\u3ci\u3eForficula Auricularia\u3c/i\u3e L. (Dermaptera: Forficulidae) in Michigan

(excerpt) Although Forficula auricularia Linnaeus, the European Earwig, has been known to occur in Ontario, Canada since prior to 1937 (Vickery and Kevan, 1967), invasion of Michigan by this species is of more recent date. A specimen in the University of Michigan Museum of Zoology was taken at Lansing in 1948 and, judging from specimens at hand, the species was fairly common there by 1964. In 1966, Thomas E. Moore, of the Museum of Zoology, took a number of specimens at Beulah in Benzie County and informed me that the earwig was rather abundant on common milkweed. Since that time there appears to have been an explosive build up of populations in the northwestern part of the state. Auricularia is reported as occurring in great numbers around Benzonia, Benzie County and in Charlevoix, Charlevoix County where they have been observed in numbers approaching tens of thousands. I have also seen specimens from Missaukee County, Harbor Springs in Emmet County, Alpena in Alpena County, and Detroit, Wayne County. An undocumented report indicates that the species was observed in 1971 in large numbers at Big Rapids, Mecosta County

Some R.R. Dreisbach Collecting Localities in South-Eastern Texas and Northeastern Mexico

Excerpt: During July and August, 1954 the late Robert R. Dreisbach of Midland, Michigan, devoted several weeks to the collection of insects in Texas and Mexico. Dreisbach was an extremely active and indefatigable person. His collecting efforts were not limited to the accumulation of materials of immediate interest to him, and he assembled large numbers of many species of insects. He maintained a general collection and, from time to time, sent portions of it to various specialists for determination. Numerous new species have been described from this material. In identifying the Orthoptera, I noted several discrepancies in the date-locality data accompanying the specimens. Fortunately. I was able to work out and clarify a number of these inaccuracies with Dreisbach before his death in 1964

\u3ci\u3eSaga Pedo\u3c/i\u3e (Pallas) (Tettigoniidae: Saginae), an Old World Katydid, New to Michigan

At least four species of Old World Tettigoniidae are known to have been introduced into, and to have become established in the United States. One of these, Phaneroptera quadripunctata Brunner was first taken at Niles, California in 1932 and was reported by Strohecker (1952). The other three have been taken during the past two decades. Strohecker (1955) recorded Platycleis tessellata (Charpentier) from a specimen captured at Placemille, California in 1951, Urquart and Beaudry (1953) recorded Metrioptera roeseli (Hagenbach) as occurring at Ville Saint-Laurent and at Montrdal, Qudbec, Canada in 1952, and Gurney (1960) stated that the first specimens of Meconema thalassinum (De Geer) were taken at Little Neck, Long Island in 1959. All four of these species are established and the last three have been extending their ranges. (Kevan, 1961; Rentz, 1963; Johnstone, 1970). M. roeseli has moved the farthest, it is found widely distributed in Qudbec and New York, and is believed to occur in Vermont, Pennsylvania and Eastern Ontario (Vickery, 1965; Vickery and Kevan, 1967)

The number of lattice paths below a cyclically shifting boundary

We count the number of lattice paths lying under a cyclically shifting piecewise linear boundary of varying slope. Our main result can be viewed as an extension of well-known enumerative formulae concerning lattice paths dominated by lines of integer slope (e.g. the generalized ballot theorem). Its proof is bijective, involving a classical “reflection” argument. Moreover, a straightforward refinement of our bijection allows for the counting of paths with a specified number of corners. We also show how the result can be applied to give elegant derivations for the number of lattice walks under certain periodic boundaries. In particular, we recover known expressions concerning paths dominated by a line of half-integer slope, and some new and old formulae for paths lying under special “staircases.