We recently shared a couple of blog posts about using statistics in ecological sampling. One was on designing the right sampling approach to your threatened species monitoring program, and one was on the ability to detect planting losses in a revegetation setting. Both of these blogs demonstrate that a small investment in the statistical approach for these types of projects at the beginning, can pay for themselves very quickly by reducing sampling effort or producing actionable results.
But to most, statistics can feel a little abstract.
“So what if an equation says I need x number of quadrats? It doesn’t seem like enough. I’ll just do more to be certain”.
While not an actual quote, we understand this sentiment.
Using GIS and some existing spatial data on your subject of interest, we can validate sample size estimations using desktop simulations.
What is a desktop simulation?
A desktop simulation requires existing spatial records for your subject of interest (let’s say, a threatened plant) and the proposed sampling approach. That’s it. We load the spatial records into our GIS, and apply the sampling approach in a virtual, map-based environment. That is, we load real data in, and then test different sampling approaches, recording the number of your subject that it counts each time. When the result matches the maths, it stabilises and begins producing a consistent result.
Case study: The Eltham Copper Butterfly.
We recently conducted a review of the methods of estimating the abundance of Eltham Copper Butterfly (Paralucia pyrodiscus lucida) in northern Victoria. The Eltham Copper Butterfly is listed as endangered in Australia and is notoriously difficult to detect. Nevertheless, our client had a good history of spatial records of the species because every time they identified it, they recorded the abundance with a GPS.
We isolated one of the Eltham Copper Butterfly sub-populations and accumulated all of the spatial records for a calendar year. We determined that there were 442 Eltham Copper Butterfly’s counted in that site across the calendar year (we didn’t adjust for timing of year). The site was 57.3 hectares in size meaning the average density was 7.7 Eltham Copper Butterfly’s per hectare.
Our statistical assessment identified that they needed 10 samples using their technique to estimate the density of Eltham Copper Butterfly’s to within 20% of the real density. While 20% is not the most precise range in the world, it is still capable of identifying wild swings in the population density which is what was at the heart of the monitoring program. This means that with an average density of 7.7 Eltham Copper Butterfly per hectare, results in the range from 6.16 to 9.24 per hectare (±20%) would not be significant. Outside of that range would be.
For the purposes of this case study, we’ll report a limited number of results:
Recall, that the ‘maths’ said we needed 10 random samples. We simulated two scenarios that were under sampled at 6 and 8 samples. The results predicted 0 per hectare (none detected) and 2.5 Eltham Copper Butterfly per hectare, respectively. Both underestimated the Eltham Copper Butterfly density (recall that is was known to be 7.7). Though, we should make it clear that under sampling does not necessarily mean underestimating. If the randomly placed samples randomly occurred over a dense area of the species, it would overestimate the density.
Next we ran three simulations with the correct number of samples (10) which yielded results of 7.6, 7.6 and 8.4 per hectare. Not only are the first two estimates very close to the actual number, but the final result is well within the 20% range mentioned above.
Finally, we ran a simulation where we over sampled with 14 samples and produced a result of 6.3 per hectare. Again, within the 20% range. If you over sample based on your strict protocols of your monitoring method, there is no issue with oversampling. In fact, from a statistical perspective, it is good, so long as your samples remain independent. However, in the real world, this comes at the cost of resources - both human and budgetary so is often avoided and not necessary.
The results are shown below.
Desktop simulations of Eltham Copper Butterfly monitoring using spatial data for a site in northern Victoria.
This simulation gives confidence to those delivering the monitoring program that they will produce accurate, repeatable results.