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Quantifying diet

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5.1 Introduction
Dietary studies of raptors and other predators help us to understand
their ecological role (Newton 1979, Marti et al. 2007). Raptors are impor-
tant actors in ecology and evolution, because their predatory habits
facilitate the development of life history traits (Valkonen et al. 2012,
Mcgraw and Berger 2013) that maintain healthy ecosystem function and
promote biodiversity (Sergio et al. 2008). Additionally, the individual and
population health of raptors can indicate the health of their system (Sergio
et al. 2008, Barraquand et al. 2014) where changes to reproductive output
of pairs may signal ecosystem disruption (Steenhof et al. 1997). Thus,
studying raptor diet provides an understanding of ecological relationships,
mechanisms involved in ecosystem functions, a measure of system health,
and critical information for conservation (Newton 1979, Nyström et al.
2006, Sergio et al. 2008, Dawson et al. 2011, Pokrovsky et al. 2014).
Gyrfalcon diet has been studied across its circumpolar range through a
variety of methods including indirect analyses by the collection of pellets
and prey remains, and direct observations at nest sites and frequently used
locations during the nonbreeding season (Bengtson 1971, Muir and Bird
1984, Poole and Boag 1988, Nielsen and Cade 1990, Dekker 2003). Most
recently the direct method of nest observations through photography has
greatly improved our understanding of Gyrfalcon prey use and diet during
the breeding season (Booms and Fuller 2003b, Robinson 2016). This chap-
CHAPTER 5
Quantifying diet
Bryce W. Robinson
Robinson, B. W. 2017. Quantifying diet. Pages 91–112 in D.L. Anderson, C.J.W.
McClure, and A. Franke, editors. Applied raptor ecology: essentials from Gyrfalcon
research. The Peregrine Fund, Boise, Idaho, USA. https://doi.org/10.4080/are.2017/005
ter summarizes techniques to quantify Gyrfalcon diet, and presents guide-
lines to conduct a study and analyze diet data obtained through cameras
deployed at nests.
5.2 Pellet and prey remains
The use of indirect methods such as pellet and prey remains analysis has
provided much insight into Gyrfalcon diet (Cade 1960, Nielsen and Cade
1990). Most descriptions of Gyrfalcon diet are based on some combina-
tion of analysis of pellets and prey remains (Dementiev and
Gortchakovskaya 1945, Hagen 1952, Cade 1960, Bengtson 1971, Rose-
neau 1972, Summers and Green 1974, Langvatn 1977, Kalyakin and
Vinogradov 1981, Poole and Boag 1988, Huhtala et al. 1996, Nielsen 1999,
Booms and Fuller 2003a, Nyström et al. 2005).
Pellets and prey remains can be collected in nests, below nests, and at
accessible perch sites at and around occupied cliffs. The timing that col-
lections are made determines the period of the Gyrfalcon life cycle for
which diet is characterized. Collections made during the egg laying period
pertain to diet during courtship and pre-incubation. To describe diet dur-
ing the brood rearing period, the pre-hatching collection must be kept and
analyzed separately from subsequent collections made during and imme-
diately after brood rearing (Booms and Fuller 2003b, Robinson 2016).
Minimizing collections during the nesting period limits disturbance to
breeding raptors. For instance, appropriate collection intervals when quan-
tifying Gyrfalcon diet during brood rearing are once at nestling age 20–30
days, and once after all nestlings have fledged and deliveries to the nest
site have ceased.
Diet can be quantified from pellets by identifying all items that repre-
sent prey types comprised by a single pellet (Poole and Boag 1988), or by
a percent contribution of prey type for each pellet (Nielsen and Cade
1990). For example, if ptarmigan and ground squirrel are equally repre-
sented in a single pellet, the pellet would receive a score of 0.5 ptarmigan
and 0.5 ground squirrel. The proportional diet composition by prey type
is calculated by dividing the cumulative score of each prey type by the
number of pellets in the analysis (Booms and Fuller 2003b).
