ISSS608 2017-18 T3 Assign Chan En Ying Grace Did Rose Pipit kick the bucket

“Mine dear rose pipits, whence did do thou vanish?”

Background

Methodology

Did Rose Pipit kicketh the bucket?

Which song belongs to thee?

Conclusion

Cluster Visualisation: "Did Rose Pipit actually kicketh the bucket?"

1. Data Overview

Different bird species were found throughout the preserve (left), but Pipits were found typically in the northeastern side of the preserve – that is, closest to the alleged Dumping Site marked by the triangle below.

We can also see a visible Pipit cluster around the Dumping Site (right). This is likely why the alleged dumping by Kasios was “accused” to cause the death of the Pipits since the Pipits were found at that location.

2. Clustering by Species

To characterize the pattern relative to the alleged dumping site (blue triangle), the following facet plot shows the clustering patterns by Bird Species, independent of time.

From the cluster locations, we can see that the Rose-Crested Blue Pipits are clustered around the alleged dumping site, explaining why the 15 test birds provided are claimed to be Rose-Crested Blue Pipits to prove the allegation wrong. We can use this facet plot to have a good overview of other bird species’ cluster locations, such as the Ordinary Snape and Lesser Birchbeere being also clustered near to the Dumping Site.

3. Assignment of Treatment & Control Groups

If the dumping indeed took place, one would expect that other birds species in this dumping area would also decrease in population as they would migrate elsewhere or die from the dumping substance, not just affecting the Rose Pipits.

Other species that are dominantly clustered around the dumping site include the Ordinary Snape and Lesser Birchbeere. These populations should also be affected by the dumping, if dumping indeed happen.

We will thus use Ordinary Snape (OS) and Lesser Birchbeere (LB) as our Control Group, and Rose-Crested Blue Pipits (Rose Pipit) as our Treatment Group.

4. Rose Pipits Only – Across the 4 Seasons

Just like other bird species, Rose Pipits population peaked in the Spring. When we analyse its population across time, we should bear in mind that seasonal or monthly population changes would not help us determine the true population patterns accurately as change in population is likely due to seasonal migration, than dumping. Thus, we will track its population changes across Year, than across month or season. However, if we later wish to zoom into a particular year, we can look at month/season.

5. Rose Pipits Only – Across Time

There are two observations here.

a. First, the Pipit population increased in 2013 to 2017.

In 2013, the cluster appeared right at the alleged dumping site. We call this the Pipit home range, where the Pipits tended to live and thrive. Population soared in 2015 and then declined gradually till 2017.

However, it is important to note that this is a short 5-year period and prior to 2013, Pipits were few and far between. One possible interpretation could be that Pipits only found the Boonseng Preserve as their home in 2013, and lived elsewhere prior to this. Another possible interpretation could be due to data quality issue. Although it is mentioned that the data is well represented, an overview of the data showed signs of data quality, especially in the earlier years (1990s-2000s) where birds across all species were reported to be very few. Due to the incompleteness of data, we will focus on years 2012-2017 for a more reliable study. We will also omit year 2018 since the data provided is till end of Q1 only.

b. Second, the home range moved away from the dumping site, from 2015 onwards even though that was the year of peak.

This could be signs of dumping. It could be that the dumping caused Pipits to fly slightly further away, but the long-run effect was that the birds population dwindled as they struggled to survive given the decline in population size (as the cluster got smaller). It could be that only those that flew away from the site survived. But given that the Kasios company provided some Pipit bird calls, we should also analyse to see if it really belongs to Pipits, and whether these calls were obtained around the dumping site or far away from it. If far away, then it could support the dumping claim.

6. Kernel Density Plot to visualize clusters (All Birds & Rose Pipit)

To visualize the above clusters more clearly, we plot the Kernel Density to visualize the cluster intensity, a method to compute the intensity of a point distribution (Silverman, 1986).

If we look at Rose Pipits (right), the Kernel Density plot gives us clearer visualization that there were 2 (not 1!) clusters formed. This could possibly indicate some sort of migration from one to the other. As the bottom cluster (the one located away from dumping site) looks bigger than the top cluster (at dumping site), it could also be a sign of dumping, as dumping chemicals could cause the population to be smaller and contributed to the Pipits' migration from its original homerange to a new homerange.

To verify this, let us do a Kernel Density plot for Rose Pipits across time for a six-year period from 2012-2017.

