Population Population EcologyEcology

Goal of Goal of Population Population Ecology is to Ecology is to Describe the Describe the Composition of Composition of Populations Populations Through Time Through Time and Understand and Understand Population Population FluctuationsFluctuations

Year

Num

ber

of A

nim

als

72 73 74 75 76 77 78 79 80

Describing Describing Population Population

CompositionCompositionSex RatioSex Ratio

Age RatioAge Ratio

Genetic CompositionGenetic Composition

Spatial StructuringSpatial Structuring

Sex Ratio Indicates Sex Ratio Indicates Important Processes in Important Processes in

PopulationPopulationPopulation growth Population growth potential--greater potential--greater male bias = less male bias = less growth ability growth ability (sexual species)(sexual species)

Breeding SystemBreeding System

DispersalDispersal

(Data from Marzluff (Data from Marzluff and Balda 1992)and Balda 1992)

Sex

Rat

io (

Mal

es:F

emal

es)

in F

lock

of

Pin

yon

Jays

72 73 74 75 76 77 78 79 80

Age Pyramids Summarize Age Pyramids Summarize Age StructureAge Structure

Differ for Increasing, Steady, and Differ for Increasing, Steady, and Declining PopulationsDeclining Populations

Indicate Bad Years, Bottlenecks in Indicate Bad Years, Bottlenecks in Reproduction, etc.Reproduction, etc.

IncreasingPopulation

StablePopulation

DecliningPopulation

Proportionin each

age class

Pinyon Jays Were Pinyon Jays Were Studied for 20 Studied for 20

Years Years Long-term Long-term studies of studies of marked animals marked animals are needed to are needed to get accurate get accurate population population growth and growth and composition composition information.information.

Age Structure Reflects Age Structure Reflects Relative Productivity of Relative Productivity of

CohortsCohortsYoung (cohort) from productive years constitute large Young (cohort) from productive years constitute large proportion of population for many years (1977, 1978)proportion of population for many years (1977, 1978)

A poor year of reproduction continues to be echoed in A poor year of reproduction continues to be echoed in population as a missing cohort (1976)population as a missing cohort (1976)

1978

73 74 75 76 77 78 79 80 81 82

YEAR

19761977

(Marzluff & Balda 1992)

Numberof Jaysin Flock

300

50

Importance of Indirect and Direct Importance of Indirect and Direct Selection Depends on Genetic Selection Depends on Genetic

Composition of PopulationComposition of Population

(Marzluff & Balda 1992)Age of Focal Individual

NumberofRelativesin Flock

Describing Change in Describing Change in Population SizePopulation Size

Managers are Managers are usually usually concerned with concerned with monitoring monitoring population population SIZE---So, How SIZE---So, How do WE Quantify do WE Quantify CHANGE in CHANGE in Population Population Size??Size??

(Lack 1966)

Year

Den

sity

of

Gre

at T

its

in 4

Are

as

Population size:

Nt = population size at time t

Nt+1 = population size at time t+1

Nt+1 = Nt + Births + Immigration – Deaths -Emigration

Growth rates:

r = exponential growth rate

λ (‘lambda’) = intrinsic population growth rate

Population size and Population size and rates of growthrates of growth

Population

Reproduction, births, natality (B)

Mortality, death (D)

Emigration (E)Immigration (I)

“BIDE”

Population growthPopulation growth

Age (yrs) N # Female births perpregnant female

_____________________________________________0 - - 0.0001 60 2 0.0172 36 14 0.1943 70 52 0.3714 48 45 0.4695 26 19 0.3656 19 16 0.4217 6 5 0.417>7 10 7 0.350___________________________________________

A fecundity schedule for Chamois from New Zealand.

Age-specific birth ratesAge-specific birth rates

2 4 6 8 10 12 14 16 18 20

males

females

Age at Death (years)

Survivors (lx)

Survivorship curves for male & female moose on Isle Royale

Emigration and Emigration and ImmigrationImmigration

Juvenile dispersal:Juvenile dispersal: movement from place of movement from place of birth to place of breedingbirth to place of breeding

Breeding dispersal:Breeding dispersal: movement by adults from movement by adults from one place of breeding to anotherone place of breeding to another

Birds: Female dispersing sexBirds: Female dispersing sex

Mammals: Male dispersing sexMammals: Male dispersing sex

############ #

#

#

#####

#

##

#

#

#

#

##

##

#

#

#

#

##

#

#

#

##

#

#

#

###

#

# ##

#

##

#

## # #

#

0 500 1000 1500 2000 2500 3000 3500 4000 Meters

American RobinAmerican Robinpost-fledging post-fledging movementsmovements

Population GrowthPopulation GrowthCarrying capacity (k)Carrying capacity (k)

