```

This tutorial provides an introduction to the array of command line tools **GenEst** provides for estimating carcass arrivals and detection probabilities. The approach is to walk through analyses of realistic but fictitious data sets representing studies of bird and bat mortality at a wind power facility.

The general steps in the analysis are:

- Construct a model for Searcher Efficiency
- Construct a model for Carcass Persistance
- Estimate mortality
- Specify the type of summary desired (e.g., mortality by species and season)

Data required for a full analysis include results of searcher efficiency trials, results of carcass persistence trials, search schedules for all units searched, the search coverage within each unit, and results of periodic carcass surveys. More information about the kinds of data required can be found in the User Guide. For convenience, data required in this tutorial are available in R as packaged lists, which can readily be loaded as described below. Alternatively, the data may be downloaded into zipped .csv files from the GUI.

To perform the analyses illustrated in the tutorial, begin by starting R and loading GenEst from the command line: `library(GenEst)`

Searcher efficiency and carcass persistence would be expected to vary with carcass size (sparrow, eagle, bat), ground characteristics (road & pad, cleared field, vegetation type), season, etc. In this first example, we limit the analysis to one carcass size (`bat`

) and one ground visibility class (`RP`

= road and pad). A more complicated scenario is analyzed in example 2.

The required data is stored in `wind_RPbat`

, a list of data frames with results for searcher efficiency (`SE`

) and carcass persistence trials (`CP`

), search schedules for all turbines (`SS`

), the search coverage or density weighted proportion (`DWP`

) of area searched at each turbine (i.e., the fraction of carcasses expected to fall in the search plots), and carcass observation (`CO`

) data.

Load the full data set into R:

To streamline the notation, extract the data from the `wind_RPbat`

list into its components:

```
data_SE <- wind_RPbat$SE
data_CP <- wind_RPbat$CP
data_SS <- wind_RPbat$SS
data_DWP <- wind_RPbat$DWP
data_CO <- wind_RPbat$CO
```

`SE`

)Searcher efficiency trials were conducted on roads and pads, with a total of 60 fresh carcasses placed in the field over the course of the entire monitoring period, evenly divided among seasons (spring, summer, fall). Carcasses that were later discovered by search teams during the course of normal carcass surveys were removed from the field. Carcasses were left in the field for up to 5 searches after carcass placement.

Results of the SE field trials are stored in the `data_SE`

data frame:

```
head(data_SE)
#> pkID Season s1 s2 s3 s4 s5
#> 1 pk1 spring 0 NA NA NA NA
#> 2 pk2 spring 0 0 NA NA NA
#> 3 pk3 spring 1 NA NA NA NA
#> 4 pk4 spring 1 NA NA NA NA
#> 5 pk5 spring 0 NA NA NA NA
#> 6 pk6 spring 1 NA NA NA NA
```

Columns `s1, s2, ..., s5`

show the fate of carcass `pkID`

on the 1st, 2nd, … 5th searches after the carcass was placed. A 1 indicates that the carcass was discovered, a 0 indicates that the carcass was present but not discovered, and NA indicates that the carcass was no longer present for discovery or no search was conducted.

`CP`

)Carcass persistence trials were conducted on roads and pads, with a total of 60 fresh carcasses placed in the field over the course of the entire monitoring period, evenly divided among seasons (spring, summer, fall). Carcasses were checked approximately 1, 2, 3, 4, 7, 10, 14, 21, and 28 days after placement in the field. Exact times were entered as decimal fractions of days after placement.

Results of the SE field trials are stored in the `data_CP`

data frame:

```
head(data_CP)
#> cpID Season LastPresent FirstAbsent
#> 1 cp1 spring 0.00 0.93
#> 2 cp2 spring 0.98 1.97
#> 3 cp3 spring 0.00 1.01
#> 4 cp4 spring 13.99 21.13
#> 5 cp5 spring 0.00 1.17
#> 6 cp6 spring 20.95 27.97
```

Exact persistence times are not known, but a carcass that was present at one check and absent at the next check is assumed to have been removed at some point in the interval. The left endpoint of the interval was entered as `LastPresent`

and the right endpoint as `FirstAbsent`

. For carcasses that had not been scavenged by the end of the study, `LastPresent`

is the time of the last check and `FirstAbsent`

is `Inf`

. For carcasses whose removal time is known exactly (e.g., scavenging was recorded by camera), `LastPresent = FirstAbsent`

. The `Season`

column gives the season at the time the carcass was placed in the field.

`SS`

)Carcass searches were conducted on roads and pads within a 120 m radius from all 100 turbines at a fictitious wind power facility. Monitoring began on 1955-04-15 and continued through 1955-11-01. Searches spanned 3 seasons: spring, summer, fall. Search intervals varied by turbine and by time of year, ranging from daily searches at some turbines in the fall and searches once every 12 days in the spring at some other turbines. Search schedules for all turbines are stored in `data_SS`

, which is a data frame with a column for search dates (including all dates that any turbine was searched); a column of 0s and 1s for each turbine, indication whether it was searched on the given date; and zero or more optional columns giving additional information about the date (e.g., season).

```
head(data_SS[, 1:10])
#> SearchDate Season t1 t2 t3 t4 t5 t6 t7 t8
#> 1 1955-04-15 spring 0 0 0 1 0 0 0 1
#> 2 1955-04-18 spring 1 0 0 0 1 0 0 0
#> 3 1955-04-21 spring 0 1 0 0 0 1 0 0
#> 4 1955-04-24 spring 0 0 1 0 0 0 1 0
#> 5 1955-04-27 spring 0 0 0 1 0 0 0 1
#> 6 1955-04-30 spring 1 0 0 0 1 0 0 0
```

Note that we have only displayed a few of the turbine columns - there are 100 turbine columns altogether (t1, …, t100).

`DWP`

)The density-weighted proportion (`DWP`

) is the expected fraction of carcasses that fell in the searched area. Carcass density is not the same at all distances from a turbine, but typically rises over a short distance then decreases eventually to 0. Searches were conducted on roads and pads within a 120 m radius from all 100 turbines to provide sufficient data with which to model the change in density with distance and from this, accurately calculate the fraction of all carcasses that are expected to land on road and pad surrounding each turbine (density-weighted proportion or DWP). The configuration of the roads and pads differs among turbines, hence the DWP must be calculated for each turbine. DWPs for bats at each turbine are stored in `data_DWP`

, which is a data frame with a column for turbine name (note that turbine names also must be included among column names in `data_SS`

, which gives the search schedule at each turbine) and a column of DWP labeled `bat`

. In other studies where, for example, mortality of birds might be of interest, `DWP`

would be expected vary with carcass size or species (e.g., the spatial distributions of bats and large birds around a turbine would likely differ from one another). In that case, each carcass size class (`large`

, `medium`

, `small`

, `bat`

) would have its own column.

`CO`

)Information about each (non-trial) carcass observed during searches is stored in `CO_data`

which is a data frame with at least 4 columns: carcass ID, the turbine (or unit) at which it was found, the date it was found and its distance from the turbine center. In `data_CO`

we also have turbine type, species, and species group variables by which we will later summarize mortality estimates.