The minimum number of individual prey items found in the diet can
be estimated through the identification of prey remains based on the most
commonly found bone, body part, or feathers representing one individual
(e.g., the keel or humerus of ptarmigan). Once items are identified, average
biomass values assigned to the number of prey items for that category pro-
vide percent contribution by prey type to overall biomass in the diet (Cade
1960, Nyström et al. 2005, Pokrovsky et al. 2014, Resano-Mayor et al.
2014). However, for biomass conversion it is important to consider that
some prey types, such as large items, cannot be consumed in one meal and
92 Robinson
their contribution is not truly represented in a single pellet or by remains
(Katzner et al. 2006). Considering this detail in relation to the suite of prey
types catalogued in the diet will ensure that proper biomass conversions
are applied.
Coupled together, pellet and prey remains analysis offers an informative
view and useful quantification of diet for Gyrfalcons. A primary advantage
of pellet and prey remains analysis is that it requires less effort and cost
than other approaches, thus allowing larger sample sizes and greater flex-
ibility to describe diet during periods when prey remains do not
accumulate in nests, such as the courtship period. However, these indirect
methods are biased in ways that limit their ability to fully represent the
true contribution of particular prey types to the diet (Marti et al. 2007,
Robinson 2016). Prey remains may underestimate the contribution of
small prey items to the diet, and overestimate the contribution of large
conspicuous prey types due to detection biases. Pellets may overestimate
the contribution of large prey items because multiple pellets may represent
only one large prey item. This is especially true for species such as Gyrfal-
con that have a tendency to cache prey. Additionally, large prey items may
be fed to multiple nestlings and consumed by the adult as well, causing
one prey item to be represented in many pellets. Pellets may also misrep-
resent the contribution of prey types because some body parts may be
more digestible than others, rendering them difficult or impossible to
detect in pellets. Therefore, pellet and prey remains analysis has been
shown to misrepresent the true contribution of some prey types, for exam-
ple a failure to detect Arctic ground squirrel (Urocitellus parryii) as the most
used prey type in one year of study (Robinson 2016).
5.3 Stable isotopes
Stable isotope analysis (hereafter referred to as SIA) is a useful tool to
investigate general patterns of prey use in raptors (Marti et al. 2007,
Resano-Mayor et al. 2014). Most avian diet studies that have used stable
isotope analysis have focused on ratios of the elements Carbon (13C/12C)
and Nitrogen (15N/14N; Inger and Bearhop 2008). Dietary items differ in
the isotopic ratios of these elements and, once incorporated into the
predator’s tissues, provide a signature that indicates their general dietary
habits (Pearson et al. 2003, Becker et al. 2007, Inger and Bearhop 2008).
In most cases, SIA provides a general view of diet and is most useful when
a diet consists of two isotopically distinct sources (Hobson and Clark
1992a, Hobson 2011). Thus, SIA is limited in its ability to describe prey
use in fine detail, and cannot replace conventional techniques that provide
more detailed information of diet, such as taxonomic distinctions between
food types. In Gyrfalcon diet studies, SIA can be useful to compare general
prey use over a temporal scale and between geographic regions, particu-
Chapter 5 | Quantifying diet 93
larly populations along coastlines that may have differing dietary compo-
sition from populations breeding inland, due to the relative contribution
of prey types such as marine birds vs. terrestrial mammals (Nielsen and
Cade 1990).
Isotopic measures can be obtained from tissue such as feathers, blood,
or talon clippings. Because tissues differ in isotopic turnover rates, it may
be necessary to collect and analyze isotopic content of numerous tissue
types to gain information on both short-term and long-term diet informa-
tion (Tieszen et al. 1983, Pearson et al. 2003). For instance, isotopic
signatures in blood represent diet over short time periods, i.e., days prior
to capture, whereas feathers and talons contain information on dietary
components at the time of tissue synthesis (Pearson et al. 2003). Analysis
of multiple tissues provides a view of broad predatory habits to assess gen-
eral trends in prey use on both a spatial and temporal scale given proper
sampling.
