Popula'onDynamics

÷  Lectureoutline/goals:o  Popula'onprocesses:determinantsofchangeo  Exponen'algrowtho  Logis'cgrowtho  Densityindependence(D.I.)o  Densitydependence(D.D.)o  Popula'oncycleso  D.I.–D.D.integra'on

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Popula'ondynamics= studyofbirths,deathsandthemovementoforganisms

÷ Cri'calto:o  Predic'on(spa'alandtemporal)o  Management(biological/silviculturalcontrol)o  Characteriza'onofpopula'ons

2

?

Popula'onprocesses:determinantsofpopula'onchange

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Population size

Mortality (deaths)

Natality (births)

Immigration Emigration + -

-

+

Population size (N) Deaths (D) Births (B) Immigration (I) Emigration (E) + - - =

Nt+1 = Nt + (B – D + I – E)

Popula'onprocesses:determinantsofpopula'onchange

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Growth rate (r) = Birth rate (b) - Death rate (d) + Immigration rate (i) - Emigration rate (e)*

Change = rate (e.g. deaths per number of individuals)

r = (b – d + i – e) *note: lower case denotes “rate”

dN dt

= rN

Time

Pop

’n s

ize

(N)

Example:Exponen'alGrowth

-  Populations increase by a constant factor per unit time -  Rare, unsustainable in natural populations

Exponen'alincreasebyforestinsects?

÷  Occasionallyduringpopula'onerup'ons

Year

1998 2000 2002 2004 2006 0

2.0

4.0

6.0

8.0

Are

a (h

a) a

ffect

ed (×

106 )

r ≈ 2

Mountain pine beetle in BC

dN dt

= rN

Example:Logis'cGrowth

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Pop’ns cannot grow at an exponential rate indefinitely due to food/space limitations, or the action of natural enemies

-  K is carrying capacity; the threshold at which population growth rate (r) is zero, negative above (i.e. the maximum sustainable population)

-  As the number of individuals (N) in the pop’n increases, b, d, i and e change due to resource limitation, predation, parasitism, disease, etc.

-  Concept critical in determining harvest levels in fishing, hunting, or mgmt of wildlife populations

Time

Pop

’n s

ize

(N)

K

dN dt = rN K - N K

Also known as the Verhulst eq’n

Factorsaffec'ngforestinsectpopula'onsize

÷  Climateandweather÷  Foodquan'ty/quality÷  Hostsuscep'bility,habitatsuitability÷  Preda'on,parasi'sm,disease÷  Intraspecificcompe''on

(i.e.withinspecies)÷  Interspecificcompe''on

(i.e.amongspecies)÷  Gene'cdefects

Rela'veimportancevariesamongpopula'ons.Func'onalclassifica'on:o  Densityindependento  Densitydependent

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Mortalityfactors

Density-independentfactors

÷  Sitecharacteris'cso  Eleva'on,slope,aspect

÷  Weathero  Wind,temperature,precipita'on

÷  Bio'cfactorso  Browsing,roottrampling/compac'on

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Defini'on: Thepropor'onateeffectonpopula'onprocesses(b,d,i,e)isnotrelatedtopopula'ondensity.

Commondensity-independentfactors:

Becausetheimpactofd-ifactorsonpopula6onsisunrelatedtopopula6onsize,theneteffectiso9endrama6cpopula6onfluctua6ons.

Time

Pop

’n s

ize

(N)

e.g. drought

Density-independenteffects:example1

÷  Earlyfrostsin2002,2005and2007causedhighmortalitytoasprucebudwormpopula'on

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Year

Pop’nbeforefrost

Pop’na/erfrost

Mortality

%Mortality

2002 1000 500 500 50

2003 800 800 0 0

2004 50,000 50,000 0 0

2005 75,000 37,500 37,500 50

2006 100 100 0 0

2007 200 100 100 50

÷  However,propor'onate(%)mortalitynotrelatedtopopula'ondensity

100

80

60

40

20

0 20 30 40 50 60 70 80

∂∂ ∂∂ ∂∂ ∂∂ ∂∂

Precipitation

% M

orta

lity

Density-independenteffects:example2÷ Mortalityand%mortalityvaryinapopula'on-isitdueto

precipita'on?

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Popula'on

Year Precip.(mm) May1 June1 Mortality %Mortality

2003 70 500 100 400 80

2004 40 2,000 1,000 1,000 50

2005 50 1,500 600 900 60

2006 30 1,000 600 400 40

2007 60 2,500 800 1750 70

÷  Propor'onatemortalityrelatedtoprecipita'on,butnotdensity

100

80

60

40

20

0 3000 2000 1000 0

% M

orta

lity

Population

X

Density-dependentfactors

÷  Compe''ono  Interferencevs.exploita'ono  Effectssome'mesnon-lethal(i.e.delayeddevelopment,reducedfecundity)

÷  Preda'onandparasi'smo  Numericalresponse:predator/parasitepopula'onincreaseswhenprey/hostabundanto  Func'onalresponse:consump'onperpredator/parasiteincreaseswhenprey/hostare

abundanto  Disease

÷  Environmentalfactors?

