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.

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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