Statistical approach
The analyses were done using Generalized Linear Mixed Models (with
Poisson distribution). The software used was R 3.2.3 (the R-Project for
Statistical Computing; //http:www.R-project.org) and the specific
packages used were glmmTMB , function glmmTMB (Brook et
al., 2017).
Three models were constructed. The first assessed whether the use of bad
alternative hosts (Little Thornbirds) depended on the availability of
optimal hosts (Great Kiskadees). The second model evaluated if the use
of bad hosts was a function of the availability of good alternatives
(Greater thornbirds). Finally, a third model assessed how availability
of optimal hosts influenced the preference of good alternative hosts.
The study unit was the whole bird community present at the study area at
a given week (Wi ). The response variables were
the mean burdens of first instar larvae on nestlings of bad alternative
hosts at a given week (first and second model), or of good alternatives
(third model). This was estimated for each week by dividing the total
number of L1 on all nestlings of the focal species by the total number
of nestlings of that species present at that moment (i.e.
baL1/ baNWi or
gaL1/ gaNWi ). We used the count of L1 and
not all instars because L1 represent recent infections (complete larval
development takes approximately 4 days), and also because the success of
larval development differs across species (e.g. most L1 fail to progress
to subsequent instars in Little Thornbirds).
The independent variable of interest was the availability of optimal
hots (first and third models) or good alternatives (second model). This
was estimated by counting the number of broods present at the study site
(40-ha forest patch) during a given week
(ohBroodsWi or
gaBroodsWi ). To take into account that the effect
of host availability may depend on the parasite abundance in the area
(host demand), the interaction between
oh/gaBroodsWi and the total count of L1 in the
whole bird community at a given week (tL1Wi ) was
included, where tL1Wi is used as a proxy of
parasite abundance (a large number of tL1 Wimeans that many gravid female flies were seeking hosts recently). This
proxy is more precise and informative than using prevalence of infected
nestlings or broods, taking into account that a gravid female of
’P. torquans c. A.’ may lay from 1 to 8 clutches of eggs,
therefore being able of parasitising a single brood or several ones
(Saravia-Pietropaolo et al. 2018). Additional independent variables were
included to adjust for potential confounding. These were weekly
precipitation (1, 2 or 1+2 weeks previously); minimum, maximum and mean
weekly temperatures (same lags); count of broods of other bird species
(potential hosts or non-hosts that are present simultaneously); and week
of the breeding season (continuous variable, ranging from 1 to 40). All
models included the random intercept ’breeding season ID’, to account
for the lack of independence of observations of the same breeding
season.
Model selection and comparison was carried out in a stepwise manner
using Akaike information criteria (AIC) (Burnham et al. 2011). All
models with AIC values no greater than 5 units compared to the best
model were considered. Using information about the AIC values, the
selected models were weighed, and then the multimodal inference was done
using the weighed mean of the β coefficient and its standard error. The
terms that were considered significant were those with a coefficient’s
95% confidence interval that did not include 0.