Isotopic mixing models quantify relative contributions of isotopic
sources to the diet (Moreno et al. 2010). Further, techniques such as
Bayesian isotopic mixing models address issues related to variation and
uncertainty in models, thus strengthening the power of inference (Moreno
et al. 2010, Parnell et al. 2010). These techniques require information on
the trophic ecology of the species to form dietary assumptions upon which
the models depend, i.e., they require that a signature represent a known
prey item in Gyrfalcon diet. Isotopic fractionation factors (hereafter
referred to as IFF’s), or the changes in isotopic ratios during assimilation
into animal tissues, differ by species and the tissues used for analysis
(Tieszen et al. 1983, Hobson and Clark 1992b). It is essential to have a
basal understanding of fractionation factors specific to the Gyrfalcon
before using this method for diet estimation. IFF’s have not been investi-
gated for the Gyrfalcon and represent yet another area of needed study for
the species. However, IFF’s have been investigated on the Peregrine Falcon
and may provide a framework for developing studies on fractionation fac-
tors specific to Gyrfalcons (Hobson and Clark 1992b).
To my knowledge, there are at present no published Gyrfalcon diet stud-
ies that have used SIA to assess dietary habits. Future diet studies should
consider this method to assess temporal or spatial patterns in prey use, and
further our understanding of the Gyrfalcon as a predator in tundra ecology.
5.4 Nest cameras
Until recently, logistical challenges have limited the application of cam-
eras as a method to study diet at raptor nests. Due to the challenges
associated with the remote breeding locations of Gyrfalcons, only two
studies have used cameras to quantify diet during nesting (Booms and
94 Robinson
Fuller 2003b, Robinson 2016), although others have used this method to
gather different information pertaining to Gyrfalcon diet and behavior
(Jenkins 1978, Poole 1988, Poole and Bromley 1988, Tømmeraas 1989).
Use of nest cameras has been limited because of high cost per unit,
increased human disturbance caused by time and effort required for cam-
era maintenance, battery maintenance, and installation procedures that
have involved long periods at nest sites (Booms and Fuller 2003c, Rogers
et al. 2005, Smithers et al. 2005). New technology (e.g., greater memory
capacity, improved battery life) reduces camera installation times and the
number of visits post installation thus reducing effort while limiting dis-
turbance (B. W. Robinson, unpubl. data).
Video systems require increased maintenance and a great deal of battery
power, which limits sample size and increases disturbance (Lewis et al.
2004). These issues limit the use of video systems for study species such
as the Gyrfalcon, which nest on widely dispersed cliffs in remote locations.
For example, studies that employed video systems in Gyrfalcon nests gath-
ered diet information from few nests in a single season (Poole 1988, Poole
and Boag 1988, Poole and Bromley 1988, Tømmeraas 1989, Booms and
Fuller 2003a).
Motion-activated cameras that capture still images have been used for
many years to monitor wildlife, however their utility for monitoring diet
in raptor nests has been limited due to cost per unit, image quality, instal-
lation schemes, programming schemes, memory/battery life, technical
failures, and altered subject behavior (Tornberg and Reif 2007, García-Sal-
gado et al. 2015, Cutler and Swann 2016). Here I describe the advantages
and uses of modern camera technology to describe Gyrfalcon diet during
the brood rearing period (Robinson 2016).
With proper camera units, motion-activated photography can now pro-
vide fine scale views of prey use over long periods of time because of low
data storage requirements, low power (battery) requirement, and menu
driven programming that is adaptable to various project needs (Robinson
2016). If programmed and installed correctly, motion-activated cameras
provide the most accurate measure of Gyrfalcon diet at nests. The use of
cameras for quantifying diet at nests provides information regarding prey
use at a scale that has not been achieved previously for Gyrfalcons, thus
overcoming the past financial and logistical constraints of this technology.