Classic growth curve,unlimited resources

Classic growth curve,limited resources (k)

time time

N N

kExponential

Logistic

The Simplest Quantification of The Simplest Quantification of Population Growth Assumes Population Growth Assumes

Exponential GrowthExponential Growth

NNtt=N=N00eertrt-----let t = 1 year-----let t = 1 year

NN11=N=N00eerr

eerr=N=N11/N/N00======LambdaLambda, Finite rate of , Finite rate of IncreaseIncrease

Lambda goes from 0 (extinction) to 1 Lambda goes from 0 (extinction) to 1 (stable growth) to positive infinity (stable growth) to positive infinity (Exponential growth of various (Exponential growth of various magnitude)magnitude)

Exponent Exponent Indicates the Indicates the Magnitude of Magnitude of

ChangeChangeeerr=N2/N1---Take ln (natural log, log=N2/N1---Take ln (natural log, logee) of ) of both sides to get:both sides to get:

r = ln(N2/N1)r = ln(N2/N1)

varies from negative infinity (decrease) to varies from negative infinity (decrease) to 0 (Stable) to positive infinity (increase)0 (Stable) to positive infinity (increase)

r, the exponential multiplier, = Intrinsic r, the exponential multiplier, = Intrinsic (instantaneous) rate of increase(instantaneous) rate of increase

Exponents provide Exponents provide consistent quantification of consistent quantification of

magnitude of changemagnitude of change

Doubling and halving of population Doubling and halving of population produces same exponent multiplier of produces same exponent multiplier of change----sign of multiplier changeschange----sign of multiplier changes

N1=50 ---N2=100--doublingN1=50 ---N2=100--doublingeerr = (lamda) = 100/50 = 2 = (lamda) = 100/50 = 2

r = ln (2) = .693r = ln (2) = .693

N1=100--N2=50---halvingN1=100--N2=50---halvingeerr = (lamda) = 50/100 = 0.5 = (lamda) = 50/100 = 0.5

r = ln (0.5) = -.693r = ln (0.5) = -.693

Units of r and Units of r and lambdalambda

Units of lambda are obviousUnits of lambda are obviousnumbers per unit timenumbers per unit timerestricted to the unit it was calculated overrestricted to the unit it was calculated overt = 1 year, then rate is change per yeart = 1 year, then rate is change per year

Units of r not obviousUnits of r not obviousit is a multiplier, not a rateit is a multiplier, not a rate““growth multiplier of ln(#s) per unit time”growth multiplier of ln(#s) per unit time”not restricted to unit it was calculated overnot restricted to unit it was calculated overr from 1 year can be transformed to r for r from 1 year can be transformed to r for each day by dividing by 365, etc.each day by dividing by 365, etc.

Lambda and r Lambda and r Both present the same information in Both present the same information in varying formatsvarying formats

Population increases at lambda per unit Population increases at lambda per unit time or r at any instant in timetime or r at any instant in time

r is useful because it can be r is useful because it can be transformed to fit time interval of transformed to fit time interval of interest, lambda is more intuitiveinterest, lambda is more intuitive

Australian rabbit (European hare)

• 1859: 24 hares introduced (for human food?)• 1865: over 20,000 hares were harvested, actual population much greater.• Mid-1800’s to mid-1900’s: major problem with too many hares; caused habitat destruction and reduction in native mammals• 2000: still present, local problems

Unlimited GrowthUnlimited Growth

No rabbitsRabbits exceeded k

Rabbit-proof fence

Carrying capacityCarrying capacity

time

# ofAnimals

(N)

k

Carrying capacity (k): the number of organisms that can be supported by a given area; the actual number of organisms fluctuates near this

Carrying capacityCarrying capacity

Adding A Limit to Adding A Limit to Population Population

GrowthGrowthMore Realistic than Exponential GrowthMore Realistic than Exponential Growth

Growth is adjusted as population Growth is adjusted as population approaches carrying capacity (K) of the approaches carrying capacity (K) of the environmentenvironment

Population growth simply stops at KPopulation growth simply stops at K

Population crashes after resource is Population crashes after resource is consumedconsumed

Population growth is under negative Population growth is under negative feedback as it approaches K and gradually feedback as it approaches K and gradually reaches Kreaches K

Population Growth is Gradually Population Growth is Gradually Reduced as Carrying Capacity is Reduced as Carrying Capacity is

Reached; Resources Renew Reached; Resources Renew Independently of Population Independently of Population

