Tuesday, 27 March 2018

Estimating conservation metrics from atlas data: the case of southern African endemic birds - the images

The publication "Estimating conservation metrics from atlas data: the case of southern African endemic birds" did not include several charts in color and so they are hard to interpret. Here they are for anyone who is interested.

Figure 2: Reporting rate change for 58 South African endemic bird species plotted against change
in reported range between SABAP1 and SABAP2. Point size represents the absolute value of
the mean z-score.

Figure 3. Reporting rate change for seven South African endemic bird species plotted against
change in range between SABAP1 and SABAP2. This figure shows the lower left hand corner of
Figure 2 in more detail - species qualifying as those of conservation concern due to range and
population decrease. Size of the points is weighted by mean z-score.

Figure 4. Presence/absence ratios for 58 endemic bird species for each atlas period. Species on the
negative end of the x-axis are generally infrequently reported, while those on the positive side are
commonly reported: negative values indicate species reported from less than 50% of cells. Shading
represents the 95% confidence interval of the regression between the values on the two axes.
Species below the 1:1 line (black diagonal) are species reported less frequently in SABAP2.
Selected species classified as Least Concern with a lower reporting rate in SABAP2 are labelled, as
are selected species with threatened status with higher reporting rates in SABAP2.

Figure 5. Mean population change across all species within each grid cell (left panel). N for each
grid cell is indicated by endemic species richness (right panel). Grids not included in this analysis
due to insufficient coverage (<2 are="" atlas="" black="" both="" for="" lists="" p="" periods="" points.="" white="" with="">

Figure 6. Connectivity (left-hand panels) and corrected connectivity (connected score/log(range);
right hand panels) for southern African endemic bird species. The lower two charts are the lower
left sections of the upper charts, indicating species with small ranges and low connectivity; QDGC
= quarter degree grid cells.

And these didn't make it into the manuscript, but are interesting:

Firstly median reporting rate within a species range:

And how large is the species range:

Why and How does the South African Bird Atlas Project (SABAP2) work in getting conservation metrics?

SABAP1 and 2 are two amazing citizen science projects: millions of bird records compiled by birdwatchers and submitted to a central database managed at the University of Cape Town.

Birdwatchers are requested to submit lists after surveying a set area (pentad) for a minimum of 2 hours, ideally covering all habitats within the 8x8 km pentad. These are known as full protocol cards.

The data can be used for many purposes, but my interest is focused on the information that can be acquired for supporting conservation decision making.

For this we need an index of relative abundance: how common is the bird? May seem like a simple question: but it isn’t. There are many problems that need to be overcome in interpreting the data that is part of the listing process.

In its simplest form, the basic unit of relative abundance is known as the ‘reporting rate’. This is the proportion of a set of lists that a species appears on. For instance, for a pentad, if 10 lists have been submitted, and a species is recorded on 6 of these, then the reporting rate is 6/10 = 0.6 (or 60%).

So our first challenge: what happens if a pentad has been surveyed only once? Then reporting rate can only be 0 (not recorded) or 1 (the species is recorded). These numbers are not very useful, so the more lists for a pentad, the better: the closer we come to a realistic probability that you will record a species should you go to a site.   Unfortunately, most of southern Africa is either inaccessible, or has few bird watchers. So much of the country is either not visited, or has been visited only once.

Here is a chart that illustrates this for the first SABAP1 conducted from 1987-1992 and SABAP2 which was initiated in 2007 and is ongoing. Here, the sampling unit is the Quarter Degree Grid Cell (QDGC), the sampling unit of SABAP1: each QDGC contains 9 pentads. The x axis (number of cards) is truncated at 50 in each case: some pentads have many more cards than this.

Both SABAP1 and SABAP2 have a very large number of QDGCs sampled only once. As the sampling effort of SABAP2 is now higher than SABAP1, there are a very large number of cells that have been visited only once (nearly 1500!).

