Revisiting the savanna sparrow point transect data.

In this exercise, we use `R`

(R Core Team, 2019) and the
`Distance`

package (Miller, Rexstad, Thomas, Marshall, & Laake,
2019) to fit different detection function models to point
transect survey data of savanna sparrows *(Passerculus
sandwichensis)* density and abundance. These data were part of a
study examining the effect of livestock grazing upon vegetation
structure and consequently upon the avian community described by Knopf
et al. (1988). This
dataset was also used to demonstrate point
transect analysis

- Fit a detection function pooling data across pastures,
- Fit pasture-specific detection functions,
- Choose most appropriate analysis using model selection.

A total of 373 point transects were placed in three pastures in the
Arapaho National Wildlife Refuge in Colorado (Figure 1).
Elevation of these pastures was ~2500m. In this example, we
**will** perform pasture-level analysis of these data.

The fields of the `Savannah_sparrow_1980`

data set
are:

- Region.Label - three pastures that constituted sections of the study
area.

- Area - size of the study region. A place holder, because pasture sizes are not known. Estimates of density and abundance will be equivalent.
- Sample.Label - point transect identifier (total of 273)
- Effort - number of visits to each point
- object - unique identifier for each detected savanna sparrow
- distance - radial distance (metres) to each detection
- Study.Area - only data for savanna sparrow (SASP) are included in this data set

This command assumes that the `dsdata`

package has been
installed on your computer. The R workspace
`Savannah_sparrow_1980`

contains detections of savanna
sparrows from point transect surveys of Knopf et al. (1988).

```
library(Distance)
data(Savannah_sparrow_1980)
conversion.factor <- convert_units("meter", NULL, "hectare")
```

The simplest way to fit pasture-specific detection functions is to
subset the data. This could be done at the time the `ds()`

function is called, but we perform the step here as a data preparation
step.

Fit half-normal key functions without adjustments to each pasture separately after performing 5% right truncation.

```
past1.hn <- ds(data=sasp.past1, key="hn", adjustment=NULL,
transect="point", convert_units=conversion.factor, truncation="5%")
past2.hn <- ds(data=sasp.past2, key="hn", adjustment=NULL,
transect="point", convert_units=conversion.factor, truncation="5%")
past3.hn <- ds(data=sasp.past3, key="hn", adjustment=NULL,
transect="point", convert_units=conversion.factor, truncation="5%")
```

The total AIC for the model that fits separate detection functions to each pasture is the sum of the AICs for the individual pastures.

This model is much simpler to fit because there is only a single call
to `ds()`

using the original data.

```
cat(paste("Stratum-specific detection AIC", round(model.separate.AIC),
"\nCommon detection function AIC", round(model.pooled.AIC$AIC)), sep=" ")
```

```
Stratum-specific detection AIC 2007
Common detection function AIC 2022
```

Because the AIC for model with stratum-specific detection functions (2007) is less than AIC for model with pooled detection function (2022), we base our inference upon the stratum-specific detection function model (depicted in Figure 2).

```
cutpoints <- c(0,5,10,15,20,30,40,53)
par(mfrow=c(1,3))
plot(past1.hn, breaks=cutpoints, pdf=TRUE, main="Pasture 1")
plot(past2.hn, breaks=cutpoints, pdf=TRUE, main="Pasture 2")
plot(past3.hn, breaks=cutpoints, pdf=TRUE, main="Pasture 3")
```

Always best to check the fit of the preferred model to the data.

```
Goodness of fit results for ddf object
Distance sampling Cramer-von Mises test (unweighted)
Test statistic = 0.0939637 p-value = 0.615284
Goodness of fit results for ddf object
Distance sampling Cramer-von Mises test (unweighted)
Test statistic = 0.0478569 p-value = 0.889167
Goodness of fit results for ddf object
Distance sampling Cramer-von Mises test (unweighted)
Test statistic = 0.0402974 p-value = 0.931609
```

Further exploration of analyses involving stratification can be found in the example of dung survey analysis.

Note there is a difference of 14 AIC units between the model using stratum-specific detection functions and the model using a pooled detection function, with the stratum-specific detection function model being preferrable. To be thorough, absolute goodness of fit for the three stratum-specific detection functions is checked, and all models fit the data adequately.

This vignette focuses upon use of stratum-specific detection functions as a model selection exercise. Consequently, the vignette does not examine stratum-specific abundance or density estimates. That output is not included in this example analysis, but can easily be produced by continuing the analysis begun in this example.

Knopf, F. L., Sedgwick, J. A., & Cannon, R. W. (1988). Guild
structure of a riparian avifauna relative to seasonal cattle grazing.
*The Journal of Wildlife Management*, *52*(2), 280–290. https://doi.org/10.2307/3801235

Miller, D. L., Rexstad, E., Thomas, L., Marshall, L., & Laake, J. L.
(2019). Distance sampling in r. *Journal of Statistical
Software*, *89*(1), 1–28. https://doi.org/10.18637/jss.v089.i01

R Core Team. (2019). *R: A language and environment for statistical
computing*. Vienna Austria: R Foundation for
Statistical Computing.