ‘survival’
(Therneau & Lumley 2014). We then analyzed L3 longevity (dependent
variable) using a GLM with a log link, including treatment (separated
between range-core and invasion-front toads), L3 origin and their
interaction (Table 1). To test if L3 use skin secretions to locate their
host, we analyzed the proportion of L3 in the treatment zone (dependent
variable) using a GLM with a binomial distribution and a logit link. We
included the scent type, L3 origin and their interactions as independent
variables (Table 1, S3).
Model selection for all analyses was based on stepwise variable
selection using Akaike’s Information Criterion corrected for small
sample size (AICc), selecting the model with the lowest
AICc (Murtaugh 2009), using the R package ‘MuMIn’(Barton
2016). Parameters that included zero within their 95% CI were
considered uninformative (Arnold 2010). We validated the most
parsimonious models by plotting the model residuals versus the fitted
values (Zuur et al. 2010). All statistical analyses were carried
out in R 4.0.3 (R Core Team 2013).