require(rmarkdown) require(knitr) knitr::opts_chunk$set( collapse = TRUE, comment = "#>" ) rm(list = ls()) library(GenEst) vers <- packageVersion("GenEst") today <- Sys.Date() set.seed(951)
In this vignette we walk through an example illustrating how GenEst command line utilities could be used to estimate mortality for different size birds at a large field of solar photovoltaic collectors. Our objective is to estimate overall mortality, as well as how mortality varies over time, whether it constant throughout the facility, and finally how different size classes of birds are affected.
The general steps in the analysis are:
There are five files in total which make up the example dataset. For convenience, these files can be accessed in R as a list:
library(GenEst) data(solar_PV) names(solar_PV)
Alternatively, the files may be downloaded as .csv files from
https://code.usgs.gov/ecosystems/GenEst/-/releases
in the "For more info"
section.
Searcher efficiency (SE) is modeled as a function of the number of times a
carcass has been missed in previous searches and any number of covariates.
The probability of finding a carcass that is present at the time of search is p
on the first search after carcass arrival and is assumed to decrease by a factor
of k
each time the carcass is missed in searches. (For further background on
field trials, and information about how to format the results for use with
GenEst, see the User Guide, which is available at the code.usgs.gov
page cited
above).
Results of the SE field trials used in this example are stored in the data_SE
data frame:
data_SE <- solar_PV$SE head(data_SE)
GenEst provides tools to construct and compare specific individual models, to
explore which subsets of variables are most useful, and to automatically
construct entire sets of models. To start we will fit a basic model in which
the probability of detecting a carcass, p
, and compounding difficulty to
detect, k
, depend only on their respective intercepts (and not other factors
such as season or size). The function pkm
is used to create a searcher
efficiency model, which is returned as a pkm
object.
SE_model <- pkm(p ~ 1, k ~ 1, data = data_SE) SE_model
To explore whether use of covariate is warranted, pkm
is used with the
allCombos = TRUE
. The specified model will be fit as will models formed
using all combinations of predictors listed for the p
and k
parameters.
orginal model. For example, p ~ Season
can be simplified into p ~ 1
, our
original model in which p
is independent of season.
SE_model_set <- pkm(p~Season, k~1, data = data_SE, allCombos = TRUE) class(SE_model_set) length(SE_model_set) names(SE_model_set) class(SE_model_set[[1]])
The set of models is contained in a pkmSet
object. We could inspect the two
models stored in the pkmSet
individually, or for convenience we can view the
AICc values simultaneously for all models using the \code{aicc} function.
Summary plots can be obtained by plotting any of the individual objects or the
set as well.
aicc(SE_model_set)
Rather than one searcher efficiency model for all birds, it is often preferable
to fit a seperate model for each size class. The sizeCol
argument of the
pkm
function is the name of the column in data_SE
that gives the size class
for each carcass in the SE trials. If a sizeCol
is provided, pkm
returns a
list of separate pk models fit for each size class.
SE_size_model <- pkm(p ~ Season, k ~ 1, sizeCol = "Size", data = data_SE) class(SE_size_model) names(SE_size_model) # A list is created with a model set per size class. class(SE_size_model$small) names(SE_size_model$small) # Each model set contains one model in this case.
To fit all combinations of models for each size class, use pkm
with a sizeCol
parameter and with allCombos = T
.
Once we have decided on which models to use for each size class, we store the corresponding pkm objects in a list for future use. In this case, we will choose the models with the lower AICc.
