Geoscience Reference
In-Depth Information
and.generate.quantitative.predictions.that.can.be.compared.with.observations..We.
can.estimate.the.relative.support.for.different.models.in.the.way.that.we.would.esti-
mate.support.for.a.null.hypothesis,.by.calculating.the.probability.of.the.data.given.
each.model..This.is.called.the.likelihood.approach,.because.the.probability.of.the.
data.given.a.model.is.deined.as.the.“likelihood”.of.the.model.given.the.data..The.
likelihood.is.proportional.to.the.full.probability.of.the.model.given.the.data,.which.
is.what.we.would.really.like.to.know..But.by.comparing.likelihoods,.we.compare.the.
relative.probabilities.of.alternative.models,.which.is.often.suficient.
The.Bayesian.approach.goes.one.step.further.by.calculating.the.full.probability.of.
each.model.given.the.data—calculations.that.were.prohibitively.dificult.for.all.but.
the.simplest.models.prior.to.the.development.of.modern.computers..The.Bayesian.
approach. is. also. particularly. useful. for. building. complex. mechanistic. models,. for.
including. multiple. types. of. evidence. in. support. of. alternative. hypotheses,. and. for.
estimating.the.probability.of.various.types.of.evidence.encountered.at.various.points.
within.a.process.
Given.a.set.of.alternative.models,.we.can.draw.on.either.likelihood.or.Bayesian.
approaches. to. calculate. an. “information. criterion”. for. each. model,. a. statistic. that.
balances.model.it.against.the.number.of.parameters.in.the.model..For.a.given.it,.
models.with.more.parameters.offer.less.information.per.parameter,.and.thus.receive.
a.penalty.for.over-itting..Calculating.an.information.criterion.for.each.model.pro-
vides.a.basis.for.model.selection.(determining.the.“best”.model).as.well.as.model.
averaging.(developing.predictions.based.on.a.weighted.average.of.models.with.rela-
tively.high.support).
In. their. research. on. the. American. pika,. Beever. et. al.. (2010). used. an. informa-
tion.criterion.to.compare.support.for.different.metrics.of.physiological.stress..This.
approach,.driven.by.a.priori.hypotheses.and.supported.by.new.data,.allowed.a.for-
mal.ranking.of.individual.predictors.of.range.retraction..Each.predictor.was.ranked.
according.to.a.weighted.average.of.the.information.in.all.models.based.on.that.pre-
dictor.. While. not. a. panacea,. this. “information-theoretic”. approach. (Burnham. and.
Anderson.2002).provides.a.relatively.robust.alternative.to.common.methods.of.infer-
ence.in.a.ield.abounding.with.observational.data.
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A.theme.that.clearly.emerges.in.this.chapter.is.that.we.still.know.very.little.about.
mammalian.response.to.climate.change..A.key.deicit.is.the.limited.availability.of.
high-quality.data.on.past.and.present.climates.and.species.occurrence..Even.for.well-
studied.organisms.such.as.pikas.in.well-studied.areas.like.western.North.America,.
accumulating.legacy.occurrence.data.useful.for.studies.in.global.change.biology.has.
proven,. based. on. our. experiences,. dificult.. The. task. of. collating. raw. occurrences.
from.natural.history.collections.databases.has.improved.with.the.advent.of.aggre-
gating. mechanisms. such. as. the. Mammal. Information. Network. System. (MaNIS,.
http://manisnet.org;.Stein.and.Wieczorek.2004).and.Global.Biodiversity.Information.
Facility. (http://data.gbif.org),. but. this. still. leaves. the. onerous. task. of. vetting. data.
records. to. determine. those. with. precise. dates. and. geographic. locations.. This. has.
proven.to.require.intensive.effort..In.addition,.the.vast.majority.of.results.from.biotic.