In this paper below I focused on calculating single index parameters of change to compare how species were doing between atlas periods:

Estimating conservation metrics from atlas data: the case of southern African endemic birds

For reporting rate change, I calculate the mean reporting rate across all QDGCs for SABAP2, subtract the mean of reporting rate from SABAP1, then divide that results by the mean of the reporting rate from SABAP1. A positive number indicates an increase in reporting rate (inferring increased abundance), while a negative number infers decreased abundance. For example, if reporting rate for SABAP2 was 100%, but only 50% for SABAP1, then the change is 100% (i.e. 100-50 / 50) i.e. a doubling in probability of reporting. Zero means no change. It might seem complicated, but it is the simplest way to look at change: there are many many more complicated ways. However, reporting rates make sense to most people, since they are proportions and percentages. Other metrics can get rather esoteric (z-scores, standardized population change, occupancy modelling probability output). And rather importantly, there is good agreement between these in terms of what they are telling us.

To create summary reporting rate figures, I did not want to use QDGCs that had been surveyed only once to avoid the bias of cells with reporting rate of 0 or 1 only, so I filtered data to include QDGCs that were filtered only twice or more for both atlas periods.

But what happens if I had not filtered at all, or if I had filtered more?

Here I illustrate what the difference is in overall reporting rate between atlas periods using different filters, from no filter all the way to using only the subset of QDGCs with 25 or more lists. My study subject of choice is the African Black Oystercatcher, South Africa’s Bird of the Year for 2018. This coastal bird has been recorded in 177 QDGCs over the course of the two atlas projects.

We can see in the above chart that without applying a filter that reporting rate change is the lowest value: 11%, while filtering the data so at least 1 card was atlased during both projects gives us the highest value (c18%). After that it is fairly stable: around 15% increase, no matter what the filter.

Similarly, range change shows an odd result for unfiltered data: here range change is negative for unfiltered data (implying a range contraction), but hovering around a 10% increase in range for most other filters. So it looks like filtering is a good idea to get rid of some of that instability introduced with too many 1s and 0s. A minimum filter would be 2 or more lists for both atlas projects.

But what about sampling bias? This is a big problem with atlas data. Most atlasing is conducted around urban areas, and these are likely not representative of the wider landscape. Also, we need to deal with spatial autocorrelation, because sites close to each other are likely not independent. So in order to get a better idea of how much reporting rate has changed between atlas periods, here I appeal to the central limit theorem and sub-sample randomly using 50 QDGCs from the range of the Oyc 1000 times i.e. I calculate a reporting rate change based on 1000 random draws from the Oyc dataset, each time calculating a change in reporting rate value. I get an answer with mean of 16% plus or minus 9%. So a 15% increase seems reasonable using the entire data set wasn’t too bad. To think of it simply, you are 15% more likely to see an Oyc now in its range than you were during SABAP1. It isn’t a huge increase, but it is on the positive side, which is good news for Oycs.

For the above random sampling, 50 seems like a good minimum value: lower than this and standard deviation starts to increase i.e. we start to become less sure about where a reasonable answer lies. This is because large numbers are key to this process, and so inference for species with small ranges is a bad idea when it comes to using atlas data.

Let’s get back to that Law of Large numbers. The law of large numbers is a principle of probability according to which the frequencies of events with the same likelihood of occurrence even out, given enough trials or instances. As the number of samples increases, the actual ratio of outcomes will converge on the theoretical, or expected, ratio of outcomes. I.e. The Law of Large Number states that when sample size tends to get very large, the sample mean equals the population mean.

With the SABAP projects, we have large numbers. Almost certainly, some of the answers we are getting from relative abundance at the pentad level will be wrong, but using them all together we start to satisfy the law of large numbers. Here I illustrate for a species with theoretical relative abundance of 65% how many pentads we would require that have been sampled 4 times (giving us pentads with possibilities of 0, 1, 2, 3, 4) before the mean value starts to become acceptable enough that we can be confident it represents the ‘real’ value. Note that the confidence intervals are pretty narrow by about 30 pentads already.

