## The detection of species and their abundance

Update (this has now been published):

McCarthy, M.A., Moore, J.L., Morris, W.K., Parris, K.M., Garrard, G.E., Vesk, P.A., Rumpff, L., Giljohann, K.M., Camac, J.S., Bau, S.S., Friend, T., Harrison, B., and Yue, B. (2013). The influence of abundance on detectabiliy. Oikos 122: 717–726.

This post is about a new paper in Oikos (Early View). Please email me if you would like a copy (clicking on the link should open your email client with an email already written).

How hard do we need to look to be sure a species is absent when it is not detected? This question is fundamental in ecology. It is relevant when determining the appropriate level of survey effort, when compiling lists of species, when determining the extinction or absence of species, and when developing surveillance strategies for invasive species.

Without sufficient survey effort, species are not detected perfectly. Imperfect detection arises because species may be temporarily absent, hidden from view, or simply require extra effort to find. The detectability of species can be defined by the rate at which individuals of a species (or groups of those individuals) are encountered.

Detectability of species will increase with abundance, all else being equal. But what is the nature of that relationship? We present a model of this relationship, with the rate of detection being a power function of abundance (Fig. 1). The exponent for this function (b) will equal 1 if individuals are encountered independently of one another. When clustering of individuals increases with abundance, we expect this exponent to be less than 1, but greater than 0.

As values for the scaling exponent approach 0, the detection rate becomes less sensitive to abundance (Fig. 1). Knowing how detection rate scales with abundance can assist when determining detection rates of rare species. This is important because detecting rare species is often important, yet estimates of detection rate are often most uncertain for these species. A scaling relationship would allow extrapolation of detection rates to cases when species are rare.

Figure 1. Examples of three functions for how detection rate (lambda; expected number individuals detected per unit time) varies with density (n). The exponent b controls the strength of the relationship. The functions were of the form $\lambda=0.25n^b$.

Our paper describes the development of our model of how detectability scales with abundance, and we used three field trials to estimate the scaling exponent. The results were consistent with our expectation that the scaling exponent would lie between 0 and 1. And as expected, a value close to 1 was obtained in a study that was designed to conform to the assumption of a random distribution of individuals.

The field trials were conducted in a remnant of eucalypt woodland in Royal Park near The University of Melbourne where searchers looked for plants and coins (Figs 2 & 3), in an exotic grassland in Royal Park (Fig. 4) searching for planted Australian native species (Figs 5 and 6), and in eastern Australian forests searching for frogs (Fig. 7).

Want to know more? Please read the paper. Email me for a copy.

Figure 2. A remnant eucalypt woodland in Royal Park. The focal chenopod plant species (Fig. 3) are the main components of the ground cover. Times to detection of four of these species and two denominations of coins were recorded within 10 quadrats. Students from the subject Environmental Monitoring and Audit at The University of Melbourne and Peter Vesk conducted the searches for this trial.

Figure 3. The four chenopod species and the two denominations of coins that were the focus of the study in the remnant woodland (Fig. 2).

Figure 4. Five Australian native species were planted in an exotic grassland in Royal Park (Figs 5 and 6), and times to detection were recorded for nine quadrats. The arrow points to the base of one of the planted individuals of Lomandra longifolia among the mass of exotic grasses. Expert botanists conducted the searches for this trial.

Figure 5. Pin-pointing the randomized location at which to plant a Dianella longifolia (in red bucket) within a quadrat at Royal Park. The three field assistants are flanked by two of the study’s authors (Georgia Garrard on the left and Joslin Moore on the right).

Figure 6. The lead author, Michael McCarthy, planting one of the specimens in a randomized location within one of the nine quadrats of the Royal Park trial.

Figure 7. Bundaroo Creek in southeast Queensland, one of the sites used in the detection study of frogs, and three of the species: the great barred frog Mixophyes fasciolatus; the cascade treefrog Litoria pearsoniana; and the red-eyed green tree frog Litoria chloris. Surveys were conducted by Kirsten Parris with the assistance of research assistants.