7. Kernel Density Plot of Rose Pipits Across Time (2012-2017)

Two Clusters Become One; New Cluster "overtook" Old

Interestingly, when we plot the Kernel Density across time, we can see that there were originally two clusters in 2012 – one at the dumping site, and one slightly away from the dumping site. The cluster at the dumping site grew in size until 2014, while the cluster away from the dumping site "took over" the growth and started to grow from 2014.

Old Cluster Vanished in 2015

More importantly, the cluster at the dumping site vanished totally from 2015 onwards, leaving only the cluster away from the dumping site, which grew in size. This could indicate a movement of birds from the dumping site cluster towards the cluster away from the dumping site, possibly indicating a trend of dumping.

8. Spatial Point Pattern Analysis (Across Time)

To more objectively determine the strength and significance of the clusters, we apply density-based followed by distance-based measures to test for cluster statistical significance, that could shed light towards the dumping allegation – namely the Quadrat Test, K-Nearest Neighbour as well as the K-Function.

a. Quadrat Analysis

Clusters still significant, but became less compact from 2015

Rose Pipit clusters were statistically significant at the 1% level of significance across 2012 to 2017, when a quadrat analysis was applied with the alternative hypothesis set as clustered. However, the Pearson X2 statistic peaked at 2015 and reduced after that, showing signs of reduction in cluster (though still statistically significant)

b. Nearest Neighbour, followed by Clarke-Evans Test

Clusters still significant, but started to disperse after 2015

Clusters were most compact in 2015, where majority of each Pipit’s neighbours were within 10units distance away. From 2016 however, the neighbouring distance expanded to beyond 10 towards 40. Though clusters were statistically significant from 2012 to 2017 (applying the Clarke-Evans test), the clusters started to disperse after 2015 which was the suspected year of dumping. This supports the same findings above which saw that year 2015 had the strongest/most compact cluster.

Note: When we conduct the Clarke-Evans test, though all clusters were significant, we see that the coefficient was highest in 2016 (not 2015). Nevertheless, 2015 saw the most compact cluster (smallest distance between neighbours).

c. K-Function

Cluster lost its significance in 2017, for radius <5

Likewise, when a K-Function was applied, the size/strength of clusters reduced overtime after year 2015 as the grey shaded envelope increased.

Eventually in 2017, the cluster lost its significance when radius was below 5. Clusters were significant only when the radius was 5 or greater. In other words, the cluster became less compact after 2015.

That said, we note that in year 2013 and 2014, the clusters were not as strongly significant for small values of radius (i.e. compact clusters not significant). Ceteris paribus, this is because there were two clusters if we refer to the earlier Kernel Density plot, rather than a decline in Pipit population, so this is not a cause for concern.

9. Did Rose Pipits die from the dumping chemical? If not, where did they flock to?

Rose Pipits could either have left the Preserve as a flight mechanism, or that they were defeated and simply died and dwindled in population due to the chemical.

I don’t think it had left for another place, but rather, I think it slowly dwindled in population (i.e. Rose Pipits kicked the bucket). Because if it left, we should see a trend of them flying away from the Dumping Site and moving towards an edge of the Preserve to migrate to another area outside of the Preserve, for example. It was unlikely for the flight to take place immediately and we should see a staggered flight pattern across the months as birds migrate elsewhere.

Facet Grid Plot

To test my hypothesis, it'd be ideal to do a Kernel Density plot by month for 2016 and 2017. Unfortunately, the plot is not possible for small data points (as some months only have 1-2 birds of data). So let’s start off with a Facet Grid Plot to see if there’s a trend where the birds are migrating. Later on, we will do the Kernel Density Plot but by quarter.

The pattern is not so clear in 2016. Birds moved away from the dumping site but also dwindled at that location.

However, in 2017, this pattern is clearer. The remaining birds were flocking to the South East of Kasios Island, even in Spring (April). This could be because their alternate homerange is in another region of the country, southeast of Kasios.

Kernel Density Plot – by Quarter

However, this is not that convincing. Let’s attempt to run a Kernel Density Plot - instead of by month (which we lack data of some months especially in the 2nd half of the year), we plot the kernel density for each quarter in 2016 and 2017.

Note that Q3 2016 and 2017 data is too few for a Kernel Density plot, so we have no choice but to omit them from our analysis.

Why did Pipits fly back to the dumping site every Winter?

Interestingly, the birds actually flew back closer to the dumping site every end of the year (winter).

Could it be that the dumping was not once-off, but during certain parts of the year e.g. did dumping took place in Q3, explaining the absence of birds? Or was the absence of birds due to seasonal changes?