SE_size_model_set <- pkm(p ~ Season, k ~ 1, sizeCol = "Size", data = data_SE, allCombos = TRUE) aicc(SE_size_model_set) SE_models <- list()
Size small:
SE_models$small <- SE_size_model_set$small[[2]]
Size Medium:
SE_models$med <- SE_size_model_set$med[[2]]
Size Large:
SE_models$lrg <- SE_size_model_set$lrg[[1]]
A carcass persistence model estimates the amount of time a carcass would persist
for, given the conditions under which it arrived. A number of carcasses have
been placed in the field and periodically checked for scavanging. Results of
the CP field trials used in this example are stored in the data_CP
data frame:
data_CP <- solar_PV$CP head(data_CP)
\code{LastPresent} and \code{FirstAbsent} represent the left (start) and right
(end) endpoints of the interval over which a carcass went missing. For further
information about CP trials and how to format results for use with GenEst, see
the User Guide (link found on help menu of the GUI, which can be accessed by
entering runGenEst()
from the R console).
Four classes of parameteric models may be used for carcass persistance:
exponential, Weibull, logistic, and lognormal. As with Searcher Efficiency we
can fit one specific model, test a set of covariates and choose our favorite
single model, or fit seperate models dependent on size class. First we will
fit a single Weibull models for all birds. Weibull distributions have two
parameters, location and scale. We will specify that the location depends on
season by setting l ~ season
, but scale only depends on the intercept using
s ~ 1
.
cpm(l ~ Season, s ~ 1, data = data_CP, left = "LastPresent", right = "FirstAbsent", dist = "weibull")
Next, we try a CP model set considering whether the season
covariate for
location is necessary, by comparing the l ~ season, s ~ 1
to l ~ 1, s ~ 1
.
CP_weibull_set <- cpm(l ~ Season, s ~ 1, data = data_CP, left = "LastPresent", right = "FirstAbsent", dist = "weibull", allCombos = TRUE) class(CP_weibull_set) aicc(CP_weibull_set)
Finally we will construct sets of CP models for each size class, however this
time we will also consider models based on both exponential and weibull
distributions. To compare models for multiple distributions, set dist
to a
vector of the distribution names to be considered. With a sizeCol
provided
and allCombos = TRUE
, cpm
returns a list of cpmSet
objects, one for
each size class.
CP_size_model_set <- cpm(formula_l = l ~ Season, formula_s = s ~ 1, left = "LastPresent", right = "FirstAbsent", dist = c("exponential", "weibull"), sizeCol = "Size", data = data_CP, allCombos = TRUE) class(CP_size_model_set) names(CP_size_model_set) class(CP_size_model_set$small) length(CP_size_model_set$small) names(CP_size_model_set$small)
We now have the flexibility to select models from different families for
different size classes. We will choose to use the models with lower AICc, which
requires storing the corresponding cpm
objects in a list for later use.
aicc(CP_size_model_set) CP_models <- list()
Size small:
CP_models$small <- CP_size_model_set$small[[4]]
Size med:
CP_models$med <- CP_size_model_set$med[[4]]
Size lrg:
CP_models$lrg <- CP_size_model_set$lrg[[2]]
Estimating mortality requires bringing together models, carcass observation data (CO), and information on how the data was gathered. In particular the search schedule (SS) and proportion of carcasses in searchable areas (the density weighted proportion, or DWP), are needed. We will breifly inspect the files. Further information on the formatting of the CO, SS, and DWP files can be found in the User Guide.
Carcass observations:
data_CO <- solar_PV$CO head(data_CO)
Search schedule:
data_SS <- solar_PV$SS data_SS[1:5 , 1:10]
(Note that there are 300 arrays columns altogether: Unit1, ..., Unit300)
Density weighted proportion:
data_DWP <- solar_PV$DWP head(data_DWP)
These elements combine in the function estM
, producing an object containing
simulated arrival, detection, and mortality distributions. We also have the
opportunity to provide the fraction of the facility being surveyed, frac
, if
it happens to be less than 100\%. Increasing the number of simulations, nsim
,
will improve the accuracy of the estimates but comes at a cost of computer
runtime.
When estimating mortality, it is not currently possible to mix CP and SE models which differ in their dependence on size. Either both models depend on size class, or both models must be independent of size class. In this case we will choose here to use size dependence.