```
head(data_CO)
#> carcID Turbine TurbineType DateFound Species SpeciesGroup Distance
#> 1 x79 t86 Z 1955-05-03 BA bat1 7.1
#> 2 x37 t19 X 1955-05-06 BB bat1 5.3
#> 3 x175 t37 Y 1955-05-12 BB bat1 9.8
#> 4 x181 t91 Z 1955-05-12 BA bat1 2.7
#> 5 x203 t38 Y 1955-05-15 BA bat1 3.8
#> 6 x291 t7 X 1955-05-18 BB bat1 112.3
```

Searcher efficiency and carcass persistence parameters are estimated by fitting models using functions `pkm`

and `cpm`

(carcass persistence model) which are patterned after familar R functions such as `lm`

and `glm`

. The “pk” in `pkm`

refers to GenEst’s model of searcher efficiency which includes two parameters: `p`

, which is the initial searcher efficiency for carcasses on the first search after they have arrived, and `k`

, which is a parameter governing the decrease in searcher efficiency in later searches. In this relatively simple example, our SE and CP field trials were conducted for one carcass size (bat) on one type of terrain (roads and pads) in three seasons (spring, summer, fall). The only potential predictor variable we have is `Season`

, which is entered as a column in both `data_SE`

and `data_CP`

.

Searcher efficiency is the probability of detection of a carcass that is present in the searched area at the time of search. Searcher efficiency typically decreases with carcass age because older carcasses tend to become harder to find as they accumulate dust or debris, fall deeper into vegetation, get blown against objects or into holes, decay, or get partially scavenged. In addition, carcasses missed in one search tend to be more likely to be missed in subsequent searches because the relatively easy-to-find carcasses are preferentially removed in the first searches after carcass arrival, leaving mostly the harder-to-find carcasses available in subsequences searches. GenEst accounts for a non-constant searcher efficiency using two parameters, `p`

(searcher efficiency on the first search after carcass arrivals) and `k`

(proportional change in searcher efficiency with each successive search). The `k`

parameter can be estimated from field trials if carcasses that are not discovered in the first search after arrival are left in the field for possible discovery in later searches.

`p`

and `k`

may both depend on covariates such as season, visibility class, or carcass size, and GenEst allows for them to be modeled as functions of different covariate combinations.

```
model_SE <- pkm(p ~ Season, k ~ 1, data = data_SE)
class(model_SE)
#> [1] "pkm" "list"
model_SE
#> $call
#> pkm0(formula_p = formula_p, formula_k = formula_k, data = data,
#> obsCol = obsCol, kFixed = kFixed, kInit = kInit, CL = CL,
#> quiet = quiet)
#>
#> $formula_p
#> p ~ Season
#>
#> $formula_k
#> k ~ 1
#>
#> $predictors
#> [1] "Season"
#>
#> $AICc
#> [1] 104.42
#>
#> $convergence
#> [1] 0
#>
#> $cell_pk
#> cell n p_median p_lower p_upper k_median k_lower k_upper
#> 1 fall 20 0.618 0.431 0.776 0.921 0.177 0.998
#> 2 spring 20 0.440 0.280 0.613 0.921 0.177 0.998
#> 3 summer 20 0.619 0.437 0.773 0.921 0.177 0.998
#>
#> $CL
#> [1] 0.9
```

NOTE: The `pkm`

family of functions by default interprets columns with names that begin with and “s” or “S” and end with a number contain search results data (carcass found = 0, not found = 1). A user can override the auto-parsing by explicitly listing the names of the search data columns in a vector of character strings in the `obsCol`

argument.

The probability of a carcass persisting a given length of time without being removed by scavengers (or other factors) is modeled as a Weibull, lognormal, loglogistic, or exponential distribution. Like the `p`

and `k`

parameters for searcher efficiency, the location and scale parameters (Therneau 2015) of the persistence distribution may depend on covariates. GenEst allows for them to be modeled as separate functions of predictor combinations.

```
model_CP <- cpm(l ~ Season, s ~ Season, data = data_CP, dist = "weibull",
left = "LastPresent", right = "FirstAbsent")
class(model_CP)
#> [1] "cpm" "list"
model_CP
#> $call
#> cpm0(formula_l = formula_l, formula_s = formula_s, data = data,
#> left = left, right = right, dist = dist, CL = CL, quiet = quiet)
#>
#> $formula_l
#> l ~ Season
#>
#> $formula_s
#> s ~ Season
#>
#> $distribution
#> [1] "weibull"
#>
#> $predictors
#> [1] "Season"
#>
#> $AICc
#> [1] 235.51
#>
#> $convergence
#> [1] 0
#>
#> $cell_ls
#> cell n l_median l_lower l_upper s_median s_lower s_upper
#> 1 fall 20 1.163 0.612 1.715 1.360 0.932 1.986
#> 2 spring 20 0.857 0.169 1.545 1.679 1.198 2.354
#> 3 summer 20 1.246 0.561 1.930 1.688 1.155 2.467
#>
#> $cell_ab
#> cell n pda_median pda_lower pda_upper pdb_median pdb_lower pdb_upper
#> 1 fall 20 0.735 1.073 0.504 3.200 1.844 5.557
#> 2 spring 20 0.596 0.835 0.425 2.356 1.184 4.688
#> 3 summer 20 0.592 0.866 0.405 3.476 1.752 6.890
#>
#> $CL
#> [1] 0.9
#>
#> $cell_desc
#> cell medianCP r1 r3 r7 r14 r28
#> 1 fall 1.943506 0.7877998 0.5968500 0.4035271 0.2504831 0.1362684
#> 2 spring 1.273808 0.6946923 0.5067622 0.3406993 0.2163474 0.1221627
#> 3 summer 1.871560 0.7459730 0.5779176 0.4168571 0.2838980 0.1714068
```

The model summary shows descriptive statistics for the cellwise estimates of the `l`

and `s`

parameters. The `location`

and `scale`

parameterization is common in survival analysis, but the `pda`

and `pdb`

parameterization (Dalthorp and Huso, 2014) is also shown. These parameterizations are convenient to work with in statistical calculations but are not as convenient for giving users quick insight into the distributions, so a third set of summary statistics about the fitted distributions is also given. Namely, the median persistence time and the `r`

statistic, which is the probability that a carcass persists until the first search after arrival (assuming uniformly distributed arrival times within the interval). Clearly, `r`

depends on the length of the search interval, and the table shows `r`

for intervals of 1, 3, 7, 14, and 28 days. A rough, back-of-the-envelope calculation for the probability of observing a carcass that arrives at a site during the monitored period would be `DWP * r * p * f`

, which is `DWP`

= fraction of carcasses that arrive in the area searched at a unit, `r`

= fraction of carcasses that persist until a search, `p`

= fraction of carcasses found on the first search after arrival (given that they persisted), and `f`

= fraction of carcasses that arrive at the units searched.

In other scenarios we might consider other predictors, like the visibility of the ground searched or the search team. We might also be interested in carcasses of different sizes (e.g., large, medium, and small birds instead of or in addition to bats). We are not restricted to using the same predictors of both SE and CP. The modeling complexity increases with each additional predictor, but, in theory, any number of predictors can be used. The only rule is that sufficient numbers of trial carcasses must be placed in each cell combination of factor levels among the selected predictors. For example, if we were to place 15 carcasses for each cell for predictors that include season (spring, summer, fall, winter), size (S, M, L, B), visibility (RP, M, D), search team (dogs, humans), and turbine type (small, medium, large), we’d need 15 x 4 x 4 x 3 x 2 x 2 = 2880 carcasses. Typically, the number of predictors is limited to a few key variables.

Each carcass’s contribution to the total mortality in each search interval is estimated using the `estM`

function.

