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Abstract Studies of long-term trends in phenology often rely on climatic averages or accumulated heat, overlooking climate variability. Here we test the hypothesis that unusual weather conditions are critical in driving adult insect phenology. First, we generate phenological estimates for Lepidoptera (moths and butterflies) across the Eastern USA, and over a 70 year period, using natural history collections data. Next, we assemble a set of predictors, including the number of unusually warm and cold days prior to, and during, the adult flight period. We then use phylogenetically informed linear mixed effects models to evaluate effects of unusual weather events, climate context, species traits, and their interactions on flight onset, offset and duration. We find increasing numbers of both warm and cold days were strong effects, dramatically increasing flight duration. This strong effect on duration is likely driven by differential onset and termination dynamics. For flight onset, impact of unusual climate conditions is dependent on climatic context, but for flight cessation, more unusually cold days always lead to later termination particularly for multivoltine species. These results show that understanding phenological responses under global change must account for unusual weather events, especially given they are predicted to increase in frequency and severity. 

In parts I and II, we determined which faithful irreducible representations V of a simple linear algebraic group G are generically free for Lie(G), i.e., which V have an open subset consisting of vectors whose stabilizer in Lie(G) is zero, with some assumptions on the characteristic of the field. This paper settles the remaining cases, which are of a different nature because Lie(G) has a more complicated structure and there need not exist general dimension bounds of the sort that exist in good characteristic. 

This paper concerns a faithful representation V of a simple linear algebraic group G. Under mild assumptions, we show that if V is large enough, then the Lie algebra of G acts generically freely on V. That is, the stabilizer in Lie.G/ of a generic vector in V is zero. The bound on dim V grows like the square of the rank and holds with only mild hypotheses on the characteristic of the underlying field. The proof relies on results on generation of Lie algebras by conjugates of an element that may be of independent interest. We use the bound in subsequent works to determine which irreducible faithful representations are generically free, with no hypothesis on the characteristic of the field. This in turn has applications to the question of which representations have a stabilizer in general position. 

We determine which faithful irreducible representations V of a simple linear algebraic group G are generically free for Lie(G), i.e., which V have an open subset consisting of vectors whose stabilizer in Lie(G) is zero. This relies on bounds on dim V obtained in prior work (part I), which reduce the problem to a finite number of possibilities for G and highest weights for V , but still infinitely many characteristics. The remaining cases are handled individually, some by computer calculation. These results were previously known for fields of characteristic zero, although new phenomena appear in prime characteristic; we provide a shorter proof that gives the result with very mild hypotheses on the characteristic. (The few characteristics not treated here are settled in part III.) These results are related to questions about invariants and the existence of a stabilizer in general position. 

Insects are possibly the most taxonomically and ecologically diverse class of multicellular organisms on Earth. Consequently, they provide nearly unlimited opportunities to develop and test ecological and evolutionary hypotheses. Currently, however, large-scale studies of insect ecology, behavior, and trait evolution are impeded by the difficulty in obtaining and analyzing data derived from natural history observations of insects. These data are typically highly heterogeneous and widely scattered among many sources, which makes developing robust information systems to aggregate and disseminate them a significant challenge. As a step towards this goal, we report initial results of a new effort to develop a standardized vocabulary and ontology for insect natural history data. In particular, we describe a new database of representative insect natural history data derived from multiple sources (but focused on data from specimens in biological collections), an analysis of the abstract conceptual areas required for a comprehensive ontology of insect natural history data, and a database of use cases and competency questions to guide the development of data systems for insect natural history data. We also discuss data modeling and technology-related challenges that must be overcome to implement robust integration of insect natural history data.