The success of camera studies to quantify Gyrfalcon diet depends on
multiple factors including camera selection, timing of camera installation,
and decisions on installation and programming. Here I present consider-
ations for conducting a camera study. A detailed description of guidelines
and appropriate considerations for conducting a camera study are given
in Appendix 2.
Chapter 5 | Quantifying diet 95
5.4.1 Formatting data from camera images
Here, I describe the process of quantifying data from camera images,
and provide sample data to conduct analyses of Gyrfalcon prey use as
obtained by cameras installed at nest sites. From this quantification comes
the ability to empirically assess dietary trends, dietary habits, and to con-
nect prey use to the broader ecosystem.
Many types of data can be recorded from nest camera photos. The fol-
lowing are suggested data categories: nest ID, date, nestling age, prey
identification (species, age), time of day, treatment of item (fully con-
sumed or not), comments, and photo organization information (e.g.,
camera period, photo group, photo number). Table 5.1 provides data
organization as adapted from Robinson (2016) for quantifying diet during
the brood rearing period. Each row represents a single prey item delivered
to the nest. Nest (column 1) is defined as the unique nest label assigned
by the researcher. For date (column 2) I recommend recording the calen-
dar date in one column, and calculating Julian date in a separate column
(column 3). Nestling age (column 4) is the age of the oldest nestling, cal-
culated by either the hatch date of the first egg as captured by the nest
camera, or backdated from data obtained from nestlings midway through
the brood rearing period (see Appendix 1 for methods on aging Gyrfalcon
nestlings). Camera period, photo group, and photo number (column 5)
all refer to the file organization path to help find the exact photo from
which the data in the spreadsheet were derived. This information differs
among camera models and is needed to find a specific image that contains
information regarding the prey item. Prey ID (column 6) is the lowest tax-
onomic level assigned to a prey item (Booms and Fuller 2003b, Robinson
et al. 2015, Robinson 2016), and varies with the observer’s confidence in
identifying items (e.g., some items are identifiable to species, sex, age, and
others only to “bird”).
Assigning items to broad taxonomic distinction such as family or order
remain helpful for biomass assignments and for understanding prey selec-
tion over time. For the sake of simplicity, all items in Table 5.1 are
identified as PTAR (a 4-letter code for ptarmigan species). Prey age (col-
umn 7) refers to the relative age of the prey item (e.g., young or adult),
which allows us to assign a more accurate biomass to individual prey items.
In the case of a partially grown item, a percentage of adult size can be
assigned by visually estimating its size as a percentage of adult size. Once
items are identified, assign average mass values for the corresponding
species or prey type to identified items for biomass calculations (column
8). In the case of a partially consumed item, an estimated percentage of
the whole prey type can be determined visually and applied the average
biomass value of the species (e.g., 70% applied to a 485 g PTAR equates
to 339.5 g).
96 Robinson
Table 5.1. Example data for quantifying Gyrfalcon prey deliveries. Each row represents one prey delivery.
101 24-May 14144 5 1,100,26 PTAR Adult 485 1601 7 N Male brought item to nest. Female fed
nestlings.
101 24-May 14144 5 1,100,62 PTAR Adult 485 1745 9 N Male brought item to nest. Female fed
nestlings.
101 24-May 14144 5 1,100,126 PTAR Adult 485 2145 10 N Item appeared in nest with female feeding
nestlings.
101 24-May 14144 5 1,100,148 PTAR Adult 485 2325 1 N Female left briefly and returned with item, then
fed nestlings.
101 25-May 14145 6 1,100,325 PTAR Adult 485 634 19 Y Male brought item to nest. Female fed
nestlings.
Nest
Date
Date
Nestling Age
Photo Info. (Period, Group, #)
Prey Id
Prey Age
Mass
Time
Duration
Item Fully Consumed?