```
Mhat <- estM(nsim = 1000, data_CO = data_CO, data_SS = data_SS,
data_DWP = data_DWP, model_SE = model_SE, model_CP = model_CP,
unitCol = "Turbine", COdate = "DateFound")
summary(Mhat)
#> median 5% 95%
#> 1428.57 1017.05 2120.42
plot(Mhat)
```

Mortality estimates may be partitioned or split into desired categories, such as species, season, or turbine type. Splits may be performed according to characteristics of the carcasses or where they were found (e.g., species, turbine or other variable found in `data_CO`

) or when they were found (e.g., season or other variable associated with search schedule and found in `data_SS`

, or a vector of specific times).

Mortality by `Species`

(a CO split because it is a column in the CO file):

```
M_species <- calcSplits(M = Mhat, split_CO = "Species", data_CO = data_CO)
summary(M_species)
#> X 5% 25% 50% 75% 95%
#> BA 42 549.52147 700.398898 821.40201 971.05619 1242.85440
#> BB 14 175.55442 266.958898 337.19668 440.56994 618.82177
#> BC 9 73.35734 117.659237 152.74771 203.55616 278.70909
#> BD 5 24.92252 60.428050 90.30333 122.87044 188.16901
#> BE 1 1.00000 4.105821 12.38460 23.34243 45.47721
#> attr(,"class")
#> [1] "splitSummary"
#> attr(,"CL")
#> [1] 0.9
#> attr(,"vars")
#> [1] "Species"
#> attr(,"type")
#> [1] "CO"
plot(M_species)
```

Mortality estimates may also be split by temporal variables that are represented as columns in `data_SS`

or as numeric vectors spanning the monitoring season (from day 0 to length of monitoring season). If several temporal splits are to be calculated, creating a specially formatted `prepSS`

object for the search schedule can streamline the calculations.

Mortality by `Season`

(an SS split because it is a column in the SS file):

```
M_season <- calcSplits(M = Mhat, split_SS = "Season", data_SS = SSdat,
split_CO = NULL, data_CO = data_CO)
summary(M_season)
#> X 5% 25% 50% 75% 95%
#> spring 18.10485 303.16912 440.5782 587.0305 780.1610 1141.1773
#> summer 10.15115 91.50569 149.9145 199.0106 256.5562 366.6490
#> fall 42.74400 420.55613 532.9981 621.4445 723.6443 922.3594
#> attr(,"class")
#> [1] "splitSummary"
#> attr(,"CL")
#> [1] 0.9
#> attr(,"vars")
#> [1] "Season"
#> attr(,"type")
#> [1] "SS"
#> attr(,"times")
#> [1] 0 60 130 200
plot(M_season)
```

Mortality by month (a temporal split that spans the monitoring period):

```
M_month <- calcSplits(M = Mhat, split_time = seq(0, max(SSdat$days), by = 28),
data_SS = SSdat, data_CO = data_CO)
summary(M_month)
#> X 5% 25% 50% 75% 95%
#> 28 6.236250 82.28976 147.17745 216.72667 303.58926 508.7781
#> 56 11.744865 170.42346 265.32898 350.04291 478.11169 712.3600
#> 84 2.118170 2.11817 27.35138 55.20833 88.93819 158.7261
#> 112 4.565143 27.20504 51.43702 77.51980 112.98855 176.9747
#> 140 10.000952 76.55617 113.22394 146.07691 182.71714 248.3944
#> 168 27.864667 272.76303 356.22389 415.00745 499.70506 654.8598
#> 196 8.469952 51.08571 81.43585 110.85448 145.78887 208.4552
#> 200 0.000000 0.00000 0.00000 0.00000 0.00000 0.0000
#> attr(,"class")
#> [1] "splitSummary"
#> attr(,"CL")
#> [1] 0.9
#> attr(,"vars")
#> [1] "time"
#> attr(,"type")
#> [1] "time"
#> attr(,"times")
#> [1] 0 28 56 84 112 140 168 196 200
plot(M_month)
```

Temporal splits that divide the monitoring season into separate time intervals (like season or month) can be plotted as the number per interval (`rate = FALSE`

, which is the default arg in `calcSplits`

) or the number per unit time (`rate = TRUE`

).

