Line transect estimation using R solution 💡

Author

Centre for Research into Ecological and Environmental Modelling
University of St Andrews

Published

December 10, 2024

Solution

Line transect estimation

Inspect duck nest data

Import and check the data.

library(Distance)
data(ducknest)
head(ducknest, n=3)
  Region.Label Area Sample.Label Effort object distance      Study.Area
1      Default    0            1 128.75      1     0.06 Monte Vista NWR
2      Default    0            1 128.75      2     0.07 Monte Vista NWR
3      Default    0            1 128.75      3     0.04 Monte Vista NWR
nrow(ducknest)
[1] 534
brks <- seq(from=0, to=2.4, by=0.3)
hist(ducknest$distance, breaks=brks, xlab="Distance (m)", main="Perpendicular distances duck nests")

Distribution of duck nest perpendicular distances. Should match the bar heights from table in Practical 1.

Fit detection functions

Fit the three models using proper units of distance measure.

The answer is another function convert_units. Arguments to this function are

  • distance_units
    • units of measure for perpendicular/radial distances
  • effort_units
    • units of measure for effort (NULL for point transects)
  • area_units
    • units of measure for the study area.
conversion.factor <- convert_units("Meter", "Kilometer", "Square Kilometer")
# Half-normal with no adjustments
nest.hn <- ds(ducknest, key="hn", adjustment=NULL, convert_units=conversion.factor)
summary(nest.hn)

Summary for distance analysis 
Number of observations :  534 
Distance range         :  0  -  2.4 

Model       : Half-normal key function 
AIC         :  928.1338 
Optimisation:  mrds (nlminb) 

Detection function parameters
Scale coefficient(s):  
             estimate        se
(Intercept) 0.9328967 0.1703933

                       Estimate          SE         CV
Average p             0.8693482  0.03902051 0.04488479
N in covered region 614.2533225 29.19681554 0.04753221

Summary statistics:
   Region  Area CoveredArea Effort   n  k        ER       se.ER      cv.ER
1 Default 12.36       12.36   2575 534 20 0.2073786 0.007970756 0.03843576

Density:
  Label Estimate       se         cv     lcl      ucl       df
1 Total 49.69687 2.936724 0.05909274 44.2033 55.87318 99.55677

In addition to the half normal key function, fit uniform and hazard rate models with possible adjustment terms.

nest.uf.cos <- ds(ducknest, key="unif", adjustment="cos", convert_units=conversion.factor)
nest.hr.herm <- ds(ducknest, key="hr", adjustment="herm",  convert_units=conversion.factor)

Assess absolute model fit

The goodness of fit for the basic model is shown below.

gof_ds(nest.hn, plot=FALSE)

Goodness of fit results for ddf object

Distance sampling Cramer-von Mises test (unweighted)
Test statistic = 0.0353634 p-value = 0.955416

Contrast competing models

A function useful for contrasting models is summarize_ds_models. A summary table of goodness of fit statistics for all models is created below.

# Summarise gof statistics
knitr::kable(summarize_ds_models(nest.hn, nest.uf.cos, nest.hr.herm, output="plain"), 
               caption="Model results for ducknest data set.", digits=3)
Model results for ducknest data set.
Model Key function Formula C-vM \(p\)-value Average detectability se(Average detectability) Delta AIC
nest.hn Half-normal ~1 0.955 0.869 0.039 0.000
nest.uf.cos Uniform with cosine adjustment term of order 1 NA 0.821 0.846 0.044 0.346
nest.hr.herm Hazard-rate ~1 0.981 0.889 0.050 1.660

Density estimates from the competing models

The density results from all models are summarized below.

Density estimates and confidence intervals for three fitted models.
Model DetectionFunction Density LowerCI UpperCI
1 Half-normal, no adjustments 49.70 44.20 55.87
2 Uniform, cosine adjustments 51.04 44.92 58.00
3 Hazard rate, no adjustments 48.59 42.52 55.54

Visualise shape of key functions with duck nest data

The detection function plots are shown below.

plot(nest.hn, nc=8)
plot(nest.uf.cos, nc=8)
plot(nest.hr.herm, nc=8)

Half normal, no adjustments

Uniform with cosine adjustment

Hazard rate, no adjustments

The half-normal detection function with no adjustments has the smallest AIC which provides support for this model. The \(\Delta\)AIC values for all three models is small. In general, you should get similar density estimates using different detection function models, provided those models fit the data well, as in this example.