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Giant rat species discoveredGreat white shark in MassachusettsXenoestrogensXenoestrogensFrog calls

Giant rat species discoveredGreat white shark in MassachusettsXenoestrogensXenoestrogensFrog calls

Population EcologyPopulation Ecology

Population (N) Group of animals, identifiable by species,

place, and timeDefined wrt population biology

Genetic definition would be more specificIndividuals comprise a populationCollective effects of individuals

Natality, mortality, rate of increase

Most management focused on populations, not necessarily individuals

Population (N) Group of animals, identifiable by species,

place, and timeDefined wrt population biology

Genetic definition would be more specificIndividuals comprise a populationCollective effects of individuals

Natality, mortality, rate of increase

Most management focused on populations, not necessarily individuals

RatesRates

Natality Births (per something)

Mortality Deaths (per something)

Fecundity Number of eggs Female births/adult female

Productivity Number of young produced

Breeding system, sex and age ratios Recruitment (net growth = R)

Natality Births (per something)

Mortality Deaths (per something)

Fecundity Number of eggs Female births/adult female

Productivity Number of young produced

Breeding system, sex and age ratios Recruitment (net growth = R)

DefinitionsDefinitions

Age structure Age pyramid

Sex ratio Male:female

Buck only deer hunting 1:10QDM at Chesapeake Farms 1:1.5Some dabbling ducks 10:1

Age structure Age pyramid

Sex ratio Male:female

Buck only deer hunting 1:10QDM at Chesapeake Farms 1:1.5Some dabbling ducks 10:1

Age PyramidsAge Pyramids

Long lived, slow turnover, low productivity, high juvenile survival

Short lived, fast turnover, high productivity, low juvenile survival

US population age pyramids

Sex Specific Age PyramidSex Specific Age Pyramid

males females

Buck only hunting

Beavers Beavers

Beaver Pop Age Structure

0

5

10

15

20

25

30

35

40

1 2 3 4 5 6 7 8 9 10

Age Class

N

Population GrowthPopulation Growth

Lambda Measure of population growth >1 population is growing <1 population is declining Important measure of pop status

Lambda Measure of population growth >1 population is growing <1 population is declining Important measure of pop status

€

λ =N t+1N t

Exponential GrowthExponential Growth

Constant per capita rate of increase Constant percentage increase 10% per year

Text “ever-increasing rate” per unit time

Means number added per unit time is ever-increasing

Population growth model

Constant per capita rate of increase Constant percentage increase 10% per year

Text “ever-increasing rate” per unit time

Means number added per unit time is ever-increasing

Population growth model

Exponential Growth

0

500

1000

1500

2000

2500

3000

3500

4000

4500

1 3 5 7 9 11 13 15 17 19

Time

NN + 1

Recuits R

Exponential Growth

1

10

100

1000

10000

1 3 5 7 9 11 13 15 17 19

Time

NN + 1

Recuits R

Exponential GrowthExponential Growth

George Reserve example Dr McCullough

Estimated per capita growth rate for unencumbered growth (rm) New species in optimal habitat Maximum per capita growth rate

Unfortunately McCullough didn’t do it quite right. Why estimate it?

George Reserve example Dr McCullough

Estimated per capita growth rate for unencumbered growth (rm) New species in optimal habitat Maximum per capita growth rate

Unfortunately McCullough didn’t do it quite right. Why estimate it?

Logistic Growth ModelLogistic Growth Model

Why worry about this?Fundamental conceptual relationship

that underlies sustained yield harvestingNC deer population

1.1mm Harvest 265,000

Is that harvest a lot, a few?Will the population increase, decline, or what?

Simple mathematical model

Why worry about this?Fundamental conceptual relationship

that underlies sustained yield harvestingNC deer population

1.1mm Harvest 265,000

Is that harvest a lot, a few?Will the population increase, decline, or what?

