introducing model-data fusion to graduate students in ecology topics of discussion: the impact of...
TRANSCRIPT
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
max
11)
1
2
2)
3) I1
2
C
DhV
I = CS
S
hDV
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.
Hypothesis (process model)
y = f(,x)
Year
Measured population size SE
1965 510 1041966 521 1031967 502 1051968 382 1171969 677 911970 502 1051971 591 971972 688 901973 467 1091974 608 961975 538 1021976 988 801977 580 981978 932 801979 826 831980 852 821981 918 801982 797 841983 1562 1191984 929 801985 1149 851986 864 811987 896 811988 978 801989 812 83
Probability model
P(yi| ,xi)
Observations = yi
Statements about hypothesis supported by observations
Outcomes of a new curriculum
4) Understanding how inferences may be influenced by temporal and spatial scale.
Fridley, J. D et al. 2007. 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.
0 0
11 1
, Norm(0, )
1 , Lognorm(1, )
t t observation
tt t t p p process
y qN
NN N rN
K
data model
process model
Outcomes of a new curriculum
5) Facility in using multiple sources of data to parameterize and evaluate models.
CalvesCalves CalvesCalves
YearlingsYearlings YearlingsYearlings
AdultsAdults AdultsAdults
Females Males
p
m
Saf
Sc
Sam
SymSyf
ScClimateClimate
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 curriculum7) Quantitative confidence needed to support a lifetime of self-teaching.
Hobbs, N. T., S. Twombly, and D. S. Schimel. 2006. Deepening ecological insights using contemporary statistics. Ecological Applications 16:3-4.
ResourcesBooks
Clark, J. M. 2007. Models for Ecological Data. Princeton University Press., Princeton, N. J.
Bolker, B. 2008. Ecological Models and Data in R. Princeton University Press, Princeton N. J.
Hilborn, R., and M. Mangel. 1997. 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
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Karieva, P., and M. Anderson. 1988. Spatial aspects of species interactions: the wedding of models and experiments. Pages 35-50 in A. Hastings, editor. Community Ecology. Springer-Verlag, New York.
97 papers
40 issues
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Update of Karieva and Anderson: Each point is take from a paper in Ecology published between January 2000-December 2006.
229 papers
80 issues