Comments
Chapter 5 | Quantifying diet 97
Additionally, a familiarity with the literature may also help place proper
biomass assignments to prey types. For instance, due to the regional vari-
ation in Arctic ground squirrel mass in western Alaska, Robinson (2016)
assigned an average mass from literature detailing squirrel biomass for
Alaska (Sheriff et al. 2013). Biomass values for unknown items may be
visually estimated by comparing them to a known item’s size (e.g., an item
approximately the size of a Lapland Longspur [Calcarius lapponicus] should
receive a mass assignment of 27 g; [Booms and Fuller 2003a]), or statistical
techniques may be applied to assign all unknown items to categories based
on the probability an unknown item is a given prey type (Robinson et al.
2015). Time (column 9) corresponds to the time the item was delivered.
Duration (column 10) tells us the length of the feeding bout, which can
indicate if a prey item was fully consumed or likely to reappear in a sub-
sequent prey delivery. Item fully consumed (column 11) refers to the
condition of prey removed by adults following feeding, which is useful to
note because it minimizes double counting of prey that are cached and
delivered to the nest more than once (Booms and Fuller 2003a). Addition-
ally, noting whole or headless prey as one item and noting individual parts
delivered during a 24-hour period helps avoid double counting, because
an individual prey item may comprise multiple parts brought to the nest
over time (Booms and Fuller 2003a, Robinson 2016). Comments (column
12) are useful because some notes regarding a prey item or adult behaviors
can be useful later in error checking the data.
5.5 Analysis of diet
5.5.1 Introduction to diet analysis
After diet has been quantified, there are a number of ways to process the
data to investigate aspects of prey use. Simple descriptive measures include
richness (the number of species comprised by the diet), evenness (repre-
sentation by number of a given prey type relative to others), or the
combination of the two, which is termed diversity (Pielou 1966). Diversity
measures used in raptor diet studies illustrate the structure of prey use by
characterizing the number of different prey groups relative to the number
of prey items in each group (Magurran 2004). Assessing diet diversity is
often of interest to illustrate where a predator, such as the Gyrfalcon, lies
on the spectrum from generalist to specialist to better illustrate its role in
its ecosystem (Glasser 1982, Malo et al. 2004). The potential broader util-
ity of diversity measures in raptor studies are, for instance, to provide a
method for diet comparison among populations or species (Steenhof and
Kochert 1985, Bellocq 2000, Miller et al. 2014), or to relate dietary trends
to other aspects of raptor life history (Korpimäki 1987).
98 Robinson
The following section provides an overview of typical measures of
dietary diversity used in raptor studies. In addition, this section provides
a stepwise explanation for processing dietary data in preparation for analy-
sis, and an example with generalized linear mixed models to investigate
trends in prey use over time.
5.5.2 Assessing the completeness of a dataset
Rarefaction curves provide a method to quantify the completeness of a
sampling effort (Gotelli and Colwell 2001) and lend greater confidence to
the inferences drawn from analyses. Rarefaction curves represent the cumu-
lative means of re-sampling the pooled individuals to produce the
statistical expectation of adding additional categories to a dataset (Gotelli
and Colwell 2001), such as prey categories in diet studies. Thus, its utility
in Gyrfalcon diet studies is illustrated by the point at which the curve
approaches an asymptote, which represents the number of samples (indi-
vidual prey items) required to capture all species constituting the diet in a
study area. Rarefaction curves are easily produced in statistical programs
or environments such as EstimateS (Colwell 2013) and R (R Core Team
2016). In our case we provide an example of how to format data for input
into R.
Here, we use a simulated dataset representing hypothetical sites in
Alaska, Iceland, and Greenland. The first row in the data table names the
sites, represented by columns one, two, and three (Table 5.2) and subse-
quent rows represent individual prey categories. Each cell therefore
contains the number of a given prey category recorded at a given site. Once
the data are loaded into R, we will use the rarecurve() function in the
package vegan (Oksanen et al. 2017) to plot the rarefaction curves for each
site. Note that we add the t() function within the code for rarecurve to
transpose the dataframe.
# plot rarefaction curve by site
rarecurve(t(prey))
Note that the rarefaction curves for Greenland and Iceland approach the
asymptote whereas the curve for Alaska does not (Fig. 5.1). Examination
of the curves therefore suggests that sampling is complete for Greenland
and Iceland, but not for Alaska.
