More pleasant distractions for your life. Have fun!
Here are three more pieces for piano and orchestra. Hope they fit somewhere in your brain!
Here is a reference I used for my Biology class some years back, in case you need it. And, as always, I add a new piece of music, which, in this case, is completely unrelated. Enjoy!
Three short compositions for you pianists to figure out. Have fun!
I call this “Everywhere I Go.”
South Texas is famous for the roadside flowers that Ladybird Johnson championed, but there are, of course, huge fields that are not planted, but simply flourish and bloom, each in its season (the top two photos). Beautiful stuff. And to go with it, two more pieces, the first a piano bit with a little orchestral backup, and the second an extended variation on a theme by Neil Young’s “If God Loved Me.” At least that’s what it reminds me of.
Here are three more themes of very different mood and tempo. Hope you like them!
Here are two of my songs, one from 1972 when the Vietnam War protests were going on, and one from about 1995, when horses were still useful. Enjoy.
Here is a case in which a generally “obvious” fact is mathematically demonstrable. The premise is that if a butterfly requires nectar from only one particular flower species, it is an extreme specialist, whereas if a butterfly will accept nectar from any flower species, it is an extreme generalist. But it is also possible to distinguish the degree of specialization by extended observation of flower visits. I have made records of about 11,400 visits by 135 butterfly species to 110 species of flowers. From these data I have produced a graph that relates the number of flower species visited frequently by a butterfly (i.e. 10+ recorded visits) to the total number of flower species that that butterfly species visits. In case it’s not obvious, let me further clarify this.
This is a picture of specialization versus generalization in nectaring. Predictably and happily, the correlation, R2 = 0.936, suggests linearity. On average, butterflies that regularly visit only one flower species can be expected to ever visit only about 5 flower species, while butterfly species that regularly visit seven different species of flowers will be found to visit about 24 species of flowers in total. Remember, these are averages.
As examples, Oarisma edwardsi (Edward’s skipperling) feeds mainly from alfalfa, but may be found on three other flower species. In the middle ground, Satyrium calanus, (the banded hairstreak) commonly visits four flower species, but has been found on 13 total flower species. A still more extreme generalist, Phyciodes cocyta (the northern crescent) is frequently encountered on nine flower species, but also visits at least 18 other flowers.
Population Densities of Butterflies in the Pikes Peak Region
The following records, drawn from my field logs of the last 59 years, sift out the average and the greatest observed densities of many of the common butterflies in the Pikes Peak Region. This work has been done so that future workers in this field can compare observations to see if populations are becoming more or less dense with time.
The “average number per trip” is calculated as the total number of individuals observed divided by the number of trips afield during which the species was encountered. Thus, if I found a total of 320 individuals of a species on 70 trips afield, the average density would be recorded as 320/70 = 4.6 / trip (not per hour). The “maximum density” is derived from the single trip afield during which the observed number of individuals of a species divided by the time afield equals the largest quotient. For example, if a three-hour trip found 29 individuals, the recorded density would be 29/3 = 9.7/hour. If on another trip, two and a half hours turned up 27 individuals, then 27/2.5 = 10.8/hour, a greater observed density. Thus, the greatest density observed is reported. “TNTC” means too numerous to count, usually reflecting population explosions.
The Pikes Peak Region is herein defined as including all of El Paso and Teller Counties, and portions of adjacent Park, Lincoln, and Kiowa Counties. Sites north of the Monument Divide are excluded, as they were poorly sampled, and in many cases include clear ecological differences from the Pikes Peak area itself. The Rampart Range is included north only to Mount Herman and Carroll Lakes. A radius of roughly thirty-five miles from Pikes Peak is roughly 3850 square miles or 2.46 million acres. The life zones include the Sonoran short grass prairie, the pinyon-juniper and oak-pine transition woodlands, the Canadian (Taiga), a thin, poorly resolved Hudsonian, and the Arctic-Alpine (Tundra) on Pikes Peak itself. At least 206 butterfly species fly in El Paso County alone, although many of them are occasional or stray species from the south and east.
This set of four pieces was written between 2008 and 2020, and includes a salute to a bright morning, a string piece with a piano as percussion, a mystery, and finally, an untitled orchestral piece I wrote in 2008. Have a good time!