```
M_various_times <- calcSplits(M = Mhat,
split_time = c(seq(0, 90, by = 15), 120, 150, seq(155, 200, by = 5)),
data_SS = SSdat, data_CO = data_CO)
plot(M_various_times)
```

Finally, splits can be calculated for combinations of splitting covariates, like species by season or species group by turbine type. No more than two splitting covariates may be used in one call to `calcSplits`

and at most one temporal split may be used (whether it is an SS split or a vector of times).

Thorough searches out to a radius of 60 m from each turbine were conducted at 23 out of 100 turbines. The searched area was divided into three visibility classes (`RP`

, `M`

, `D`

) according the difficulty of finding carcasses.

Searcher efficiency and carcass persistence would be expected to vary with carcass size (sparrow, eagle, bat), ground characteristics (road & pad, cleared field, vegetation type), season, etc. In this example, we perform a full analysis of scenario with four classes of carcass (`lrg`

, `med`

, `sml`

, and `bat`

), three visibility classes (difficult = `D`

, moderate = `M`

, and road & pad = `RP`

), and three seasons (`spring`

, `summer`

, and `fall`

).

The required data is stored in `wind_cleared`

, a list of data frames with results for searcher efficiency (`SE`

) and carcass persistence trials (`CP`

), search schedules for all turbines (`SS`

), the search coverage or density weighted proportion (`DWP`

) of area searched at each turbine (i.e., the fraction of carcasses expected to fall in the search plots), and carcass observation (`CO`

) data.

Load the full data set into R:

To streamline the notation, extract the data from the `wind_cleared`

list into its components:

```
data_SE <- wind_cleared$SE
data_CP <- wind_cleared$CP
data_SS <- wind_cleared$SS
data_DWP <- wind_cleared$DWP
data_CO <- wind_cleared$CO
```

In searcher efficiency and carcass persistence trials, 15 trial carcasses were placed in each combination of visibility class (`D`

, `M`

, `RP`

), season (`spring`

, `summer`

, `fall`

), and size class (`lrg`

, `med`

, `sml`

, `bat`

). Data formats are like those of example 1:

```
head(data_SE)
#> pkID Size Season Visibility s1 s2 s3 s4 s5
#> 1 pk1 bat spring RP 0 NA NA NA NA
#> 2 pk2 bat spring RP 0 0 NA NA NA
#> 3 pk3 bat spring RP 1 NA NA NA NA
#> 4 pk4 bat spring RP 1 NA NA NA NA
#> 5 pk5 bat spring RP 0 NA NA NA NA
#> 6 pk6 bat spring RP 1 NA NA NA NA
head(data_CP)
#> cpID Size Season Visibility LastPresent FirstAbsent
#> 1 cp1 bat spring RP 0.00 0.93
#> 2 cp2 bat spring RP 0.98 1.97
#> 3 cp3 bat spring RP 0.00 1.01
#> 4 cp4 bat spring RP 13.99 21.13
#> 5 cp5 bat spring RP 0.00 1.17
#> 6 cp6 bat spring RP 20.95 27.97
```

With 36 combinations of covariate levels (3 visibilities x 3 seasons x 4 sizes) and two parameters (`p`

and `k`

), the number of possible models to consider for searcher efficiency is unwieldy using simple calls to `pkm`

, but `pkm`

has powerful model building and model selection capabilities that can be accessed via the arg list: `allCombos`

and `sizeCol`

, which are discussed below.

When `allCombos = TRUE`

, `pkm`

fits the set of submodels of the given covariate combinations, including the full model, the null model, and everything in between. For example, if the parameter models are `p ~ Visibility * Season`

and `k ~ Visibility`

, `pkm`

with `allCombos = TRUE`

would fit all combinations of possible `p`

models (`p ~ Visibility * Season`

, `p ~ Visibility + Season`

, `p ~ Visibility`

, `p ~ Season`

, and `p ~ 1`

) and possible `k`

models (`k ~ Visibility`

and `k ~ 1`

), or 10 models in all.

Carcasses in different size classes would be expected to have different searcher efficiency and carcass persistence parameters and would even be likely to be affected by covariates in different ways. When analyzing data with carcasses in different size classes, it is recommended that separate CP and SE models be fit for size classes separately. This can be accomplished using the `sizeCol`

argument in `pkm`

and `cpm`

, where `sizeCol`

gives the name of the column that gives the carcass size classes in `data_SE`

.

```
pkModels <- pkm(p ~ Visibility * Season, k ~ Visibility * Season, data = data_SE,
allCombos = TRUE, sizeCol = "Size")
class(pkModels)
#> [1] "pkmSetSize" "list"
names(pkModels)
#> [1] "bat" "lrg" "med" "sml"
```

When `allCombos = TRUE`

and `sizeCol`

is defined, `pkm`

returns a list of sets of models for each size class. The sets of models for each size class include the full spectrum of models that can be constructed using simple combinations of the covariates.

```
names(pkModels[["sml"]])
#> [1] "p ~ Visibility * Season; k ~ Visibility * Season" "p ~ Visibility + Season; k ~ Visibility * Season"
#> [3] "p ~ Season; k ~ Visibility * Season" "p ~ Visibility; k ~ Visibility * Season"
#> [5] "p ~ 1; k ~ Visibility * Season" "p ~ Visibility * Season; k ~ Visibility + Season"
#> [7] "p ~ Visibility + Season; k ~ Visibility + Season" "p ~ Season; k ~ Visibility + Season"
#> [9] "p ~ Visibility; k ~ Visibility + Season" "p ~ 1; k ~ Visibility + Season"
#> [11] "p ~ Visibility * Season; k ~ Season" "p ~ Visibility + Season; k ~ Season"
#> [13] "p ~ Season; k ~ Season" "p ~ Visibility; k ~ Season"
#> [15] "p ~ 1; k ~ Season" "p ~ Visibility * Season; k ~ Visibility"
#> [17] "p ~ Visibility + Season; k ~ Visibility" "p ~ Season; k ~ Visibility"
#> [19] "p ~ Visibility; k ~ Visibility" "p ~ 1; k ~ Visibility"
#> [21] "p ~ Visibility * Season; k ~ 1" "p ~ Visibility + Season; k ~ 1"
#> [23] "p ~ Season; k ~ 1" "p ~ Visibility; k ~ 1"
#> [25] "p ~ 1; k ~ 1"
class(pkModels[["sml"]])
#> [1] "pkmSet" "list"
```

To estimate mortality, one model for each size class must be selected from the long list of models fit. GenEst provides several tools for guiding the selection. First, the models can be listed by AICc, which gives a score for the quality of the model for the given data. Complicated models that use many parameters may fit the data more closely than a simpler model but are penalized because of their complexity and relative instability. The scores have meaning only in comparison with other models’. AICc provides a rough but useful guide for model selection, but should in no way be relied upon as definitive. Its utility is in identifying relatively poor models and in narrowing the choice of plausible models to a manageable number.

The `aicc`

function lists the fitted models in order of \({\small \Delta}\)AICc for each size class (if applicable). For this discussion, we will focus on `sml`

only, but for a full analysis, all size classes would need to be similarly analyzed.