Chapter 5 | Quantifying diet 99
100 Robinson
Table 5.2. Hypothetical data for use in constructing rarefaction curves for
Gyrfalcon diet in three study areas. Rows correspond to prey species, and
numbers are counts of prey items from each study area.
Iceland Greenland Alaska
202 300 38
103 25 0
68 39 5
61 0 3
28 3 2
32 0 11
35 19 10
18 12 6
39 0 7
0 7 1
0100200300400500600700
0 5 10 15 20 25
Sample Size
Species
Iceland
Greenland
Alaska
Figure 5.1. Rarefaction
curves generated from
data in Table 5.2. Where
curves approach the
asymptote (e.g.,
Greenland, Iceland),
sampling is considered
adequate for further
statistical inference.
5.5.3 Characterizing diversity of diet
Diversity measures such as Simpson’s index and Shannon index, or
niche diversity measures such as Levin’s index of diet breadth (Shannon
and Weaver 1949, Simpson 1949, Hurlbert 1978, Krebs 1999) are fre-
quently used to characterize raptor diet. Diversity measures represent the
relative structure of groups in a sample set, such as prey in the diet of Gyr-
falcons. Diversity generally incorporates two components: richness (the
number of different categories), and evenness (the uniformity of individ-
uals represented in each category; Pielou 1966). Below are diversity
measures most commonly used in raptor studies:
Simpson’s index:
where piis the relative proportion of each category iin the diet. As D
increases, diversity increases. For this reason Simpson’s index is usually
expressed as 1 – D or 1/D
Shannon index:
where piis the relative proportion of category iin the diet. Larger values
resulting from this equation indicate a greater diversity in the diet.
Levins’ index:
where piis the relative proportion of category iin the diet. Larger values
resulting from this equation indicate a greater diversity in the diet.
Standardized version of Levins’ index:
where nis the number of categories in the sample, and piis the relative
proportion of category i. The standardized version of Levins’ index pro-
vides values that range from 0 to 1, where values closer to 0 indicate
dominance of one prey type over others and values closer to 1 indicate a
more even representation of categories included in the calculation.
Chapter 5 | Quantifying diet 101
Bi= 1
Spi
2
Bi= 1
n–1
1
Spi
2
—1
[ ]
D = Spi2
H' = Spilog pi
Traditional diversity measures have been criticized because they fail to
account for the availability of prey species, i.e., rare and abundant prey
species are weighted equally (Smith 1982). Newer diversity measures (Saikia
2012) incorporate prey use and availability, thus providing a measure for
prey preference in raptors. Comparisons of prey use and availability eluci-
date the relative importance of prey types to reproduction, and can detect
shifts in the use of particular prey species in raptor diet (Robinson 2016).
5.5.4 Assessing dietary trends with generalized linear mixed
models in R
Modeling can be used to assess trends in Gyrfalcon prey use over time.
Here we describe an example from Robinson (2016) in which we test the
hypothesis that temporal factors of year and nestling age influence the
importance of ptarmigan during the brood rearing period. We use two
steps in this analysis. First, we construct generalized linear mixed models
(GLMMs; binomial response variable) that represent our competing
hypotheses of date and nestling age. We then use an information theoretic
approach, e.g., Akaike’s Information Criterion (Akaike 1974, Burnham et
al. 2011) to test the support of multiple parameters against the intercept-
only model.
The data we use were simulated to resemble a typical dataset that would
be extracted from nest cameras. In the example data set the variable nest
identifies a nest site; year is the year of study; week expresses the age of the
nestling period for the entire study population, i.e., week 1 is the first week
that Gyrfalcon nestlings were observed; age is the age in weeks of the
brood in question; and ptar is a binomial variable indicating whether a
prey item is a ptarmigan (1) or not (0). In the data set (Table 5.3), the first
row of data represents nest site 108 in year 2014, week 9 of the nestling
period for the population, age of 8 weeks for nest 108, and 0 ptarmigan
delivered during that time period.
