Introducing model-data fusion to graduate students in ecology Topics of discussion: The impact of NEON on ecology What are the desired outcomes from a basic curriculum? Content of a 1-2 semester course

data poor data rich few, isolated effects and interactions multiple effects, composite forces, contingencies manipulative observational quantitative training optional quantitative training essential ANOVA, regression, multivariates ? plot scale continental scale heterogeneity minimized heterogeneity embraced

Outcomes of a new curriculum 1) The ability to represent ecological processes as mathematical models. max 1 1) 1 2 2) 3) I 1 2 C D h V I = CS S h DV      Plant Density (m -2 ) Intake Rate (g/min) Plant Density (m -2 ) Intake Rate (g/min) time between bites time between bites Bite Density (m -2 )

Outcomes of a new curriculum 2) A an understanding of the use of process models, observations, and probability models as routes to insight.

Outcomes of a new curriculum 4) Understanding how inferences may be influenced by temporal and spatial scale. Fridley, J. D et al The invasion paradox: Reconciling pattern and process in species invasions. Ecology 88:3-17.

Outcomes of a new curriculum 3) The ability to represent “hidden processes” including all sources of stochasticity. data model process model

Outcomes of a new curriculum 5) Facility in using multiple sources of data to parameterize and evaluate models. Data sources: Census: 15 years Sex / age ratios 22 years Survival: 3 years Annual harvest and culling Annual weather records Literature estimates of survival, fertility Response to perturbation

Outcomes of a new curriculum 6) The ability to collaborate with statisticians and mathematicians in a way that is mutually beneficial. PRogram for Interdisciplinary Mathematics, Ecology, and Statistics PRIMES “Plug and play” is good news and bad news….

Outcomes of a new curriculum 7) Quantitative confidence needed to support a lifetime of self-teaching. Hobbs, N. T., S. Twombly, and D. S. Schimel Deepening ecological insights using contemporary statistics. Ecological Applications 16:3-4.

Resources Books Clark, J. M Models for Ecological Data. Princeton University Press., Princeton, N. J. Bolker, B Ecological Models and Data in R. Princeton University Press, Princeton N. J. Hilborn, R., and M. Mangel The Ecological Detective: Confronting Models with Data. Princeton University Press, Princeton, N. J. Software R, WinBugs Courses Univeristy of Washington, Duke, Colorado State University, University of Florida, Cornell

Syllabus: NR 575, Systems Ecology Deterministic models in ecology –Mathematical basis for dynamic models in discrete and continuous time –A modeler’s toolbox of useful functions –Composing models to represent mechanisms Basic probability and probability distributions Stochastic models and data simulation Likelihood –Support, strength of evidence –Likelihood ratios –Likelihood profiles, profile confidence intervals –Prior information –Multiple sources of data Information theoretics –Kullback-Leilbler information discrepancy –AIC and its allies –Akaike weights –Multimodal inference More sources of stochasticity: Process variance, observation error, random effects Introduction to Bayesian methods –Relationship between likelihood and Bayes –Monte Carlo Markov Chain –Hierarchical, state-space models –Bayesian model selection and model averaging Laboratory: Programming in R and WinBugs Examples from organismal, population, community, ecosystem ecology

chi-square analysis of variance linear regression t - test maximum likelihood model selection Bayesian Statistical Analyses Used in Journals of the Ecological Society of America

Karieva, P., and M. Anderson Spatial aspects of species interactions: the wedding of models and experiments. Pages in A. Hastings, editor. Community Ecology. Springer-Verlag, New York. 97 papers 40 issues

Update of Karieva and Anderson: Each point is take from a paper in Ecology published between January 2000-December papers 80 issues