```
aicc(pkModels[["sml"]])
#> p Formula k Formula AICc <U+0394>AICc
#> 24 p ~ Visibility k ~ 1 318.55 0.00
#> 19 p ~ Visibility k ~ Visibility 319.69 1.14
#> 14 p ~ Visibility k ~ Season 321.42 2.87
#> 21 p ~ Visibility * Season k ~ 1 321.53 2.98
#> 22 p ~ Visibility + Season k ~ 1 322.17 3.62
#> 16 p ~ Visibility * Season k ~ Visibility 322.98 4.43
#> 17 p ~ Visibility + Season k ~ Visibility 323.14 4.59
#> 9 p ~ Visibility k ~ Visibility + Season 323.44 4.89
#> 11 p ~ Visibility * Season k ~ Season 323.97 5.42
#> 12 p ~ Visibility + Season k ~ Season 324.33 5.78
#> 7 p ~ Visibility + Season k ~ Visibility + Season 326.33 7.78
#> 6 p ~ Visibility * Season k ~ Visibility + Season 326.51 7.96
#> 4 p ~ Visibility k ~ Visibility * Season 327.99 9.44
#> 2 p ~ Visibility + Season k ~ Visibility * Season 331.07 12.52
#> 1 p ~ Visibility * Season k ~ Visibility * Season 333.47 14.92
#> 20 p ~ 1 k ~ Visibility 339.51 20.96
#> 10 p ~ 1 k ~ Visibility + Season 342.41 23.86
#> 18 p ~ Season k ~ Visibility 342.74 24.19
#> 8 p ~ Season k ~ Visibility + Season 344.10 25.55
#> 25 p ~ 1 k ~ 1 346.45 27.90
#> 5 p ~ 1 k ~ Visibility * Season 347.47 28.92
#> 15 p ~ 1 k ~ Season 347.66 29.11
#> 23 p ~ Season k ~ 1 350.35 31.80
#> 13 p ~ Season k ~ Season 350.44 31.89
#> 3 p ~ Season k ~ Visibility * Season 350.49 31.94
```

Preference should normally be given to models with \({\small \Delta}\)AICc less than 6 or 7. Models with differences of less than 3 or 4 are generally considered indistinguishable by this measure. Choices among such models should be based on other criteria.

Diagnostic plots can be used to identify potential problems with model fits and to help distinguish between models with similar AICc scores. The `plot`

function is defined for `pkm`

(one model) and `pkmSet`

(set of models for a given size class) objects. For example, `plot(pkModels[["sml"]][[1]])`

would produce the single figure for the first model for the `sml`

size class. `plot(pkModels[["sml"]])`

would create plots for each model fit for the `sml`

size class. To plot a specific single model from the full set, use the `specificModel`

argument. For example, diagnostic plots for the model with the lowest AICc score are shown below:

The top row shows box plots of estimated `p`

and `k`

parameters for all cells (i.e., combinations of covariate levels, like `D.fall`

for difficult visibility in the fall) for both the selected model (black) and the full model (gray). With the full model, the fits for each cell are based solely on data from that specific cell. The advantage is that each cell’s estimates are untainted by data from other cells. The disadvantage is that the sample size for each estimate is relatively small and the error bars large. In the reduced models, estimates for one cell borrow strength from estimates in related cells. This gives smaller error bars but can lead to errors if the model structure does not properly reflect the dependence of searcher efficiency parameters on cell characteristics.

In the figure, the estimates of `p`

from the selected model are markedly less variable than the estimates from the full model, while the locations of the boxes are very similar for the two models. Thus, this selected model (the one with the lowest AICc) appears to be an improvement over the full cell model for estimating `p`

.

The \({\small \Delta}\)AICc for the full model is 12.52, which indicates a serious deficiency in comparison to the model with the best fit, `"p ~ Visibility; k ~ 1"`

. The boxplots for `k`

highlight one particular problem with the fit of the reference model. In some of the cells, the boxes extend from 0 to 1, which suggests that the reference model is unable to estimate `k`

for the given cell. Selecting a simpler model for `k`

often remedies this problem. If all models display this 0-1 phenomenon, a fixed `k`

of 1 is appropriate if a smaller proportion of carcasses was found on the first search occasion than on later searches.

By comparison, the model with the highest \({\small \Delta}\)AICc (= `{r max(aicc(pkModels[["sml"]]))}`

routinely estimates `p`

and `k`

either well above or well below the reference model but has fairly tight error bars–bad estimates but quite confident about them!

A similar model selection exercise gives the same form of model (`p ~ Visibility; k ~ 1`

) for large birds, medium birds, and bats. These can all be collated into a list for later analysis of detection probabilities and mortality rates.

The work flow for carcass persistence modeling is similar to that for searcher efficiency except that in addition to selecting covariates for two different parameters (location = `l`

and scale = `s`

), there are four model forms to choose from: Weibull, lognormal, loglogistic, and exponential.

```
cpModels <- cpm(
l ~ Visibility * Season, s ~ Visibility * Season,
data = data_CP, left = "LastPresent", right = "FirstAbsent",
dist = c( "weibull", "lognormal", "loglogistic", "exponential"),
allCombos = TRUE, sizeCol = "Size"
)
```

The list of models is long:

```
lapply(aicc(cpModels), nrow)
#> $bat
#> [1] 80
#>
#> $lrg
#> [1] 80
#>
#> $med
#> [1] 80
#>
#> $sml
#> [1] 80
aicc(cpModels[["sml"]])
#> Distribution Location Formula Scale Formula AICc <U+0394>AICc
#> 25 weibull l ~ 1 s ~ 1 780.00 0.00
#> 24 weibull l ~ Visibility s ~ 1 780.16 0.16
#> 15 weibull l ~ 1 s ~ Season 780.38 0.38
#> 19 weibull l ~ Visibility s ~ Visibility 780.97 0.97
#> 20 weibull l ~ 1 s ~ Visibility 781.32 1.32
#> 10 weibull l ~ 1 s ~ Visibility + Season 782.00 2.00
#> 14 weibull l ~ Visibility s ~ Season 782.04 2.04
#> 22 weibull l ~ Visibility + Season s ~ 1 782.55 2.55
#> 74 loglogistic l ~ Visibility s ~ 1 782.57 2.57
#> 21 weibull l ~ Visibility * Season s ~ 1 782.77 2.77
#> 49 lognormal l ~ Visibility s ~ 1 782.84 2.84
#> 23 weibull l ~ Season s ~ 1 782.88 2.88
#> 71 loglogistic l ~ Visibility * Season s ~ 1 783.06 3.06
#> 13 weibull l ~ Season s ~ Season 783.16 3.16
#> 50 lognormal l ~ 1 s ~ 1 783.18 3.18
#> 75 loglogistic l ~ 1 s ~ 1 783.30 3.30
#> 9 weibull l ~ Visibility s ~ Visibility + Season 783.33 3.33
#> 16 weibull l ~ Visibility * Season s ~ Visibility 783.42 3.42
#> 46 lognormal l ~ Visibility * Season s ~ 1 783.86 3.86
#> 47 lognormal l ~ Visibility + Season s ~ 1 783.86 3.86
#> 40 lognormal l ~ 1 s ~ Season 783.88 3.88
#> 11 weibull l ~ Visibility * Season s ~ Season 783.95 3.95
#> 72 loglogistic l ~ Visibility + Season s ~ 1 784.00 4.00
#> 17 weibull l ~ Visibility + Season s ~ Visibility 784.09 4.09
#> 48 lognormal l ~ Season s ~ 1 784.13 4.13
#> 69 loglogistic l ~ Visibility s ~ Visibility 784.28 4.28
#> 65 loglogistic l ~ 1 s ~ Season 784.30 4.30
#> 12 weibull l ~ Visibility + Season s ~ Season 784.48 4.48
#> 73 loglogistic l ~ Season s ~ 1 784.54 4.54
#> 44 lognormal l ~ Visibility s ~ Visibility 784.58 4.58
#> 18 weibull l ~ Season s ~ Visibility 784.85 4.85
#> 66 loglogistic l ~ Visibility * Season s ~ Visibility 784.85 4.85
#> 64 loglogistic l ~ Visibility s ~ Season 784.95 4.95
#> 39 lognormal l ~ Visibility s ~ Season 785.01 5.01
#> 38 lognormal l ~ Season s ~ Season 785.09 5.09
#> 45 lognormal l ~ 1 s ~ Visibility 785.14 5.14
#> 6 weibull l ~ Visibility * Season s ~ Visibility + Season 785.29 5.29
#> 70 loglogistic l ~ 1 s ~ Visibility 785.31 5.31
#> 8 weibull l ~ Season s ~ Visibility + Season 785.43 5.43
#> 61 loglogistic l ~ Visibility * Season s ~ Season 785.47 5.47
#> 41 lognormal l ~ Visibility * Season s ~ Visibility 785.68 5.68
#> 63 loglogistic l ~ Season s ~ Season 785.71 5.71
#> 36 lognormal l ~ Visibility * Season s ~ Season 785.89 5.89
#> 35 lognormal l ~ 1 s ~ Visibility + Season 786.07 6.07
#> 42 lognormal l ~ Visibility + Season s ~ Visibility 786.15 6.15
#> 37 lognormal l ~ Visibility + Season s ~ Season 786.29 6.29
#> 67 loglogistic l ~ Visibility + Season s ~ Visibility 786.30 6.30
#> 7 weibull l ~ Visibility + Season s ~ Visibility + Season 786.48 6.48
#> 43 lognormal l ~ Season s ~ Visibility 786.48 6.48
#> 60 loglogistic l ~ 1 s ~ Visibility + Season 786.56 6.56
#> 62 loglogistic l ~ Visibility + Season s ~ Season 786.56 6.56
#> 68 loglogistic l ~ Season s ~ Visibility 786.89 6.89
#> 59 loglogistic l ~ Visibility s ~ Visibility + Season 786.94 6.94
#> 34 lognormal l ~ Visibility s ~ Visibility + Season 787.01 7.01
#> 56 loglogistic l ~ Visibility * Season s ~ Visibility + Season 787.41 7.41
#> 33 lognormal l ~ Season s ~ Visibility + Season 787.71 7.71
#> 31 lognormal l ~ Visibility * Season s ~ Visibility + Season 787.87 7.87
#> 58 loglogistic l ~ Season s ~ Visibility + Season 788.35 8.35
#> 32 lognormal l ~ Visibility + Season s ~ Visibility + Season 788.83 8.83
#> 57 loglogistic l ~ Visibility + Season s ~ Visibility + Season 789.12 9.12
#> 5 weibull l ~ 1 s ~ Visibility * Season 789.98 9.98
#> 4 weibull l ~ Visibility s ~ Visibility * Season 791.45 11.45
#> 3 weibull l ~ Season s ~ Visibility * Season 793.01 13.01
#> 1 weibull l ~ Visibility * Season s ~ Visibility * Season 794.00 14.00
#> 30 lognormal l ~ 1 s ~ Visibility * Season 794.47 14.47
#> 2 weibull l ~ Visibility + Season s ~ Visibility * Season 794.50 14.50
#> 55 loglogistic l ~ 1 s ~ Visibility * Season 794.95 14.95
#> 29 lognormal l ~ Visibility s ~ Visibility * Season 795.13 15.13
#> 54 loglogistic l ~ Visibility s ~ Visibility * Season 795.14 15.14
#> 28 lognormal l ~ Season s ~ Visibility * Season 795.65 15.65
#> 53 loglogistic l ~ Season s ~ Visibility * Season 796.37 16.37
#> 51 loglogistic l ~ Visibility * Season s ~ Visibility * Season 796.80 16.80
#> 26 lognormal l ~ Visibility * Season s ~ Visibility * Season 797.20 17.20
#> 27 lognormal l ~ Visibility + Season s ~ Visibility * Season 797.36 17.36
#> 52 loglogistic l ~ Visibility + Season s ~ Visibility * Season 797.70 17.70
#> 76 exponential l ~ Visibility * Season NULL 835.23 55.23
#> 79 exponential l ~ Visibility NULL 839.78 59.78
#> 77 exponential l ~ Visibility + Season NULL 840.96 60.96
#> 80 exponential l ~ 1 NULL 842.24 62.24
#> 78 exponential l ~ Season NULL 844.75 64.75
```

It is not uncommon to see the fits for the exponential distribution at the bottom of the AIC list. The exponential distribution has only one parameter and does not have nearly as much flexibility as the others, which each have two-parameters. An implicit assumption of the exponential model is that the scavenging rate is constant, regardless of carcass age. When that assumption is not met, the exponential provides an inferior fit.

To compare among a set of cp models with plausible AICs, use, for example, `plot(cpModels[["sml"]])`

to browse through all the models or `plot(cpModels[["sml"]][["p ~ Visibility; k ~ 1"]])`

to view a single model specified by name. It can be seen from the AICc table (`aicc(cpModels[["sml"]])`

) that the top 10 models according to AICc are:

```
cp_smlCandidates <-
names(cpModels[["sml"]])[c(25, 24, 15, 19, 20, 10, 14, 22, 74, 21)]
cp_smlCandidates
#> [1] "dist: weibull; l ~ 1; s ~ 1" "dist: weibull; l ~ Visibility; s ~ 1"
#> [3] "dist: weibull; l ~ 1; s ~ Season" "dist: weibull; l ~ Visibility; s ~ Visibility"
#> [5] "dist: weibull; l ~ 1; s ~ Visibility" "dist: weibull; l ~ 1; s ~ Visibility + Season"
#> [7] "dist: weibull; l ~ Visibility; s ~ Season" "dist: weibull; l ~ Visibility + Season; s ~ 1"
#> [9] "dist: loglogistic; l ~ Visibility; s ~ 1" "dist: weibull; l ~ Visibility * Season; s ~ 1"
```

These can be compared in graphs as follows:

The figure shows the raw persistence data (fraction of carcasses remaining after the given time) for each cell, as a black stair case with Kaplan-Meier confidence intervals as dashed lines. In addition, the fitted curves for each of the distributions are shown in color, with the `specificModel`

distribution having a thicker than the others. The two-parameter models (Weibull, lognormal, and loglogistic) tend to be very similar and a relatively close fit to the data. The exponential model tends to be somewhat removed from the others. Clicking on the graphing window brings up the next set of figures.

We’re looking for a good fit between the selected model and the data in as many cells as possible. The first several models among the `cp_smlCandidates`

seems to provide a reasonably good fit in all cells, although there seems to be a trade-off between fitting the RP.spring cell well or fitting the RP.summer cell well. `Visibility`

occurs frequently in the top models, while `Season`

appears more frequently in the bottom models. This indicates that `Season`

is probably not a strong predictor of carcass persistence, while `Visibility`

is.

Selecting the top AICc model for use in mortality estimation:

Following a similar model selection process for the other size classes, we select the following:

```
cp_med <- cpModels[["med"]][["dist: weibull; l ~ Visibility; s ~ Season"]]
cp_lrg <- cpModels[["lrg"]][["dist: exponential; l ~ Visibility + Season; NULL"]]
cp_bat <- cpModels[["bat"]][["dist: weibull; l ~ Visibility + Season; s ~ 1"]]
```

NOTE: For large carcasses, the exponential distribution was at the top of the AICc list. The exponential requires only one parameter (`l`

), so no scale parameter is provided in the model.

Again, we collate the models into a list for later analysis of detection probabilities and mortality rates.

Each carcass’s contribution to the total mortality in each search interval is estimated using the `estM`

function. The function call is largely similar that used in the simple scenario discussed in example 1. However, there are some important differences. First, `model_SE`

and `model_CP`

are lists of models, one element for each size class. In addition, the name of the size class variable is provided as `sizeCol = "Size"`

. Finally, the `frac`

argument represents the sampling fraction or the fraction of carcasses expected to fall at the units that were searched. In this example, 23 out of 100 turbines were searched, and `frac`

is set equal to 0.23 under the assumption that the mortality rates at the unsearched turbines did not differ substantially from the rates at the searched turbines.

```
Mhat <- estM(nsim = 1000, data_CO = data_CO, data_SS = data_SS, frac = 0.23,
data_DWP = data_DWP, model_SE = pkMods, model_CP = cpMods,
sizeCol = "Size", unitCol = "Turbine", COdate = "DateFound")
summary(Mhat)
#> median 5% 95%
#> 1950.08 1504.79 2481.56
plot(Mhat)
```

This estimate is for the total number of fatalities among all size classes combined, from hummingbirds and bats to eagles and may be too vague to be very useful. Fortunately, mortality estimates may be partitioned or split into desired categories, such as species, size, or season. Splits may be performed according to characteristics of the carcasses or where they were found (e.g., species, turbine or other variable found in `data_CO`

) or when they were found (e.g., season or other variable associated with search schedule and found in `data_SS`

, or a vector of specific times).

Carcasses were categorized not only by size but also by species, species group, the type of turbine they were found at, the visibility class of the ground where they were found, and distance from nearest turbine.

Although species groups may extend across different size classes (e.g., `raptors`

could include kestrels, red-tailed hawks, and golden eagles; `passerines`

could include sparrows and ravens), splits according to species group can easily be accomplished:

```
M_speciesGroup <- calcSplits(M = Mhat,
split_CO = "SpeciesGroup", data_CO = data_CO)
summary(M_speciesGroup)
#> X 5% 25% 50% 75% 95%
#> bat0 4 15.84518 42.98304 65.01039 91.34760 135.41455
#> bat1 49 821.84502 998.38426 1124.09486 1271.42917 1506.81883
#> brd1 19 318.59130 430.98311 540.65594 649.76438 893.06034
#> brd2 10 67.21578 106.40486 136.80853 169.60623 229.47310
#> brd3 5 16.93379 37.59497 52.46463 70.57275 99.00156
#> attr(,"class")
#> [1] "splitSummary"
#> attr(,"CL")
#> [1] 0.9
#> attr(,"vars")
#> [1] "SpeciesGroup"
#> attr(,"type")
#> [1] "CO"
plot(M_speciesGroup)
```

Split by species and season:

