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Worm Math

January 31, 2010

Update: Three weeks with the flashlight have reduced the numbers to an insignificant level.  At this point,  migration into the test plot, and new hatches will probably keep me finding a worm or two every night for quite a while.  While out picking worms I also started picking slugs and keeping track of those numbers.  They show much more variability night to night depending upon the temperature… but that’s another post.

Since I discovered the cutworms infesting my garden last week I have been diligently picking the worms off the plants.  Many gardeners know the benefits of hand picking pests when they are visible (which is often best done at night).  But how effective are our efforts?  This episode with the cutworms provides a nice illustration about what you can learn by keeping track of the number of pests you eradicate.

The chart shows the number of cutworms I hand picked each day this last week. The first few times I went out I found lots of worms, more than thirty the first night. On subsequent nights, the numbers gradually diminished as my efforts reduced their numbers. My chance of finding a particular worm, is just that – chance.   Not all the worms come out to feed at any given time, and even if they are out and about, I might not see them. This means that the number of worms I’m likely to find will equal the total population of worms, times some unknown chance of finding any particular worm as I make my rounds. It’s handy to plot the numbers as a semi-log graph because the expected exponential decay from the statistics will show up as a straight line on the graph. (Back in the days before Excel, I would plot the points and draw the best fit line by “eyeball”, then measure the slope with a ruler to figure out the decay constant.) Since the data fits pretty well to a straight line on the semi-log graph, we can use the best fit equation to tells us a few things about our infestation.

First, how many of these things were there when I discovered this problem?  Thats just the integral of the equation from day zero to day infinity, when I finally will have pick the last one.  Using the coefficients from the equation Excel found for us, and a little elementary calculus, we find, N = 30.9/0.152 = 204  worms living in my garden before I started picking them.

Next, how efficient are my searches?  The fraction that remain night after night is given by the exponential.  The fraction remaining after a nights search will be,  f = exp(-0.152) = 0.86 = 86%.  So every night I’m finding about 14% of the remaining critters.

Finally, about how many are left?  That’s pretty easy.   We can evaluate the integral of the decay equation from Day 20 to infinity:  R = 30.9/0.152 exp(-20*0.152) = 10.

Hand picking pests is one of the very best organic practices we have.  Keep track of the numbers and you will quickly learn how serious is the problem, and how effective are your eradication efforts.

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2 Comments leave one →
  1. Dan Smellow permalink
    February 4, 2010 11:53 pm

    Though I didn’t track my numbers, I saw the same line removing snails from my squash beds last year. For the squash hills, I dug out 5ft circles in a sea of hypericum which I think must house hundreds of snails. I checked for snails every night for three weeks and noticed the logarithmic decline, with some spikes on wetter nights. The squash did poorly for other reasons, but the snail harvest was great and the chickens loved them.

  2. February 5, 2010 8:43 am

    Presently I’m picking and counting slugs as well. At some point the curves should level off and we will get to just the “source term” which will represent hatchings or migrations into the count area. But the random error gets pretty big when you finding less than 10/night so it might take a while before the trend becomes obvious. I’ve noticed that the slugs take a marked drop on dry nights – wet nights are the norm this time of year!

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