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Success of integrating annual forages into crop and livestock systems throughout Nebraska may be variable depending on field location, field/forage crop management, and precipitation. There are many different warm- and cool-season annual forage species available for integrating crop and livestock systems at different times of the year. Mixtures of cereal species, such as oats (Avena sativa)) and spring peas (Pisum sativum)), are often used to optimize forage quantity and forage quality. Our two-year, three location study across Nebraska’s precipitation gradient suggested that forage quantity and quality may vary by location due to different precipitation amounts received during the spring growing season. Data also suggested, that in low rainfall environments, including spring peas with oats did not always increase crude protein levels in forages produced. However, this was more likely to occur in higher precipitation areas. If this is the case, the elevated seed cost due to the addition of spring peas may be unwarranted in low precipitation environments with lower forage production. No mixture of oats and spring peas produced significantly more biomass than an oats monoculture. This suggested that if the primary goal was biomass production, adding spring peas may be unnecessary. Data collected from different farms using annual forages for grazing throughout Nebraska suggests that annual grasses, when included in annual forage seed mixtures, will almost always be the greatest producers of biomass compared with other functional groups (i.e., legumes, brassicas, and other). Harvest efficiency of grazing animals was affected by the large amounts of biomass production from annual forages. Our data suggested that harvest efficiency levels may often be low (17-41%), resulting in large amounts of biomass being left within the field as standing biomass or trampled residue. Producers within the study felt that grazing annual forages was economical, but a number of variables may affect forage biomass which is a key factor in the economic sustainability and ecological benefit of including annual forages in integrated crop and livestock systems. Advisors: Mitch Stephenson and Daren Redfearn

We study two dimension estimates regarding linear series on algebraic curves. First, we generalize the classical Brill-Noether theorem to many cases where the Brill-Noether number is negative. Second, we extend results of Eisenbud, Harris, and Komeda on the existence of Weierstrass points with certain semigroups, by refining their dimension estimate in light of combinatorial considerations. Both results are proved by constructing chains of elliptic curves, joined at pairs of points differed by carefully chosen orders of torsion, and smoothing these chains. These arguments lead to several combinatorial problems of separate interest.