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Abstract Alpine grassland vegetation supports globally important biodiversity and ecosystems that are increasingly threatened by climate warming and other environmental changes. Trait-based approaches can support understanding of vegetation responses to global change drivers and consequences for ecosystem functioning. In six sites along a 1314 m elevational gradient in Puna grasslands in the Peruvian Andes, we collected datasets on vascular plant composition, plant functional traits, biomass, ecosystem fluxes, and climate data over three years. The data were collected in the wet and dry season and from plots with different fire histories. We selected traits associated with plant resource use, growth, and life history strategies (leaf area, leaf dry/wet mass, leaf thickness, specific leaf area, leaf dry matter content, leaf C, N, P content, C and N isotopes). The trait dataset contains 3,665 plant records from 145 taxa, 54,036 trait measurements (increasing the trait data coverage of the regional flora by 420%) covering 14 traits and 121 plant taxa (ca. 40% of which have no previous publicly available trait data) across 33 families. 

We show that in an ultraproduct of finite fields, the mod-n nonstandard size of definable sets varies definably in families. Moreover, if K is any pseudofinite field, then one can assign "nonstandard sizes mod n" to definable sets in K. As n varies, these nonstandard sizes assemble into a definable strong Euler characteristic on K, taking values in the profinite completion hat(Z) of the integers. The strong Euler characteristic is not canonical, but depends on the choice of a nonstandard Frobenius. When Abs(K) is finite, the Euler characteristic has some funny properties for two choices of the nonstandard Frobenius. Additionally, we show that the theory of finite fields remains decidable when first-order logic is expanded with parity quantifiers. However, the proof depends on a computational algebraic geometry statement whose proof is deferred to a later paper. 

We consider existentially closed fields with several orderings, valuations, and p-valuations. We show that these structures are NTP2 of finite burden, but usually have the independence property. Moreover, forking agrees with dividing, and forking can be characterized in terms of forking in ACVF, RCF, and pCF. 

Let T be a theory. If T eliminates ∃∞, it need not follow that Teq eliminates ∃∞, as shown by the example of the p-adics. We give a criterion to determine whether Teq eliminates ∃∞. Specifically, we show that Teq eliminates ∃∞ if and only if ∃∞ is eliminated on all interpretable sets of “unary imaginaries.” This criterion can be applied in cases where a full description of Teq is unknown. As an application, we show that Teq eliminates ∃∞ when T is a C-minimal expansion of ACVF.