```
M_speciesseason <- calcSplits(M = Mhat,
split_CO = "Species", data_CO = data_CO, split_SS = "Season", data_SS = data_SS)
summary(M_speciesseason)
#> $BA
#> X 5% 25% 50% 75% 95%
#> spring 7.000 78.68072 137.18020 195.26080 256.0427 356.7320
#> summer 3.298 19.82287 50.38625 77.08528 115.0918 169.5093
#> fall 22.702 276.44418 363.01598 427.44177 503.4913 622.4957
#>
#> $BB
#> X 5% 25% 50% 75% 95%
#> spring 3.00 20.47164 73.790644 120.23929 175.75976 269.60596
#> summer 1.16 1.16000 9.071708 25.13283 49.52027 93.72569
#> fall 6.84 53.96284 96.621052 130.95137 168.83725 230.84013
#>
#> $BC
#> X 5% 25% 50% 75% 95%
#> spring 1.0268462 1.0268462 10.636498 31.03901 60.31171 110.12849
#> summer 0.9771538 0.9771538 4.946332 19.78637 37.66492 73.19923
#> fall 2.9960000 6.3243014 29.496171 50.14685 72.08144 118.37653
#>
#> $BD
#> X 5% 25% 50% 75% 95%
#> spring 0.000 0.000 0.00000 0.00000 0.00000 0.00000
#> summer 0.001 0.001 0.00100 0.00100 0.00100 0.00100
#> fall 1.999 1.999 16.31902 30.97829 49.17108 82.05275
#>
#> $BE
#> X 5% 25% 50% 75% 95%
#> spring 0 0 0.00000 0.00000 0.00000 0.00000
#> summer 0 0 0.00000 0.00000 0.00000 0.00000
#> fall 2 2 17.14743 30.77357 48.04273 76.40644
#>
#> $LA
#> X 5% 25% 50% 75% 95%
#> spring 2 2 8.555167 17.72575 25.82777 39.90630
#> summer 0 0 0.000000 0.00000 0.00000 0.00000
#> fall 2 2 10.194308 19.42077 30.43512 46.60259
#>
#> $LB
#> X 5% 25% 50% 75% 95%
#> spring 1 1 2.674087 8.946747 15.82697 29.95302
#> summer 0 0 0.000000 0.000000 0.00000 0.00000
#> fall 0 0 0.000000 0.000000 0.00000 0.00000
#>
#> $LC
#> X 5% 25% 50% 75% 95%
#> spring 1.0158 1.0158 2.695199 9.129528 15.69643 26.82076
#> summer 0.9842 0.9842 2.287289 7.543386 14.58640 24.50108
#> fall 0.0000 0.0000 0.000000 0.000000 0.00000 0.00000
#>
#> $LE
#> X 5% 25% 50% 75% 95%
#> spring 0.087 0.087 0.0870000 0.087000 0.08700 6.445489
#> summer 0.913 0.913 0.9952762 7.140495 14.29492 25.192103
#> fall 0.000 0.000 0.0000000 0.000000 0.00000 0.000000
#>
#> $MA
#> X 5% 25% 50% 75% 95%
#> spring 1 1 5.707589 15.74499 29.47723 53.64422
#> summer 1 1 3.120553 11.20351 20.40262 36.91600
#> fall 1 1 4.199945 11.18814 19.92479 35.77385
#>
#> $MB
#> X 5% 25% 50% 75% 95%
#> spring 0.000 0.000 0.000000 0.000000 0.00000 0.0000
#> summer 0.019 0.019 0.019000 0.019000 0.01900 0.0190
#> fall 0.981 0.981 3.033781 9.684645 18.79628 33.6486
#>
#> $MC
#> X 5% 25% 50% 75% 95%
#> spring 1.274 1.274 6.681613 18.268957 37.20375 66.01064
#> summer 0.726 0.726 0.726000 8.274581 25.18611 52.12935
#> fall 0.000 0.000 0.000000 0.000000 0.00000 0.00000
#>
#> $MD
#> X 5% 25% 50% 75% 95%
#> spring 1 1 3.116223 12.19992 22.93843 40.46101
#> summer 0 0 0.000000 0.00000 0.00000 0.00000
#> fall 0 0 0.000000 0.00000 0.00000 0.00000
#>
#> $ME
#> X 5% 25% 50% 75% 95%
#> spring 0.000 0.000 0.000000 0.000000 0.00000 0.00000
#> summer 0.002 0.002 0.002000 0.002000 0.00200 0.00200
#> fall 0.998 0.998 2.898933 9.806992 18.36537 31.29255
#>
#> $MF
#> X 5% 25% 50% 75% 95%
#> spring 0 0.000000 0.0000 0.00000 0.00000 0.00000
#> summer 0 0.000000 0.0000 0.00000 0.00000 0.00000
#> fall 3 6.897434 25.7585 43.01517 62.13042 95.69283
#>
#> $MH
#> X 5% 25% 50% 75% 95%
#> spring 1 1 3.836125 12.07272 20.70674 39.93509
#> summer 1 1 2.835275 10.33258 18.37792 33.87546
#> fall 0 0 0.000000 0.00000 0.00000 0.00000
#>
#> $SA
#> X 5% 25% 50% 75% 95%
#> spring 1 1 7.648649 33.70525 64.615 126.0807
#> summer 0 0 0.000000 0.00000 0.000 0.0000
#> fall 0 0 0.000000 0.00000 0.000 0.0000
#>
#> $SB
#> X 5% 25% 50% 75% 95%
#> spring 0.405 0.405 0.405 0.405 20.76413 94.00243
#> summer 0.595 0.595 0.595 0.595 35.14302 93.22410
#> fall 0.000 0.000 0.000 0.000 0.00000 0.00000
#>
#> $SC
#> X 5% 25% 50% 75% 95%
#> spring 3 19.06864 62.73431 102.8238 158.5472 250.9796
#> summer 0 0.00000 0.00000 0.0000 0.0000 0.0000
#> fall 0 0.00000 0.00000 0.0000 0.0000 0.0000
#>
#> $SD
#> X 5% 25% 50% 75% 95%
#> spring 1.1176154 1.1176154 7.503196 25.46817 49.09367 91.82499
#> summer 0.8823846 0.8823846 4.009613 23.73235 49.22902 101.20259
#> fall 0.0000000 0.0000000 0.000000 0.00000 0.00000 0.00000
#>
#> $SE
#> X 5% 25% 50% 75% 95%
#> spring 0.007 0.007 0.007000 0.00700 0.00700 0.0070
#> summer 0.993 0.993 8.083627 26.25676 51.53088 101.7816
#> fall 0.000 0.000 0.000000 0.00000 0.00000 0.0000
#>
#> $SG
#> X 5% 25% 50% 75% 95%
#> spring 3.044125 22.121279 67.69724 108.13860 157.41909 271.0455
#> summer 1.955875 1.955875 31.21642 58.96103 93.62312 160.7319
#> fall 0.000000 0.000000 0.00000 0.00000 0.00000 0.0000
#>
#> attr(,"class")
#> [1] "splitSummary"
#> attr(,"CL")
#> [1] 0.9
#> attr(,"vars")
#> [1] "Season" "Species"
#> attr(,"type")
#> [1] "SS" "CO"
#> attr(,"times")
#> [1] 0 60 130 200
plot(M_speciesseason)
```

There are so many vertical panels that it is difficult to glean any useful information out of the graph. However, the panels may be transposed and graphed for better interpretability: