This study applies a novel, vertically stratified fogging protocol to document arthropod abundance, density, and biomass across a vertical gradient in a primary, lowland dipterocarp forest canopy in Borneo. We fogged arthropods at 5 m vertical intervals and 20 m horizontal intervals along six full‐canopy transects and measured leaf surface areas along the same transects. The results show that arthropod biomass in the aboveground regions was 23.6 kg/ha, the abundance was 23.9 million individuals/ha, and the density on leaf surfaces was 280 individuals/m2 leaf area. All three numbers are five to ten times higher than estimated by previous surveys of tropical lowland rain forest canopies using mass‐collection techniques. Arthropod abundance and biomass were analyzed in relation to canopy structure, composition, vapor pressure deficit (VPD), photosynthetic photon flux density (PPFD), and height. Using stepwise regression we found that 13 of 14 arthropod groups had significant positive relationships with one‐sided leaf area, 11 had significant negative relationships with VPD, 3 had significant relationships with height, and none showed positive relationships with light. Classifying the 14 taxa based on their responses to leaf area and VPD created three groups that corresponded roughly to the biology of these taxa. This study suggests that the biomass and abundance, and perhaps therefore—by extrapolation—the biodiversity, of tropical canopy arthropods may be very much higher than previously estimated.

We characterize words in a finitely generated free group with the property that any endomorphism fixing them is necessarily an automorphism. They are those words not contained in proper retracts.

Much work recently has been focused on the issue of fixed words for automorphisms of free groups - see [2] and papers referred to there. Bestvina and Handel [1] have announced a powerful structure theorem for automorphisms of free groups that has as a consequence a proof of what has become known, to the amusement of Peter Scott, as the ‘so-called’ Scott Conjecture: if F is a free group of rank n and α:F→F is an automorphism, then Fix (α) = {w∈F|α(w) = w} has rank at most n.

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