Mest <- estM( nsim = 100, frac = 1, data_CO = data_CO, data_SS = data_SS, data_DWP = data_DWP, model_SE = SE_models, model_CP = CP_models, unitCol = "Unit", sizeCol = "Size", COdate = "DateFound", SSdate = "DateSearched" )
We are now able to get a confidence interval for estimated total mortality by taking summary of the estM object. Plotting it shows us us the estimated probability density for number of fatalities.
plot(Mest)
A point estimate for overall sitewide mortality is listed at the top of the
plot, satisfying our first objective. The period of inference only covers the
period over which we have have fatality monitoring data, which in this case is
from r min(data_SS$DateSearched)
to r max(data_SS$DateSearched)
.
Having calculated the estimated arrival densities for each of the carcases, we can now use them to create a variety of summaries. Suppose that we are interested in how mortality changes with respect to three kinds of variables:
To create summaries, we split the data by differnt covariates, using a function
called calcSplits
. This requires the simulated mortality $Mhat
and arrival
times $Aj
stored in the estM
object, plus the search schedule and carcass
observation data.
Splits to the search schedule (splits in time) are specified by assigning a
covariate to split_SS
. These must be variables present in the Search Schedule
file. To investigate differences in mortality between season, we will set
split_SS
to Season
.
unique(data_SS[, "Season"]) M_season <- calcSplits(M = Mest, split_SS = "Season", data_SS = data_SS, split_CO = NULL, data_CO = data_CO )
Splitting the estM creates a splitFull
object, a plot of which shows boxplots
for each season.
plot(M_season)
Taking a summary of the splitFull
object gives us a confidence interval for
each level of the split covariate. The size of the confidence interval can be
specified for both plots or summaries using the CL argument.
summary(M_season, CL = 0.95)
To get a finer summary of mortality, we need to parse the search schedule, using
the function prepSS
. This allows us to specify the exact time intervals over
which we will split, in this case we will create a weekly summary.
SSdat <- prepSS(data_SS) # Creates an object of type prepSS. schedule <- seq(from = 0, to = max(SSdat$days), by = 7) tail(schedule)
When we plot the splitFull object for a split with a custom schedule, we must
specify that the rate is per split catagory by setting rate = T
.
M_week <- calcSplits(M = Mest, split_time = schedule, data_SS = SSdat, data_CO = data_CO ) plot(x = M_week, rate = TRUE)
Next we will look at at splitting by covariates present in the Carcass Observation file. We specify a CO split by assigning split_CO to the name (or names) of the variables we wish to split on. Suppose we would like a summary of estimated mortality by unit.
M_unit <- calcSplits(M = Mest, split_CO = "Unit", data_CO = data_CO, data_SS = data_SS ) plot(M_unit, rate = FALSE)
There are 300 units in this example, each one gets a boxplot when we plot the splitFull. For those arrays which have at least one observation, we can create a summary. In this case we will only create a summary for arrays 8 and 100.
dim(summary(M_unit)) # only 164 arrays had observations. # A list of the arrays without observed carcasses: setdiff(paste0("Unit", 1:300), data_CO$Unit) # Create summaries for arrays Unit12 and Unit100. whichRow <- rownames(summary(M_unit)) %in% c("Unit12", "Unit100") summary(M_unit)[whichRow, ]
It is possible to create summaries that split on both Carcass Observation
variables and Search Schedule variables. To do so, include both a split_SS
and a split_CO
argument.
M_unit_and_species <- calcSplits(M = Mest, split_SS = c("Season"), split_CO = c("Size"), data_CO = data_CO, data_SS = data_SS ) plot(M_unit_and_species, rate = FALSE)
Two CO variables can be compared simultaneously by specifying an ordered pair of
covariates for split_CO
, however currently there are a limited total number
(two) of splits which can be allocated among temporal or carcass covariates.
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