For this analysis we are using the function glmer() to run a generalized
linear mixed model (GLMM), which is included in the lme4 package
(Bates et al. 2015). See Chapter 7 for a thorough description of GLMMs.
We use a GLMM because our data represent whether a prey item is a
ptarmigan as a function of time in weeks. The response variable is bino-
mial (0 or 1), where prey items have been coded as a ptarmigan (1) or not
ptarmigan (0). For mixed effects models where we expect certain variables
to have an influence, we can include random intercepts such as the vari-
able nest in the format (1|nest), and include year as a fixed effect. Here, we
give the model the name model1, glmer is the function, ptar is the
response variable predicted by week, year, and the random intercept
(1|nest). We set family to binomial as indicated by the binomial response
variable (ptarmigan = 1, no ptarmigan = 0). We also set data to ptarmigan,
the name of our dataset. Note that I rounded some of the output for sim-
plicity.
102 Robinson
# build GLMM
model1=glmer(ptar ~ week + year + (1|nest),
family = binomial, data = ptarmigan)
# examine output
summary(model1)
# output
Generalized linear mixed model fit by maximum likelihood
(Laplace
Approximation) [glmerMod]
Family: binomial ( logit )
Formula: ptar ~ week + year + (1 | nest)
Data: dataname
AIC BIC logLik deviance df.resid
76.6 85.5 -34.3 68.6 65
Scaled residuals:
Min 1Q Median 3Q Max
-3.1777 -0.50 -0.0980 0.5478 1.6603
Random effects:
Groups Name Variance Std.Dev.
nest (Intercept) 2.469 1.571
Number of obs: 69, groups: nest, 8
Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 4.22 1.50 2.82 0.01 **
week -1.12 0.34 -3.31 0.00 ***
year2015 -2.26 1.49 -1.52 0.13
—-
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Correlation of Fixed Effects:
(Intr) week
week -0.78
year2015 -0.58 0.20
Chapter 5 | Quantifying diet 103
Note the effect of week, indicated as significant by P-value and asterisks.
We next code other possible combinations and run GLMMs to create all
models with variables included that might influence whether an item is a
ptarmigan.
model2<-glmer(ptar ~ year + (1|nest), family = binomial,
data = ptarmigan)
model3<-glmer(ptar ~ (1|nest), family = binomial,
data = ptarmigan)
Once all models investigating the predictors of an output variable are
coded and entered into R, we create the AIC table using the function
aictab where cand.set refers to the candidate set of the models, listed
as model1, model2, model3. The modnames statement codes models to
names that will appear in the AIC table. Note that we are here using AICc
which is corrected for sample size, and we round some of the output for
simplicity.
# create AIC table
aictab(cand.set= list(model1, model2, model3),
modnames = c(‘model1’,’model2’,’model3’))
# output
Model selection based on AICc:
K AICc Delta_AICc AICcWt Cum.Wt LL
model1 4 77.18 0.00 1 1 -34.28
model3 2 88.97 11.79 0 1 -42.40
model2 3 89.63 12.45 0 1 -41.63
104 Robinson
Table 5.3. Example of coding a data set for assessing dietary trends in
Gyrfalcons with linear models. Data coding is described in the text.
nest year week age ptar
108 2014 9 8 0
104 2014 6 4 0
101 2015 1 1 0
101 2015 2 2 1
Chapter 5 | Quantifying diet 105
654321
1.00.80.60.40.20.0
migan probabilityrPta
eekW
Figure 5.2. Probability that
a prey delivery to
Gyrfalcon nestlings is
ptarmigan as a function of
“week.” Gray shading
indicates the 95%
confidence interval. As
“week” increases, the
probability of ptarmigan as
a prey item decreases.