SizeSize Logistic GrowthLogistic Growthsimple favorite in simple favorite in wildlife wildlife managementmanagement

Rate of Increase is Rate of Increase is only a function of only a function of Population DensityPopulation Density

Assumes resources Assumes resources are not damaged are not damaged by large by large populationspopulations

Wildebeast don’t Wildebeast don’t affect grass rootsaffect grass rootsTime

#s

Ln

(#s)

K

Inflection Point

Logistic MathLogistic MathVerhulst (1838) and Pearl & Reed (1920) Verhulst (1838) and Pearl & Reed (1920) independently derived equationindependently derived equation

Verhulst-Pearl Equation (Sigmoidal Growth)Verhulst-Pearl Equation (Sigmoidal Growth)

dN/dt = derivative form of change in N dN/dt = derivative form of change in N with respect to timewith respect to time

dN/dt = rdN/dt = rmmN(1-N/K)N(1-N/K)

dN/dt = rdN/dt = rmmN = exponential growthN = exponential growth

As N approaches K, N/K approaches 1. As N approaches K, N/K approaches 1. Therefore rTherefore rmmN(1-N/K) approaches 0N(1-N/K) approaches 0

With K and Typical Seasonal Patterns of

Reproduction, There is Often A “Doomed

Surplus”Mink control distribution of muskrats

those in poor sites including dispersers are eaten

Predators often take the young, homeless, sick, injured, dispersing, or old individuals

so effect on species or community is less

Good Sites Poor Sites

High Pops

LowPops

Den

sity

of

Mus

krat

s

DeepWater

DryUpland

(Errington 1946)

Logistic Growth Model Logistic Growth Model May be Used to Calculate May be Used to Calculate

HarvestHarvestMaximum Maximum Sustainable Yield Sustainable Yield is at Inflection is at Inflection Point Point

Growth is Growth is Maximum and Maximum and Population is at Population is at Largest SizeLargest Size

Larger Populations Larger Populations Start to Have Start to Have Slower GrowthSlower Growth

Time

#s

Ln

(#s)

MaximumYield=1/2 K

K

Another View of Another View of Logistic GrowthLogistic Growth

Growth rate Growth rate starts slow, starts slow, peaks, and ends peaks, and ends slowslow

Maximum Maximum Sustainable Yield Sustainable Yield is at rate of is at rate of fastest fastest population population growthgrowth

N

dN/dt

K

Inflection PointMax SustainableYield

Assumptions of Assumptions of Logistic GrowthLogistic Growth

All individuals contribute equally to All individuals contribute equally to population growth--equal reproduction population growth--equal reproduction regardless of age or sexregardless of age or sex

Growth rate is constant regardless of Growth rate is constant regardless of environmental variationenvironmental variation

K is constant--not affected by growthK is constant--not affected by growth

Reduction in growth as population Reduction in growth as population approaches K is linear and instantaneous approaches K is linear and instantaneous (no time lags)(no time lags)

Populations fluctuate Populations fluctuate due todue to

Density dependent factorsDensity dependent factorsEx: Predation, competition, habitat Ex: Predation, competition, habitat availabilityavailability

change population growth in predictable change population growth in predictable waysways

N is driven by population densityN is driven by population density

Density independent factorsDensity independent factorsRandom or Random or StochasticStochastic events events

Ex. Weather, accidentsEx. Weather, accidents

BreedingBreeding

14 aug 2007

Reindeer(caribou)

Bighorn sheep

Population density (top) or size (bottom)

# youngproduced

High food addition

Low food addition

No food added

Shaded area is winter

Townsend’s vole

Population regulation: Population regulation: foodfood

Population cycles: Ex. peaks in lynx populations show time lag behind peaks in snowshoe hare populations

Pop

ulat

ion

size

Snowshoe hare

Lynx

Time (years)

Population regulation: food

Population regulation: Population regulation: climateclimate

CompetitionCompetition – demand by 2 or more individuals of – demand by 2 or more individuals of the same or different species for a common the same or different species for a common resourceresource

Between 2 individuals of same species: Between 2 individuals of same species: IntraspecificIntraspecific

Between 2 individuals of different species: Between 2 individuals of different species: InterspecificInterspecific

Limited supply of resource: Limited supply of resource: ExploitationExploitation

Not limited but interaction detrimental: Not limited but interaction detrimental: InterferenceInterference

Population regulation: competition

Inter- or Intraspecific competition?Inter- or Intraspecific competition?Exploitation or Interference Exploitation or Interference

competition?competition?

Population regulation: Population regulation: competitioncompetition