### Tennessee Cave Survey - Caves Described over Time

I'm often asked, "How many caves are there in Tennessee?" What they are really asking is, "how many caves do we know about in Tennessee?" or "how many caves have been described in Tennessee?" I like to say "described" as opposed to "discovered" since most caves that are newly described were likely known to historic and prehistoric people. Sometimes there is direct evidence to support this.

The simple answer to the question is to state the number of caves as it was described in the last Tennessee Cave Survey data release. But a more thorough answer would note that number changes annually. Let's explore just how much it has changed, and maybe speculate on how much it will change into the future.

History of Cave Documentation in Tennessee

At some unknown date in 1973, the Tennessee Cave Survey incorporated. Based on the scattered notes I was able to determine that at that time, there were exactly 1,163 described caves in their dataset.

By 1987, the TCS was managing records for exactly 4,663 caves. That's exactly 3,500 more than when TCS incorporated 14 years earlier.

I arrived on the scene with the TCS in 2006 when we were still below 10k described caves with 9,107. It would be 2014 when we finally reported more than 10k (10,067 to be precise). In a short period of time this number grew 11,283 in 2020.

I take you on this brief walk down the history of our organization to make a point. We cannot continue to find new caves forever. At some point, we will run out of caves with natural entrances, and caves with entrances obvious to us as being able to be enlarged to permit entry.

Estimating Cave Totals by Regression, Part 1

Let's start with an observation that is much tossed around in the caving community about caves with no entrances. I am paraphrasing, but it goes something like, "For every cave that has an entrance, there are 10 that do not". How did we arrive at this number? I don't know. And I cannot speak to its authenticity. I think someone was perhaps making a point about there being a lot of things that are unknown.

Could we estimate the number of known caves using data on the number of cave entrances that we do know of? For example, if we know how many caves have 1 entrance, how many caves have 2 entrances, and so on, can we estimate the number of caves that have zero entrances?

Depending on what trendline we choose to fit our data with, we end up with wildly different numbers, each of which are obviously incorrect. If we use linear regression we end up with an R²=0.336. A logarithmic fit looks good, has an R²=0.616, but never crosses the Y axis, so there are an infinite number of caves with no entrances. Sadly, this may be the closest real answer that one can model. There may be millions of caves in Tennessee alone with no entrance, buried in bedrock and collapse, but which otherwise qualify with the TCS definition of a cave.

Figure 1: Cave Entrance Frequency

Estimating Cave Totals by Regression, Part 2

Here's an idea of how one can estimate caves with natural entrances (or caves whose entrances are

*about to be natural*). If we use a scatterplot graph and place on the X axis dates, and Y axis number of caves described, then we see a steadily rising graph, like the one below.

To this scatterplot I have added a second order polynomial trendline. This is our estimating line. As the polynomial line reaches its peak we are saying that's our best guess for the peak number of caves.

Figure 2: Caves Described over Time [Google Sheets]

When You've Broken Math, Make Stuff Up

Right now I'm saying that there are at least 14,000 caves with natural, or nearly natural entrances in Tennessee. This estimate is based on my intuition of the data, the geology, and transforming technologies to find and access caves. Sources? Ummmm, the above? It can't be infinity. It can't be less than the observed number. Fourteen thousand seems like a safe guess. :)

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