Looking at the output, column 1 comprises the list of the candidate
models. K is the number of parameters included in each model. AICc is a
number provided by the information theory approach for a given model
to then be compared to the AICc value of competing models. Delta_AICc
is the difference between the AICc of the model and AICc of the lowest
model in the candidate set (AICi– AICmin). AICcWt is the probability that
the respective candidate model is the best among the set of the models.
Cum.Wt indicates the cumulative weight of the addition of each model to
the candidate set. In the example, Model1 is by far the most parsimonious
model and thus we can base our inference on this single model. We con-
clude that time in weeks best explains changes in Gyrfalcon prey use. Next,
we build a figure (Fig. 5.2) to visualize the change in Gyrfalcon diet over
the study period.
# make figure
# build dataframe to use in prediction
p=data.frame(week=unique(ptarmigan$week),year=’2014’)
# use model to predict probability during each week
pred=data.frame(predictSE(model1,p),week=p$week)
# plot predictions and 95% confidence interval
plot(p$week,pred$fit,type=”n”,xlab=’Week’,
ylab=’Ptarmigan Probability’, ylim=c(0,1))
lines(p$week,pred$fit)
polygon(c(p$week,rev(p$week)),c(pred$fit - 1.96 *
pred$se.fit,rev(pred$fit + 1.96 *
pred$se.fit)),col=rgb(0, 0, 0,0.5),border=NA)
5.6 Conclusion
Although many previous studies have provided a solid characterization
of Gyrfalcon diet, quantitative analysis and hypothesis testing remain a
frontier for research, and much remains to be learned about the role of the
Gyrfalcon as an apex predator in the tundra ecosystem. Advances in cam-
era technology provide tools for in-depth diet quantification across the
breeding season. Robinson (2016) reported dietary shifts by Gyrfalcons
breeding in Alaska from ptarmigan to ground squirrel between and within
years that were missed by the indirect method of prey remains analysis.
This finding highlights the benefits of improved camera technology for
dietary studies in raptors.
The differences in dietary description provided by camera analysis
(Robinson 2016) represent the need for continued implementation of
these techniques for quantifying diet and assessing trends in prey use. With
the proper considerations of camera placement and programming,
researchers can quantify diet at a scale not seen in previous Gyrfalcon stud-
ies. These fine scale data across time provide the ability to empirically
analyze data to assess dietary trends and connect Gyrfalcon prey use to
ecological trends such as those precipitated by global climate change.
Stable isotope analysis represents an untouched area of study for under-
standing patterns in Gyrfalcon prey use. Its utility could provide further
insight into Gyrfalcon dietary habits across both spatial and temporal
scales. Additionally, in light of the potential impacts of climate change on
tundra ecology it is increasingly important to monitor prey use on a con-
stant basis. Trends in prey use may serve to track and assess changes in
interactions among community members and underscore the impacts of
climate change to Gyrfalcon life history, an understanding of which will
be the foundation for the formation and implementation of conservation
protocols when necessary.
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Chapter 5 | Quantifying diet 111
112 Robinson
... The analysis of birds' pellets may overestimate larger and conspicuous prey and underestimates small (Robinson 2017) and soft-bodied prey (Barrett et al. 2007). However, this method has been extensively used in studies of raptors diet as a good proxy of prey abundance (Heisler et al. 2016;Formoso et al. 2016;Cheli et al. 2019) if provided large sample sizes with a minimum disturbance, and it has proven to be very useful for diet comparison between species (Robinson 2017). ...
... The analysis of birds' pellets may overestimate larger and conspicuous prey and underestimates small (Robinson 2017) and soft-bodied prey (Barrett et al. 2007). However, this method has been extensively used in studies of raptors diet as a good proxy of prey abundance (Heisler et al. 2016;Formoso et al. 2016;Cheli et al. 2019) if provided large sample sizes with a minimum disturbance, and it has proven to be very useful for diet comparison between species (Robinson 2017). Additionally, it has previously been used to determine the diet of both the Burrowing Owl and American Kestrel (Rodríguez-Estrella 1997; Sarasola et al. 2003;Nabte et al. 2008;Carevic et al. 2013). ...
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