And the last question I will answer in this post is: how does presence/absence data (binomial distribution) i.e. 0s and 1s eventually create a value that is between 0 and 100? Here, the Central Limit Theory is what is important.  The Central limit Theorem states that when sample size tends to infinity, the sample mean will be normally distributed.  For our example of pentads with 4 checklists, see how quickly the distribution becomes normal. Here the p value is a significant deviation away from normal. We get lift off (i.e. normal data) once we start hitting 30 pentads. Certainly then, 30 (pentads or QDGCs) is the minimum that would be required to make inference from atlas data for a population.

Don’t forget though: single value conservation metrics are not the whole picture, they are simply something easy to grasp in a complex world. But more about complex modelling another day.

Monday, 19 March 2018

Bloupunt Ascent

The break of dawn was heralded by squabbling familiar chats. We had slept well under winter down duvets at the Rock Cottage of Meijer's Rust, just to the west of Meiringspoort. All the same, day three of the most recent cold front soon had us dressed in jackets and beanies. I was vaguely surprised that we were ready to go by 7am: an early night brings its own rewards.

Our target for the day was the peak of Bloupunt, marked as 2066m asl on the map of the Klein Karoo by Peter Slingsby. Anja and I had failed to make the summit two years earlier:

It is an impressive peak, most beautiful when approaching Meiringspoort from the Klaarstroom side in the early morning.

And the start of this attempt was also looking very touch-and-go. Anja was just getting over a bout of nasty flu and had been off the tread-mill for 2 weeks. I’d been doing way too much laptop time, despite the occasional jaunt into the mountains or early morning job. But more to the point: a strong north-easterly was blowing mist over the mountains, and the peak remained concealed.

However, a few factors were in our favour: a massive veld-fire in December 2016 meant the fynbos was thin on the ground. Also, we had a plan of attack based on our previous attempt. And this time the Jimney was working, so we were able to drive about 2km from the Rock Cottage towards the campsite. However, the last section is all washed out due to the floods that closed Meiringspoort a year ago, so we couldn’t get all the way. Never-the-less, we were cautiously optimistic with our first steps northwards.

We chose a line of approach that would keep us on the south-west facing slope out of the blast of the mornings wind. Still, there was little need to rush, as the low lying cloud seemed none-to-keen to dissipate. As such we dawdled our way up at a comfortable pace, stopping frequently to admire honeybush, Tritoniopsis and a few other smatterings of late summer flowers. And record Rockjumpers and siskins. We made Bloupunt Junior at about 10:30, and decided for an early brunch in the shelter of some rocks to see if the cold winds would blow out. And our patience was rewarded: the mist blasting over the north-east face abated, and a line towards the summit could be seen.

Our traverse across the ridge to the peak was made more interesting when our line of approach topped out over a 10m cliff. Faced with up or down, we chose up, skirting the wet rocks nervously towards the summit, not sure if we’d have a way around. Luckily, we managed a route across eventually, close to the north-east face. Then the way to the top was more or less straight-forward: a watsonia covered slope of 40-50 degrees, with creek bubbling away under the rocks in the nearby valley.

And we smiled more broadly than the gods that had cleared the weather from our path on reaching the first summit at 2066m at 1pm, with clear views over Karoo, Little Karoo and west and east along the magnificent Swartberg range. The true summit, a small walk away stands about 30m higher. And there we stood, against the odds, with cold but splendid weather and a feeling of great satisfaction!
The descent was fairly straightforward: the Bloupunt spur comes down close to the old Meijers Rust campsite. It just felt a very, very long way before we got to the Jimney, sitting at 900m, at just after 5pm. Those fitter and younger should have no problem with this hike.

Fresh at the start, about half a km from the old campsite

Slightly pensive at the start with the cold wind and low cloud

Honeybush and Flame Erica

Waiting for the mist to lift

The view Westwards. Supposedly Tierkop is higher, but I don't think so. 

The veld on the Karoo side still looks barren from the fires

Pine tree felled with a pen-knife 
The mountain gives this drift through Meiringspoort its name

Route marked by birds: the ascent the eastern spur, the descent the western line.

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