Spatial reproductive success
We identified all camera trap images containing white-tailed deer and
created a monthly detection-nondetection dataset with three states:
breeding, non-breeding, or no deer detected. We discretized continuous
camera sampling into monthly survey occasions. If a fawn(s) appeared in
an image within the survey month, we classified that site as ”breeding”
for that survey (Fig. 2). If fawns were not detected, we classified the
site as ”non-breeding” – which includes males and/or females that did
not successfully rear a fawn into spring and summer
Multiple approaches are used for modelling serial occurrence data
generated by camera traps (Rota et
al. 2009; ; Burton et al. 2015).
We therefore analysed camera data using two approaches. First, we sought
to account for false absences which is a potential problem in wildlife
surveys (MacKenzie 2005), including
camera-trap surveys (Burton et al.2015). Just as species may be detected imperfectly, age-sex classes may
also be detected imperfectly, when neither age nor sex is known with
accuracy. In our case, ”breeding” sites could be misclassified as
”non-breeding” if we missed photographing extant fawns at the cameras.
To account for this error, we used occupancy models
(MacKenzie et al. 2002) which
estimate the probability of detecting that species if present (p )
and based on p , the probability of site occupancy (ψ ).
With hierarchical multi-state occupancy models (Nichols et al. 2007;
MacKenzie et al. 2009) we estimated the probability for each site
that deer were either absent, present without breeding, or present with
breeding. We also estimated the probability that deer were detected in
each of the two occupied states. Occupancy models can be considered as
simultaneous generalized linear models (GLMs) applied to the detection
and occupancy submodels, with binomial errors (logistic link).
We separated continuous camera data into month-long (30.4 day)
”secondary” survey periods sensuMacKenzie et al. (2003). Three
such surveys comprised a three-month ”primary” sampling season within
which occupancy states were assumed to be closed. We considered only the
fawning season (spring, April – June), and post-fawning (summer, July
– September). We assumed non-Markovian variation in deer site-use among
months within a 3-month season primary season
(MacKenzie et al. 2006). In an
occupancy framework this variation represents “detection error”,
attributed mainly to movement in and out of the camera detection zone
(Burton et al. 2015). The full
data frame for the study is thus 6 seasons, with 3 repeated monthly
surveys within each season, for a total of 18 surveys at each site with
each survey comprised of deer detection-nondetection within the month.
With this dataset, we ran several competing models, each with different
assumptions about how detectability, breeding occupancy, and
non-breeding occupancy varied through time and in relation to landscape
features. We tested whether the probability of detection was either (1)
constant over time, (2) varied among seasons, or (3) varied among
surveys. We likewise tested whether site occupancy of breeders and
non-breeders was either (1) constant across the study area, or (2)
varied in relation to landscape features. We used hierarchical models in
the program Presence (ver. 6.2) to estimate deer occupancy (ψ),
detectability (p ), and breeding state (R), where:
ψi = probability that site i is occupied,
regardless of reproductive state
Ri = conditional probability that young occurred, given
that site i is occupied
ψi(breeding) = unconditional probability that sitei is occupied with breeding = ψi *Ri
p(1)it = probability that occupancy is detected for sitei , period t , given that true state = 1 (non-breeding),
p(2)it = probability that occupancy is detected for sitei , period t , given that true state = 2 (breeding),
δit = probability that evidence of successful
reproduction is found, given detection of occupancy at site i ,
period t , with successful reproduction (Nichols et al. 2007).
Occupancy models provide a per-survey estimate of p , and from
this we calculated the probability of false absence (PFA) across the
three surveys in each sampling season as
[1-p ]3 (Longet al. 2008).
It has been argued that the variation among secondary surveys (months)
due to deer movement is an important part of the ecological signal, and
not error as assumed in occupancy models
(Neilson et al. 2018;
Stewart et al. 2018;
Broadley et al. 2019). We therefore
also treated zeros as signal, not error, and used an alternative
modelling approach–generalised linear models (GLMs)–to determine
whether fawn occurrence varied with landscape features. In this analysis
each month can be considered an independent Bernoulli trial in which
adult female deer with fawns were detected (1) or not (0). We summed the
number of spring months (April, May, June) with and without fawns across
all three survey years creating a 0-9 response variable (3 spring months
over 3 years). We modelled number of breeding-months as a binomial count
model (GLM; binomial errors, log link) in R ver. 3.1.1
(R Foundation for Statistical Computing
2014) against explanatory variables from three spatial digital resource
inventories (Supplementary Information Table S1).
Alberta Vegetation Inventory (AVI), a digital forest inventory dataset,
provided percent cover of land cover types within a 1-km radius around
each camera site (Fisher, Anholt & Volpe
2011; Fisher et al. 2020).
Alberta Biodiversity Monitoring Institute (ABMI) 2010 Human Footprint
Map Ver 1.1 provided percent of area of polygonal anthropogenic
features. ABMI’s Caribou Monitoring Unit (CMU) provided a GIS layer
derived from 2012 SPOT satellite imagery to calculate area of linear
features (buffered to create polygons from polylines) around each
camera. In all models, we omitted correlated variables (r >
0.7) from multiple-variable models (Zuur,
Ieno & Elphick 2010) to prevent multicollinearity. We combined
variables only sparsely represented in the data (< 1-2% of
area) into a single, combination variable (Table 1), and rescaled each
variable (mean=0, s.d.=1) to compare effect sizes.
In occupancy models, we placed covariates on ψ and R in
hypothesis models or kept them constant in null models (Supplementary
Information Table S2). In GLMs we created multiple a priorimodels, each corresponding to a hypothesis about the landscape features
explaining variation in deer reproduction (Table 1). As a priorimodels may still contain uninformative parameters that should be
discarded (Anderson 2007), we created a
fully reduced model using AIC-based stepwise regression (R;stepAIC package) to determine the most parsimonious model
explaining variation in deer reproduction.
For both the occupancy models and generalized linear models, we weighed
the evidence in support of models corresponding to competing hypotheses
using model selection in an information-theoretic framework
(Burnham & Anderson 2002). Each model
produces an Akaike Information Criterion (AIC) score that balances
deviance explained by the model with model complexity – the number of
parameters; low AIC scores suggest a best-supported model. We normalized
AIC scores into 0-1 AIC weights, analogous to the probability that a
given model is the best supported of the candidate set
(Burnham & Anderson 2002). We further
validated best-supported models using k-fold cross validation in R
package boot , and calculated deviance explained (Zuur et al.
2009).