CommentaryUsing conditional circular kernel density functions to test hypotheses on animal circadian activity
Highlights
► We describe conditional circular kernels to test hypotheses in animal activity. ► The models allow control of the smoothing parameter and density isopleth. ► We apply our models to camera-trap data on large mammals from the Pantanal. ► The models adequately describe the timing of main activity peaks. ► Activity range and activity overlap prove useful in comparing the species.
Section snippets
Circular kernel density estimation
Nonparametric kernel density estimation is a widely used technique for nonparametric estimation of densities based on a data set (Silverman 1986; Wand & Jones 2005). Kernel density estimators for circular/directional data sets are discussed in several studies, such as those of Hall et al. (1987), Bai et al. (1988), Prayag & Gore (1990), Hendriks (1990), Kim (1998) and Klemelä (2000). Because we are interested in estimation on a circle, that is, circular data, we can restrict our attention to
Testing the Effect of the Parameters on the Activity Range and Overlap
The analytical methods described here were applied to data obtained through camera-trap monitoring conducted at the Nhumirim Research Station (18°59′S, 56°37′W), in the Pantanal wetlands of Brazil. The study was approved under license number ICMBio-21560-1 issued by Brazil's federal environmental agency. We established a 50-trap-station grid, with camera traps (Tigrinus Equipment Research Ltd, Timbó, Santa Catarina, Brazil) systematically placed 1.5–2 km apart, covering 80 km2. The entire grid
Results
The graphic representation of the activity patterns fitted using our circular kernel approach described the raw data distribution in accordance with our previous expectation, both from field experience and from the exploratory analysis of the raw data (Fig. 1c, d; Appendix, Fig. A2). The estimated activity range conditioned to any given isopleth was smaller for higher κ values (overfitted functions) for all species (Fig. 1a, b; Appendix, Fig. A3). However, this tendency was stronger for species
Case Study: Activity Ranges and Overlap among the Invasive Feral Hog and Two Peccary Species
The feral pig, Sus scrofa, has been introduced worldwide and is considered to be one of the most harmful invasive species in the world, causing damage to populations, communities and ecosystems (Lowe et al. 2000). As it was introduced in the Pantanal approximately 200 years ago and shares several ecological, behavioural (Kiltie 1982; Desbiez et al. 2009), morphological and physiological (Bodmer 1991; Sicuro & Oliveira 2002; Elston et al. 2005) features with the South American peccary species,
Activity range and activity overlap models
The major advantages of using kernel functions to fit activity data are related to their continuous and circular structure. These factors allow us to avoid problems associated with the arbitrariness of the timescale categorization and definition of the origin (usually noon or midnight in linear approaches). Additionally, as nonparametric functions, they can adequately fit either a bimodal or multimodal pattern, which are both widespread among animals.
For our purposes, the automated smoothing
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