Local adaptation to climate in temperate forest trees involves the integration of multiple physiological, morphological, and phenological traits. Latitudinal clines for the relevant component traits are frequently observed for species that have a north-south distribution, but these relationships do not account for climatic variation within a given latitudinal band, which may be reflected in adaptive traits. We used black cottonwood (Populus trichocarpa) as a model to characterize the interplay between geography, climate, and adaptation to abiotic factors. Twelve traits (height, diameter, volume index, crown diameter, number of branches, number of sylleptic branches, relative number of branches, Relative canopy depth, Bud set, Bud flush, cold index of injury, carbon isotope ratio) were measured in a range-wide sample of 124 P. trichocarpa genotypes grown in a common garden. Heritability's were moderate to high (0.24 to 0.55) and significant population differentiation (QST > 0.3) suggested adaptive divergence. When climate variables were taken as predictors and the 12 traits as response variables in a multivariate regression tree analysis, aridity (Eref) explained the most variation, with subsequent splits grouping individuals according to mean temperature of the warmest month, frost-free period (FFP), and mean annual precipitation (MAP). This grouping matches relatively well the splits using geographic variables as predictors: the northernmost groups (short FFP and low Eref) had the lowest growth performance, and the highest cold hardiness. The groups spanning the south of British Columbia (low Eref and intermediate temperatures) displayed an average growth and cold hardiness. The group from the coast of California and Oregon (high Eref and FFP) had the best growth performance and the lowest cold hardiness. The southernmost and high-elevated group (with High Eref and low FFP) performed poorly, had a low cold hardiness and a significantly lower WUE. / Master of Science

Syftet med denna studie är att bidra med kunskap om hur matematikundervisning kan utformas genom att använda variationsteorin för att undersöka matematikundervisning om positionssystemet i årskurs 2. Metoden i studien delar likheter med design research genom att undervisning har planerats, genomförts och prövats i en autentisk klassrumsmiljö. Undervisning iscensattes genom två olika undervisningsdesigner: en undervisingsdesign baserad på variationsteoretiska principer och en undervisingsdesign baserad på lärarhandledning. Datainsamlingen i studien består av för- och eftertester samt transkript av genomförd undervisning. Datan analyserades med stöd av variationsteorin. Studien indikerar att variationsteorin kan fungera som ett konkret verktyg när matematikundervisning och elevernas möjliga lärande planeras, utformas och analyseras. Studien visar även att båda designerna tycks ha givit eleverna möjlighet att lära sig det som var planerat. / The aim of this study is to contribute to an understanding for how mathematical instructions can be designed. By investigating how the Variation theory of learning can be applied in mathematical education regarding the positional system in grade 2. The methodology of the study shares similarities with design research, as mathematical instructions were planned, implemented, and tested in an authentic classroom environment. Two different instructional designs were staged: one based on variation-theoretical principles and one based on the teacher’s instructional guidebook. The collected data in the study consists of pre- and posttests as well as transcriptions of the enacted lessons. The data was analyzed with the support of the Variation theory. The study demonstrates that the variation theory can serve as a guiding for teachers when planning, designing, and analyzing mathematics instruction and students’ potential learning development. Furthermore, the study also indicates that both designs seem to have given the students an opportunity to learn what was planned.