Simple mathematical model

Logistic Growth ModelLogistic Growth Model

Parameters have intuitive biological meaning K = carrying capacity N = population size rm = maximum per capita intrinsic growth rate

(potential)Species and habitat specific

r = realized (actual) per capita growth rateFor exponential growth r = rmOnly occurs for small populations for a short timeMcCullough should have estimated rm

Parameters have intuitive biological meaning K = carrying capacity N = population size rm = maximum per capita intrinsic growth rate

(potential)Species and habitat specific

r = realized (actual) per capita growth rateFor exponential growth r = rmOnly occurs for small populations for a short timeMcCullough should have estimated rm

One specific form of sigmoid growth Growth model

R = net growth = recruits K = carrying capacity r = realized growth rate

One specific form of sigmoid growth Growth model

R = net growth = recruits K = carrying capacity r = realized growth rate

Logistic Growth ModelLogistic Growth Model

€

R = Nrm(K −N)

K

Logistic Growth ModelLogistic Growth Model

As N approaches K, r = 0

When N small, then r = rm

As N approaches K, r = 0

When N small, then r = rm

€

(K −N)

K= 0

€

(K −N)

K=1

€

R = Nr

€

r = rm(K −N)

K

Logistic Growth ModelLogistic Growth Model

€

r = rm(K −N)

KDensity-dependent growth

€

R = Nr = Nrm(K −N)

K

Year Recruits Residual N r N + 11 3 9 0.333 122 4 12 0.333 163 5 16 0.313 214 7 21 0.333 285 9 28 0.321 376 12 37 0.324 497 16 49 0.327 658 19 65 0.292 849 24 84 0.286 108

10 26 108 0.241 13411 28 134 0.209 16212 29 162 0.179 19113 30 191 0.157 22114 30 221 0.136 25115 30 251 0.120 28116 30 281 0.107 31117 26 311 0.084 33718 20 337 0.059 35719 14 357 0.039 37120 11 371 0.030 38221 8 382 0.021 39022 6 390 0.015 39623 3 396 0.008 39924 1 399 0.003 40025 0 400 0.000 400

Density Dependent GrowthDensity Dependent Growth

Combined effects of natality and mortality Births decline as N increases Deaths increase as N increases

Combined effects of natality and mortality Births decline as N increases Deaths increase as N increases

Density Dependent GrowthDensity Dependent Growth

Residual population (N) Population size which produces the

recruits ( R) Pre-recruitment population Stock population

Birth pulse population Births occur about the same time

Deer in spring

Residual population (N) Population size which produces the

recruits ( R) Pre-recruitment population Stock population

Birth pulse population Births occur about the same time

Deer in spring

Sustained YieldSustained Yield

See population growth model exampleInflection point (I)

Sigmoid curve slope changes from positive to negative

Peak hump-shaped SY (or R) curveMaximum R per unit time

Point of MSY

See population growth model exampleInflection point (I)

Sigmoid curve slope changes from positive to negative

Peak hump-shaped SY (or R) curveMaximum R per unit time

Point of MSY

Sustained Yield Curves

Density Dependent GrowthDensity Dependent Growth

Fundamental relationship that underlies sigmoid growth. As N increases, per capita growth r decreases.

George Reserve Deer George Reserve Deer

€

SY = R

€

R

N= r = h = β

r per capita growth, h is per capita harvest rate

Hump-shaped, not bell-shaped

George Reserve Deer George Reserve Deer

€

R = Nr

R = SY

SY = Nr

MSY ≈1

2K •

1

2rm

MSY occurs at the inflection point I

George Reserve Deer George Reserve Deer

€

SY

N= h

R

N= r

Theoretically, sustainable harvests range from 0-90%;MSY about 50%

George Reserve Deer George Reserve Deer

€

R

N= h = β

Harvest a number, say 30, then there is ambiguity. When a rate, h, then no ambiguity.

George Reserve Deer George Reserve Deer

€

R = SY

Right side of MSY (I) stable

negative feedback between N and R

George Reserve Deer George Reserve Deer

€

R = SY

Left side of MSY (I) unstable

Positive feedback between N and R

Logistic Growth AssumptionsLogistic Growth Assumptions

All individuals the sameNo time lagsObviously, overly simplisticDoes provide conceptual bases for

management.

All individuals the sameNo time lagsObviously, overly simplisticDoes provide conceptual bases for

management.

Population ModelsPopulation Models

Forces thinking Conceptual value

Requires data What needs to be known? How are those data acquired?

Predict future conditions Assess management alternatives

Forces thinking Conceptual value

Requires data What needs to be known? How are those data acquired?

Predict future conditions Assess management alternatives

NC Deer NC Deer

NC deer population1.1mmHarvest 265,000

Can this model suggest anything about the harvest level in NC?