Well, when we look at the Pipit distribution by season in the earlier graph, we can see that Summer should be the 2nd highest peak season of Pipit population. There is no reason why it should be 0 in population. Just possibly, this could be signs of dumping takes place every year in Spring/Summer from 2015 onwards.

However, I must note that the data points are too few to analyse the birds in 2016 and 2017 even by quarter and make such concusions. Even by visualizing the facet plot, it is clear that the KD plot can be not representative because of the few data points. Instead, let us focus on our Control Groups to shed greater light onto the fate of our Rose Pipits.

10. Were Rose Pipits the only ones affected?

Rose Pipits could either have left the Preserve as a flight mechanism, or that they were defeated and simply died and dwindled in population due to the chemical.

Treatment vs Control Groups

If there were dumping, even our Control Groups should also be affected unless there were biological reasons why they were “immune” to the chemical. Interestingly, our Control Groups showed that they were not as affected by the Dumping Site. The OS & LB were chosen as control groups because they were found to be clustered around or near the Dumping Site.

a) Ordinary Snape (Control Group 1)

1. For the Ordinary Snape birds, their homerange remained near the Dumping Site, unlike the Rose Pipits whose homerange moved away from the dumping site.

2. Moreover, the Ordinary Snape increased in population, unlike the Rose Pipits that decreased.

Facet Plot

This could be a sign that dumping did not take place since the OS were not affected by it. However, we cannot rule out dumping. Because this could be also demonstrate Survival of the fittest, where the OS were less affected by the chemical of the dumping site, and were the stronger species that survived since it did not seem to be as affected in the same period.

Kernel Density Plot

To objectively confirm this, we apply the Kernel Density Plot across 2012-2017 to confirm the significance and size of the clusters. True enough, the homerange did not move and the clusters did increase very slightly in 2016-2017 as can be seen by the smudging of the kernel density plot towards the dumping site.

K-Function

The significance of clusters also grew from 2012 to 2017, thus confirming our hypothesis that the Ordinary Snapes were not affected by the dumping, if dumping did take place.

K-Cross

For more rigorous analysis, we will also perform the K-Cross between the Rose Pipit and Ordinary Snape.

The aim of the bivariate analysis is to identify if the spatial distribution of Ordinary Snape is independent of the distribution of Rose Pipit (Null Hypothesis). An estimate of Kordinarysnape,rosepipit(r) is a useful summary statistic in exploratory data analysis of a multitype point pattern. If the migratory behaviour of Ordinary Snape were independent of the migratory behaviour of Rose Pipits, then Kdrdinarysnape,rosepipit(r) would equal pi*r^2. Deviations between the empirical Kordinarysnape,rosepipit(r) curve and the theoretical curve pi*r^2 may suggest dependence between the points of Ordinary Snape and Pipits.

"Close" Dependence pattern found between Pipits & OS

From above, our observed K-cross curve above the theoretical curve means that type j points (Ordinary Snapes) prefer to cluster around type i points (Rose Pipits). That is, Ordinary Snapes are found closer to Rose Pipits than would be expected under complete spatial randomness.

It looks like there is strong dependence between the 2 species, but let's look at it by Year to better understand how this dependence changes across time, in relation to the suspected dumping year of 2015.

K-Cross Across Years (2012-2017)

When we compare across years from 2012-2017, we can see that the dependence between Pipits & OS was strongest in 2015. If we recall, this is the year of peak population for the Rose Pipits. In 2016, the 2 species were still spatially dependent. But in 2017, they were spatially dependent only up till radius = 40.

What does this imply? This could mean that the 2 species were spatially close, but yet, Ordinary Snapes thrived and Pipits started to dwindle. If dumping too place, then the OS must be affected too, especially in 2015 since the 2 species were spatially dependent! However, the OS were not affected in population and homerange. Thus, we cannot say for sure that dumping too place.

Well, possibly, the chemical (released in 2015) only affected the Rose Pipits.

b) Lesser Birchbeere (Control Group 2)

1. As for the Lesser Birchbeere, its population dwindled slightly.
2. But its homerange moved even closer towards the Dumping Site, as can be seen by the Kernel Density plot.

Since the deaths were only limited to Rose Pipits, one hypothesis is that the dumping did not take place.

Another hypothesis is that the dumping did take place, but the chemicals being released were only affecting the Pipits, where the other species survived and some even thrived. Possibly because Pipit population was reduced, there could be less competition for food so other species thrived over there.