Birds killed by cats in Canada

I was reading this news article about causes of bird death that are related to humans and found interesting that cats is ranked at the top, with around 75% of the birds deaths, that is 200 millions per year.That was not so surprising to me, but I immediately wondered how they could estimate such a number. And how precise it could be. I mean, I am not questioning the methodology, or the result, but I knew this is not an easy thing to estimate and as such a precision measure would be important. You cannot interview a random sample of cats and ask them how many birds they kill per year. So, knowing the number of birds killed is hard, but it does not stop there, it is also hard to get a random sample of cats or estimate the number of cats for that matter. My experience was sort of telling me that this is so hard to estimate and requires so many assumptions that results would be imprecise and reader should know that. Of course, that does not go well with media stories that want to catch people's attention.

So, I tracked down the actual paper where the estimation was performed. It is a simple paper, mathematically speaking. They use many estimates, from different sources, which makes the estimation work very arduous and add challenges related to the precision of the estimates. I will go quickly through each of these estimators, although I have to say that I did not go deep into the literature used.

• This part is about the data used, its quality and assumptions made. Just a flavour, though.

The number of domestic cats in Canada, around 8 millions, seems consistent even though estimated by non-random (online) sample and even though I had a first impression that the figure were too high. But I can't really say, so.

19% of the Canadian population live in rural areas and based on information that they own more cats in average than people living in urban areas, the % of cats in the rural area was estimated to be around 1/3. I found the proportion of Canadians living in rural areas sort of high, but that comes from Stats Canada and should be precise. The thing is that Canada is huge, so even if the density of people in rural areas is low, the total population may add up to a considerable amount. The idea that they own more cats, I think that is fair too. This was gotten from a research in Michigan, so not too far from Canada, although we need to remember, again, that Canada is huge.

The number of feral cats is estimated to be between 1.4 and 4.2 million and is based in mostly unknown sources that appears in media reports. The estimate for Toronto, for example, is between 20 and 500 thousands. Such a wide interval is next to useless. This is specially problematic given that feral cats are considered to kill much more birds than domestic cats. 

Only the cats that have access to outdoor are supposed to be able to kill birds. That proportion is reported for the US in some papers and seems to have some consistency although the range used in quite wide - from 40% to 70%.

Now the number of birds killed by cats is the real problem. It seems that no good source of the direct information exists. So, the estimate is built from the reported number of birds brought home by cats, using this as the number of preyed birds. There are a few studies which reports this sort of estimate, but due to different location and methodology, I guess, the imprecision is quite high - 0.6 to 6.7 birds per year. At first even the high end of the range seems low considering that we are talking about a whole year. The range used of 2.8 to 14 seems conservative, but I cannot really say. It is very wide, though. The thing is that rural cats are usually very free, and there are reasons to believe they may kill birds very often without anybody see. Rural cat owners usually care less about their cats, but this is from my experience, that is, very anecdotal. 

They also use an adjustment factor for the birds that are killed but not brought home. The factor is difficult to estimate and a range between 2 to 5.8 was considered based on some studies. These are numbers really hard to judge, they are again, for sure very imprecise.

The estimate of birds killed by feral cat is based on the content of the stomach of the cats. It is again a very indirect method, which includes assumptions and may have large inaccuracies.  

I don't mean to criticize by listing these data sources because the fact is that many times this is all we have. We need more and more to be able to use this sort of data and be able to understand assumptions and model the unknowns.That is fine. But I also think it is important that assumptions and caveats are stated. They are in this paper, but when the findings gets translated into the popular language of the news media, they get lost, all the statistical aspect of the findings gets lost. When we say that cats are responsible for 200 millions birds killed in Canada, how precise is this? The usual reader will think it is quite precise, I mean, you will if you just read the CBC article. The paper is pretty simple, so I set out to calculate this precision. It turns out that Figure 2 is all you really need, but I wanted to have some fun, so I decided to replicate it.This is the R code, just using the information in the paper.

nsim = 10000

nPC = rnorm(nsim,8.5,0.25) # Number Pet Cats
pRC = runif(nsim,0.27,0.33) # % Rural Cats
pOd = runif(nsim,0.40,0.70) # % Outdoor Cats
BpU = runif(nsim,0.6,6.70) # Avg Birds by Urban Cats
BpR = runif(nsim,2.8,14) # Avg Birds by Rural Cats
Adjust = runif(nsim,2,5.8) # Adj. for non Returned Birds
nFC = runif(nsim,1.4,4.2) # Number of Feral Cats
KpF = runif(nsim,24,64) # Lill per Feral Cat

BKu = nPC*(1-pRC)*pOd*BpU*Adjust
BKr = nPC*pRC*pOd*BpR*Adjust
BKf = nFC*KpF
TotalBird = BKu + BKr + BKf

library(ggplot)
ggplot(tb, aes(x=TotalBird))+geom_histogram(aes(y=..density..), binwidth = 5,fill = "darkgreen")+ ggtitle("Birds Killed by cats in Canada")+xlab("Number of Birds in Millions")+ylab("Density")

quantile(TotalBird, c(0.025, 0.975))
2.5%     97.5%
107.3296 357.0416

I think despite the difference in the graph formatting, they are very similar. So, we see that the 200 Millions birds killed by cats (domestic + feral) in Canada each year is not precisely 200 MI, a 95% Interval shows it is between  around 100 and 360 million birds. It is a pretty wide interval, but it just reflects the uncertainty in the source data.

Another thing interesting in the paper is that they calculate the relative importance of each term in the equation. I thought about this a little bit, because they use regression but the calculation is not linear as we can see in the equation in the R code above. I ran the regression and got an R2 = 95%, so perhaps with such a high R2 the relative variance given by linear regression is acceptable. I don't know, this seems to be an interesting question.

Then a final point is that as we can see in the code above, the terms used in the calculation are all assumed to be independent. I am not sure how to do it any better, but this independence is also an assumption that should be considered.