NC Deer NC Deer

NC deer population1.1mmHarvest 265,000

€

SY

N= h =

265,000

1,100,000 − 265,000≈ 30%

Density Dependent FactorsDensity Dependent Factors

Density dependent (proportional)MortalityNatality

Density independentAsian openbill storks example

Compensatory mortality and natality

Density dependent (proportional)MortalityNatality

Density independentAsian openbill storks example

Compensatory mortality and natality

Isle Royale LessensIsle Royale Lessens

Wolves

Moose

Isle Royale LessonsIsle Royale Lessons

Predator/prey dynamic balance?Populations fluctuate due to a myriad of

factors Food, disease, weather, competition,

genetics, random events, etc.Disequilibrium

No such thing as the “balance of nature”

Predator/prey dynamic balance?Populations fluctuate due to a myriad of

factors Food, disease, weather, competition,

genetics, random events, etc.Disequilibrium

No such thing as the “balance of nature”

Demographic RatesDemographic Rates

Birth rate (b)Death rate (d)Emigration (e)Immigration (i)Realized population growth rate r

Birth rate (b)Death rate (d)Emigration (e)Immigration (i)Realized population growth rate r

€

r = b− d( ) + i − e( )

DefinitionsDefinitions

Sex ratios and mating systemsKnow them!!!

Not going to repeat all of them here!!!!

Sex ratios and mating systemsKnow them!!!

Not going to repeat all of them here!!!!

Importance to ManagementImportance to Management

Sex ratio and breeding systems Monogamous

Balanced sex ratio Ducks -- sexually dimorphic

Sexes w/ different susceptibility to predation, hunting Canada geese -- monomorphic

PolygynousManage for a preponderance of females

Pheasants, turkeys -- dimorphic Ruffed grouse, quail -- monomorphic

PromiscuousDeer

To grow, unbalanced sex ratio QDM, balanced sex ratio

Sex ratio and breeding systems Monogamous

Balanced sex ratio Ducks -- sexually dimorphic

Sexes w/ different susceptibility to predation, hunting Canada geese -- monomorphic

PolygynousManage for a preponderance of females

Pheasants, turkeys -- dimorphic Ruffed grouse, quail -- monomorphic

PromiscuousDeer

To grow, unbalanced sex ratio QDM, balanced sex ratio

Age-Specific Birth RatesAge-Specific Birth Rates

Age-specific natality (female young/female)

Natality

Immature Adults

AGE

Age-Specific NatalityAge-Specific Natality

Deer reproduction Table 5-2 PA dense, IA sparse Fawns pregnant only in Iowa

Fawns only breed when populations are low Corpora lutea per doe (ovulation sites)

Less in PA (1.6) than in IA (2.23) Fetuses/pregnant doe

Less in PA (1.4) than in IA (2.1)George Reserve rm = 0.956

Deer reproduction Table 5-2 PA dense, IA sparse Fawns pregnant only in Iowa

Fawns only breed when populations are low Corpora lutea per doe (ovulation sites)

Less in PA (1.6) than in IA (2.23) Fetuses/pregnant doe

Less in PA (1.4) than in IA (2.1)George Reserve rm = 0.956

Additive vs. CompensatoryAdditive vs. Compensatory

Harvest rate

Survival

rate

Compensation

Additive

Additive vs. CompensatoryAdditive vs. Compensatory

Additive mortality As more mortality factors are added, e.g. hunting,

survival decreasesCompensatory mortality

As more mortality factors are added, survival remains the same (up to a point).

Rationale to justify huntingWould have died anyway, why not by hunting?

In terms of N remaining constant, could be compensation in natality, mortality, both

Additive mortality As more mortality factors are added, e.g. hunting,

survival decreasesCompensatory mortality

As more mortality factors are added, survival remains the same (up to a point).

Rationale to justify huntingWould have died anyway, why not by hunting?

In terms of N remaining constant, could be compensation in natality, mortality, both

Survivorship CurvesSurvivorship Curves

BioEd Online

Survivorship CurvesSurvivorship Curves

Life TablesLife Tables

Actuarial tables Actuarial tables

Life TablesLife Tables

x lx dx qx = dx/lx ex

1 1000 54 54/1000=0.054

2 1000-54=946

145 145/946=0.153

Table 5.4

Life TablesLife Tables life tables.xls Methods to calculate Birth rates and death rates constant for appropriate time (life

span) Age distribution (Sx) must be stable Sx is the proportion of the number born that are alive at a given age

fx/f0

Mark individuals at birth and record age at death (lx) Calculate number dying in a particular interval

Know number alive at age x and x+1 (lx) Know age distribution and rate of increase

lx = product of Sx and rate of increase, i.e., number born What to estimate?

