Butterfly and Moth Biodiversity

Do you have any idea how many moth species live in the Pikes Peak Region? Take a guess. A hundred? A thousand? Ten thousand? Well, it turns out, if you have data like I have, a reasonable estimate can be made. I used the Clench equation, taken from Harry K. Clench’s paper* on estimating butterfly biodiversity on reserves. It is useful after a few years (or hours) of data points are available. If you want the answer, you can skip the math and go to the case study, below. But in case you’re interested…

The equation shows that the eventual number of species (Se) in a locality can be estimated as a function of a constant, K, and the number of hours spent in the field (N).


As K approaches zero, N + K approaches N, and Se = S. In this equation, S represents the number of species taken at any given time and N represents the number of years (or hours) afield. Simplified, the equation looks like this:


Data that show a positive curve will not apply, of course. This can result if the first expedition is poor but the second is extraordinary. But as more data accumulate, a negative curve is generated, and any two points roughly on the curve can be used to estimate the asymptote, which is equivalent to Se.

Let us assume that after two years, 62 species have been cataloged (2, 62), and that after an additional 2 years, a total of 81 have been recorded (4, 81). Using these to create a system of equations allows us to calculate K, and then Se, as follows.

2Se = (2)(62) + 62K

4Se = (4)(81) + 81K

multiplying the first equation by –2 yields this pair:

– 4Se = –248 – 124K

4Se =   324 + 81K

eliminating the Se term,

0 = 76 – 43K

– 76 = –43K

K = 1.77

Substituting into the original equation yields an estimate of

Se = 124 + 110 = 234 species


screen-shot-2017-01-14-at-1-20-43-pm*Clench, H. K. 1979 How to make regional lists of butterflies: some thoughts. Journ. Lepid Soc 33(4) 216-231


The Evangelist in the Bathtub

In 1972, when I was twenty-seven years old, Young Life, Inc. fired me for heresy. I’d made the mistake of putting Buddha and Jesus in the same sentence, and while I tried to remind them that I was a folk singer, not a preacher, they insisted that my “message” had become “confusing” as I tried to navigate the troubled confluence of a historic religion with real life experience. “Confusing” was an understatement. Tragically, I had come up with a sense of “Christ” as being an ineffable presence, not so much tied to a historic event as to the immediate spiritual aspect of emotional life, and this seemed to me similar to the Buddhists’ seeking of a state of Nirvana. Silly me. The salvation story starts and ends with the cross, with Jesus’ sacrifice two thousand years ago, and only intersects with your current condition through his holy name. It’s not a state of enlightenment or seeking enlightenment. You are a sinner, straight up. It’s all and only about accepting the story line as fact. I thought I could accept the story line and still try to find some nameless spiritual essence hovering around me, and this seemed similar to some Eastern religious practices. So I threw in a Buddha, and that slammed the door behind me. Continue reading “The Evangelist in the Bathtub”

New Pieces of Music

Here is some reading music to carry you away through the next few articles. All songs Copyright Samuel A. Johnson, 2016

Reading Music


Everywhere I go:


Cricket Song:


Theme 5 for Guitar and Piano:


Theme 4:





Increasers and Decreasers


In his 1982 book, Where the Sky Began, which concerned the settlement of the great American prairie, John Madson drew a distinction between increasers and decreasers. The former were animals such as house finches, pigeons, and fox squirrels that increased their populations when living in human habitations. The latter, species like bears, coyotes, foxes–in short, predators–experienced population crashes as a result of human invasions.

But with time, these distinctions have become less clear. When I was a kid, in the 1950’s, the city had pushed out almost all larger wildlife. We never saw deer, bears, coyotes, or foxes in town. They were left in the distant countryside. Now, however, deer thrive in the city in large populations, bears roost in our trees at night, and coyotes take poodles off leashes in parks for lunch.

Once I asked the Fish and Wildlife Department if our school could collar and track a bear. They said no, and the reason was telling: “If the people in Broadmoor had any idea how many bears there are in the trees, they’d freak. We don’t do anything to call attention to bears.”

Moths and Flowers

Litocala sexsignata on Salix fls.Lycomorpha grotei on Rhus fls.

Above, a Litocala sexsignata moth on willow flowers; A Lycomorpha grotei moth on sumac flowers.

Almost everyone has the butterfly/flower thing down, although many people don’t realize that butterflies are not good pollinators. Generally, their long legs keep them far above or away from the stamens, which carry pollen, and their long probosces reach delicately through the reproductive parts to extract nectar. Butterflies, generally, are nectar thieves.

It might come as a surprise that moths are similar, but most tend to visit flowers at night. Not all moths feed as adults, but many of those that do are also poor pollinators, for the same reason that butterflies are. And lots of moths are diurnal–let’s keep in mind that butterflies and moths are not really different. Butterflies form a set of Lepidopterans that have adapted to living during the daylight, and therefore use color and pattern more than most moths do. Otherwise they’re just day-moths. But several families of moths are diurnal, and especially at high altitudes where the nights are very cold. Here are a few moths visiting flowers during the day.

Eriplatymetra coloradensissyngrapha

An Eriplatymetra coloradensis moth on Monarda flowers; Syngrapha angulidens moths on nodding thistles. Note that in scientific nomenclature, Latin names are italicized, as they are foreign words. Also, the genus name is always capitalized, while the species name is never capitalized. All this to make Karl Linné feel better.