The advent of site-specific weed management has generated research aimed at predicting weed spatial distributions from existing weed maps or correlations with soil properties and edaphic factors. Forecasting the spatial distribution of annual weeds requires knowledge of fecundity, dispersal, management, and suitable habitat distribution. We hypothesized that wild oat habitat was limited by field-scale heterogeneity in plant-available water. We eliminated seed number and dispersal limitations by seeding wild oat in areas with and without historical wild oat patches in three similarly managed spring wheat fields that differed in soil properties and wild oat infestations and were situated within a 160-km radius of Great Falls, MT. Wild oat habitat was quantified by wild oat leaf area growth rate, mature shoot biomass, seeds produced per plant, biomass water use efficiency, and competitive ratio with spring wheat. Soil texture and plot elevation correlated with existing wild oat patch areas in individual fields, but no site properties consistently correlated with wild oat patch areas in all three fields. Soil water use (SWU) and almost all habitat-defining variables for wild oat were similar between historic patch and nonpatch areas. Wild oat grew and produced seed regardless of existing patch boundaries and field-scale heterogeneity in SWU. This research suggested that (1) wild oat habitat may be unlimited in cereal grain cropping systems of the Northern Great Plains and (2) soil properties are a poor predictor of weed distribution for a generalist such as wild oat.

In the job shop scheduling problem k-units-J m , there are m machines and each machine has an integer processing time of at most k time units. Each job consists of a permutation of m tasks corresponding to all machines and thus all jobs have an identicaldilation D. The contribution of this paper are the following results;(i) for $d=o(\sqrt{D})$ jobs and every fixed k, the makespan of an optimal schedule is at most D+ o(D), which extends the result of [3]for k=1; (ii) a randomized on-line approximation algorithm for k-units-J m  ispresented. This is the on-line algorithm with the best known competitiveratio against an oblivious adversary for $d = o(\sqrt{D})$ and k > 1; (iii) different processing times yield harder instances than identicalprocessing times. There is no 5/3 competitive deterministic on-linealgorithm for k-units-J m , whereas the competitive ratio of the randomizedon-line algorithm of (ii) still tends to 1 for $d = o(\sqrt{D})$ .

In on-line computation, the instance of the problem dealt is notentirely known from the beginning of the solution process, but itis revealed step-by-step. In this paper we deal with on-lineindependent set. On-line models studied until now for this problemsuppose that the input graph is initially empty and revealedeither vertex-by-vertex, or cluster-by-cluster. Here we present anew on-line model quite different to the ones already studied. Itassumes that a superset of the final graph is initially present(in our case the complete graph on the order n of the finalgraph) and edges are progressively removed until the achievementof the final graph. Next, we revisit the model introduced in[Demange, Paradon and Paschos, Lect. Notes Comput. Sci.1963 (2000)326–334] and study relaxations assuming that somepaying backtracking is allowed.