What’s the relationship between a species’ abundance and an observer’s chance of spotting it?
By Mick McCarthy (This article was first published in the February 2013 issue of Decision Point, The Monthly Magazine of the Environmental Decisions Group)
Strange scenes were recently reported in Royal Park next to Melbourne Uni. People were spotted planting tiny native plants in seemingly random patterns in the grass. And nearby these same people were said to have been dropping five and ten cent pieces in the bush. But there was method in this madness. We were preparing an experiment that would help us understand the relationship between detectability and abundance.
How hard do we need to look to be sure a species is absent when it is not detected? Detectability lies at the heart of much ecology and environmental decision making. This question 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.
All else being equal, detectability of species will increase with abundance. The more individual specimens there are in an area you’re searching, the more likely you will spot at least one of those individuals. But what is the nature of that relationship? It’s important to understand the relationship between detectability and abundance because it can be used to determine an adequate survey effort. But the nature of this relationship has received relatively little attention in the detectability literature.
So, we set out to model the relationship between detectability and abundance, and then evaluated that model using field data. The time it takes to detect a species is equivalent to the time to detection of the first encountered individual of that species. Therefore, the model is based on the time it takes to encounter each individual at a site, and then finding the minimum of those times.
If individuals are encountered randomly, we show that the average time to detection of the species will be inversely proportional to abundance. This is equivalent to the rate of detection increasing proportionally with abundance. If the degree of clustering of individuals increases with abundance, then the detection rate will still increase with abundance but less than proportionally.
Therefore, we model the rate of detection as 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.
“How hard do we need to look to be sure a species is absent when it is not detected? Detectability lies at the heart of much ecology and environmental decision making.”
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 using different measures of abundance. 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.
We tested the model’s scaling relationship with empirical data from three independent field studies. The first study focused on detecting naturally occurring chenopod groundcover plants in a red gum remnant in Royal Park (near The University of Melbourne). Five- and ten-cent coins (19mm and 24mm in diameter respectively) were also placed haphazardly over the site. Because of the possibility that surveyors might misidentify species and the relatively high cover of some of the target species, the coins were used as a benchmark for which identification was certain and occurrence was low. The searchers were mainly masters students studying at The University of Melbourne.
The second study examined the time to detection of randomly planted species across an abundance gradient. Five native species were planted at known densities in nine quadrats in Royal Park. We used more masters students for this study, but we also had experienced field botanists, including some of Australia’s most experienced. Planting occurred approximately two months prior to the search experiment so that disturbance due to planting was less obvious to searchers.
And the third study examined the relationship between the probability of detection of forest stream-dwelling frogs via audio recordings of frog calls, using abundance data measured by the number of individuals observed during nocturnal field surveys. These data were collected in the 1990s as part of Kirsten Parris’s PhD on stream dwelling frogs of eastern Australia. The detection data were analysed using statistical models to estimate the scaling relationship and determine whether it conformed to the assumptions of the model.
Our theoretical model places bounds on the abundance-detectability relationship, and provides a means of extrapolating detection probabilities to rare species with greater confidence. The model is useful when assessing the likelihood that non-detection represents a true or false negative, when allocating search effort to detect rare species, or when estimating abundance from detection time and search effort with greater precision.
Common field applications, such as threatened species surveys for development proposals, and eradication or control measures for invasive species would benefit from these applications. In these, detection of rare species is important, and this model helps determine what the detection rate of these species is likely to be if they are present.
McCarthy MA, JL Moore, WK Morris, KM Parris, GE Garrard, PA Vesk, L Rumpff, KM Giljohann, JS Camac, SS Bau, T Friend, B Harrison & B Yue (2012). The influence of abundance on detectability. Oikos. DOI: 10.1111/j.1600-0706.2012.20781.x
- The detection of species and their abundance (mickresearch.wordpress.com)
- ￼Detecting species without species-specific guides: ￼a new, trait-based model of detectability (qaeco.com)
- Designing and implementing fauna surveys (qaeco.com)