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Defini'on: Thepropor'onateeffectonpopula'onprocesses(b,d,i,e)isrelatedtopopula'ondensity.

Commondensity-dependentfactors:

Density-dependenteffects:example1

÷  Popula'onlevelsandmortalityduetodisease;densitydependence?

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Year Popula6on Mortality %Mortality

2002 1,000 10 1

2003 5,000 500 10

2004 100,000 90,000 90

2005 800 8 1

2006 10,000 2,000 20

2007 50,000 25,000 50

÷  Asthepopula'onincreases,the%mortalityincreases,thereforeeffectofdiseaseispropor6onatetopopula'ondensity

40,000 80,000 120,000

Density-dependenteffects:roleinpop’ndynamics

÷  Popula'onregula'on,andthereforepersistence,isonlypossiblethroughac'onofdensity-dependentfactors

÷  Density-independentfactorsohencauselargelevelsofmortalityinapop’n,butwithoutd.d.factorspop’nswillul'matelygotoex'nc'on

Time

Pop

’n s

ize

(N)

K

Complexdensitydependence1:thecurseofsmallpopula'ons

÷  Implica'onstoendangeredspecies,invasiveso  Athresholdpopula'ondensityisrequiredforaspeciestopersist

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Normally,birthrate(b)increasesaspopula'onsdecrease;however,inverysmallpopula'ons,thebirthratemaydeclinedueprimarilytodifficul'esinmateloca'on(orinbreeding):TheAlleeeffect

Population size (Nt)

Rat

e of

cha

nge

(r)

Birth rate (b)

Allee effect

Complexdensitydependence2:popula'onerup'ons

÷  Themountainpinebeetleasanexampleo  Density-independentperturba'onsshihendemic-epidemiccurvessothattheyintersectaboveR=0,

allowingendemicpopula'onstoentertheepidemicphaseandachieveposi'vefeedbacksforashort'me.

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Erup'vespeciesarecharacterizedbydis'nctpopula'onphases–endemic(sub-outbreak)wherenega'vefeedbackspredominate,andepidemic(outbreak)whereposi'vefeedbacksfacilitaterapidpopula'ongrowth/spreadun'lnega'vefeedbacksreassertthemselves

Year

1998 2000 2002 2004 2006

0

2.0

4.0

6.0

8.0

Are

a (h

a) a

ffect

ed (×

106 )

Log 1

0 gen

erat

ion

recr

uitm

ent,

R

Log10 attack density, X

0

-1

1

From: Cooke and Carroll 2017

Endemic phase Epidemic phase

Density-independent perturbation

Therela'verolesofdensity-dependentanddensity-independentfactors

÷  Considerablepopula'onfluctua'ons–d.i.factors÷  Detectablepopula'oncycle,30–40years÷  Whatcausespopula'onstocycle?÷  Roleofd.d.factors?

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e.g. The eastern spruce budworm

Adapted from Royama 1992

Popula'oncycles:predator-preyinterac'onsandlags1

÷  Insect(i.e.prey)pop’nincreasestowardK(rememberlogis'cgrowth),rdeclines÷  ApproachingK,d.d.effectsofsomepredators/parasitesincreasepropor'onately,but

responselags(func'onal/numericalresponse)

÷  Peakpredator/parasiteimpactsmanifestaherinsectpop’nsini'atedecline(duetoK),andinsectpop’nfalls

÷  Insectscarcitycausespredator/parasitepop’nstodecline,insectpop’nsrebuild

The Lotka-Volterra model (without the math!)

One prey cycle

Time

Num

ber o

f pre

dato

rs o

r pre

y

Prey

Predator

Popula'oncycles:predator-preyinterac'onsandlags2

÷  35-yearcyclecausedbylaggedd.d.mortalityoccurringinthelate-larvalandpupalstages

÷  Generalistpredators,parasitoidsandpossiblypathogens

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Predator/parasite – prey/host interactions and the eastern spruce budworm?

Adapted from Royama 1992

Time

Adapted from Régnière and Nealis 2007

Popula'oncycles:predator-preyinterac'onsandlags3

÷  HistoricdatafromHudsonBayCo.trappingrecords÷  Noteregularperiodicity,andlagbylynxpop’ns

http://theglyptodon.wordpress.com/2011/05/02/the-fur-trades-records/

Integra'ngdensity-dependentanddensity-independentfactors

÷  MPBpopula'onssynchronizedatdistances>900km

÷  Weather(temp.,precip.)correlatedoversimilararea

÷  TweedsmuirParknotthesourceoftheMPBoutbreak

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Popula'onsynchronyviadensity-independentfactors:theMoraneffect

Geographically disparate populations with similar population processes will become temporally synchronized when exposed to a density-independent perturbation that is correlated over large areas (e.g. drought, El Niño, etc.)

The mountain pine beetle

Adapted from Aukema et al. 2006