N might be enough Demographic rates more diagnostic

life tables.xls Methods to calculate Birth rates and death rates constant for appropriate time (life

span) Age distribution (Sx) must be stable Sx is the proportion of the number born that are alive at a given age

fx/f0

Mark individuals at birth and record age at death (lx) Calculate number dying in a particular interval

Know number alive at age x and x+1 (lx) Know age distribution and rate of increase

lx = product of Sx and rate of increase, i.e., number born What to estimate?

N might be enough Demographic rates more diagnostic

Life TablesLife Tables

Take home message Need constant schedules of mortality and

natality so the age distribution stabilizes Nearly impossible to meet these conditions

for wild populations So, actually constructing a life table for a

wild population is not likely to be possible BUT, life tables are of great conceptual

value in modeling populations

Take home message Need constant schedules of mortality and

natality so the age distribution stabilizes Nearly impossible to meet these conditions

for wild populations So, actually constructing a life table for a

wild population is not likely to be possible BUT, life tables are of great conceptual

value in modeling populations

Population DataPopulation Data

Two problems in estimating N First observability

Proportion of animals seen p is observabilityC = count

Two problems in estimating N First observability

Proportion of animals seen p is observabilityC = count

€

C = pN

N =C

p

Estimating NEstimating N

Count 43 salamanders and you know you observe 10%, then

Count 43 salamanders and you know you observe 10%, then

€

N =C

p

N =43

0.1= 430

Population DataPopulation Data

Two problems in estimating N Second sampling

Too expensive in time and money to count everywhere all the time.

Estimating populations and demographic rates is another course FW 453/553

Graduate course by Dr. Pollock

Two problems in estimating N Second sampling

Too expensive in time and money to count everywhere all the time.

Estimating populations and demographic rates is another course FW 453/553

Graduate course by Dr. Pollock

Population IndexPopulation Index

€

N =C

p

Population Index = assume p is constantUsed to make comparisons over time or space

Unfortunately, probably rarely true.

€

N1 =C1

p

N2 =C2

p

€

N1 =C1

N2 =C2

HIP and Duck StampsHIP and Duck Stamps

Migratory Bird Harvest Information System HIP certification on hunting license Used to sample hunters of doves, woodcock, and

other webless migratory birdsDuck Stamps

All duck, geese, swan hunters purchase 1934 drawn by “Ding” Darling $600mm for refuges Used to sample hunters

Migratory Bird Harvest Information System HIP certification on hunting license Used to sample hunters of doves, woodcock, and

other webless migratory birdsDuck Stamps

All duck, geese, swan hunters purchase 1934 drawn by “Ding” Darling $600mm for refuges Used to sample hunters

BBSBBS

Breeding Bird Survey Volunteers About 4,000 routes in US and Canada 50 stops on roads at 1/2 mile intervals Record birds seen and heard w/i 1/4 mi Began 1966 Over 40 years of trend data BBS

Breeding Bird Survey Volunteers About 4,000 routes in US and Canada 50 stops on roads at 1/2 mile intervals Record birds seen and heard w/i 1/4 mi Began 1966 Over 40 years of trend data BBS

Bird BandingBird Banding

Amateur and professionalsFederal bird banding lab

Early 1900’s # bands, color, petagial tags, collars, etc. Migration patterns, distributions, survival,

behavior, philopatry

Amateur and professionalsFederal bird banding lab

Early 1900’s # bands, color, petagial tags, collars, etc. Migration patterns, distributions, survival,

behavior, philopatry

Patuxent Wildlife Res. CenterPatuxent Wildlife Res. Center

1936USGS

PatuxentBBL, BBS, zoo curators, scientists,

toxicologistsWhooping cranesVideoUltralight

1936USGS

PatuxentBBL, BBS, zoo curators, scientists,

toxicologistsWhooping cranesVideoUltralight

MetapopulationsMetapopulations

Subpopulations of varying sizes somewhat isolated from each other

Genetic exchange within subpopulations > between them

Subpopulations might wink in and out of existence Unoccupied patches still important

Dispersal and recolonization are critically important

Habitat fragmentation might exacerbateModel

Subpopulations of varying sizes somewhat isolated from each other

Genetic exchange within subpopulations > between them

Subpopulations might wink in and out of existence Unoccupied patches still important

Dispersal and recolonization are critically important

Habitat fragmentation might exacerbateModel