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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
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