What is a species?

What is a species?1) Pre-mating isolating mechanisms.

a) Temporal isolation. b) Ecological isolation. c) Behavioral isolation.

d) Mechanical isolation. 2) Post-mating isolating mechanisms.

a) Gametic incompatibility. b) Zygotic mortality. c) Hybrid inviability. d) Hybrid sterility. e) Hybrid breakdown.

Population Ecology• Population (N)

– Group of animals, identifiable by species, place, and time• Defined by population biology

– Genetic definition would be more specific• Individuals comprise a population• Collective effects of individuals

– Natality, mortality, rate of increase

• Most management = – Populations– not individuals

Rates• Natality

– Births (per something)• Mortality

– Deaths (per something)• Fecundity

– Ability to reproduce– Number of eggs– Female births/adult female

• Productivity– Number of young produced

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

Definitions• Age structure

– Number of individuals in different age classes

• Sex ratio– Male:female

• Buck only deer hunting 1:3• QDM at Chesapeake Farms 1:1.5• Some dabbling ducks 10:1

Age Pyramids

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

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

Age 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 Pyramid

males females

Buck only hunting

Age pyramid

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 Growth – 2 main models

Exponential Growth Logistic Growth

• Assumes resources unlimited

• Considers carrying capacity

Population Growth

• Lambda– Measure of population growth– Ratio of population sizes – No Units– >1 population is growing– <1 population is declining– Important measure of pop status

N t1N t

Demographic Rates

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

r b d i e

Population Growth

• r– actual growth rate of population– birth rate – death rate (Exponential Model)– (Birth rate + immigration rate) – (death rate +

emigration rate) - > more realistic

Exponential Growth• Constant per capita rate of increase (r)

– Constant percentage increase– Ex: 10% per year

• Text– “ever-increasing rate” per unit time

• Means number added per unit time is ever-increasing

• Population growth model

Year N N + 1 Recuits R Lambda r1 100 120 202 120 144 243 144 173 294 173 207 355 207 249 416 249 299 507 299 358 608 358 430 729 430 516 86

10 516 619 103

Year N N + 1 Recuits R Lambda r1 100 120 20 1.20 0.202 120 144 24 1.20 0.203 144 173 29 1.20 0.204 173 207 35 1.20 0.205 207 249 41 1.20 0.206 249 299 50 1.20 0.207 299 358 60 1.20 0.208 358 430 72 1.20 0.209 430 516 86 1.20 0.20

10 516 619 103 1.20 0.20

• population growth

• Population of 100 individuals (N)• Each individual can contribute 1/3 (0.33) of an individual

to the population in a given unit of time (r)• What is rN?• ΔN/Δt?• Nt+1 ?

Exponential Growth

• George Reserve example

– Dr. Dale McCullough

• Estimated per capita growth rate for unencumbered growth (rm)– New species in optimal habitat– Maximum per capita growth rate– Why estimate it?

Problems with Exponential Growth Model

• Assumes unlimited resources for population growth– Birth rates and death rates remain constant

When is this true??

Quiz1) T/F? Both lambda and r increase through

time in the exponential growth model. 2) T/F? Both lambda and r change through time

in the logistic growth model. 3) Humans have a Type I survisorship curve4) Are feral cat killings of songbirds a type of

compensatory or additive mortality?

Logistic Growth Model

• Why worry about this?• Fundamental conceptual relationship that

underlies sustained yield harvesting• NC 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 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 rate• For exponential growth r = rm

• Only occurs for small populations for a short time• McCullough should have estimated rm

Logistic Growth Model

• One specific form of sigmoid growth– Growth model

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

RNrm(K N)

K

Logistic Growth Model

• As N approaches K, r = 0

• When N small, then r = rm

(K N)

K0

(K N)

K1

RNr

rrm(K N)

K

Logistic Growth Model

rrm(K N)

K

Density-dependent growth

RNrNrm(K N)

K

YearRecruitsResidual 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 49.. .. .. .. ..20 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

Year Recruits Residual N r N + 1 3 9 0.333 122 4 12 0.333 16 3 5 16 0.313 21 4 7 21 0.333 285 9 28 0.321 376 12 37 0.324 49.. .. .. .. ..20 11 371 0.030 382 21 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

rrm(K N)

K

dN/dt = rN(K-N)/K

K

NKNrNrR m

)(

r vs population size

population size versus time

# Recruits vs population size

dN/dt = rN(K-N)/K

rrm(K N)

K

K

NKNrNrR m

)(

dN/dt = rN(K-N)/K

rrm(K N)

K

K

NKNrNrR m

)(

Density Dependent Growth

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

Density-dependent factors vs density-independent factors

Density Dependent Growth

• Combined effects of natality and mortality– Births decline as N increases above a certain point– Deaths increase as N increases above a certain point

Density 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

Sustained Yield

• Inflection point (I)– Sigmoid curve slope changes from positive to

negative– Peak hump-shaped SY (or R) curve

• Maximum R per unit time

– Point of MSY (K/2)

Population Growth

George Reserve Deer

SY R

R

Nrh

r per capita growth, h is per capita harvest rate

Hump-shaped, not bell-shaped

George Reserve Deer

RNrRSYSY Nr

MSY 12K 1

2rm

MSY occurs at the inflection point I

George Reserve Deer

SY

Nh

R

Nr

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

George Reserve Deer

RSYRight side of MSY (I) stable

negative feedback between N and R

George Reserve Deer

RSYLeft side of MSY (I) unstable

Positive feedback between N and R

Logistic Growth Assumptions

• All individuals the same• No time lags• Obviously, overly simplistic• Does provide conceptual bases for

management.

Population Models

• 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 population1.1mmHarvest 265,000

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

NC Deer

NC deer population1.1mmHarvest 265,000

SY

Nh

265,000

1,100,000 265,00030%

Density Dependent Factors

• Density dependent (proportional)– Mortality– Natality

• Density independent– Asian openbill storks example

• Compensatory mortality and natality

A population of Spotted Fritillary butterflies exhibits logistic growth. If the carrying capacity is 500 butterflies and r = 0.1 individuals/(individuals x month), what is the maximum population growth rate for the population? (Hint: maximum population growth rate occurs when N = K/2).

In the question you're given the following information: K = 500 r = 0.1 maximum population growth at K/2 Therefore, the maximum population size = K/2 = 500/2 = 250 dN/dt = rN[1-N/K] - this is the logistic growth equation dN/dt = (0.1)(250) [1 - (250)/500)] dN/dt = 12.5 individuals/month

Isle Royale Lessons

Wolves

Moose

Isle 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”

Mating• Sex ratio and breeding systems

– Monogamous• Balanced sex ratio

– Ducks -- sexually dimorphic» Sexes w/ different susceptibility to predation, hunting

– Canada geese -- monomorphic– Polygynous

• Manage for a preponderance of females– Pheasants, turkeys -- dimorphic– Ruffed grouse, quail -- monomorphic

– Promiscuous• Deer

– To grow, unbalanced sex ratio– QDM, balanced sex ratio

Age-Specific Birth Rates

Age-specific natality (female young/female)

Natality

Immature Adults

AGE

Age-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

Additive vs. Compensatory

• Additive mortality– As more mortality factors are added (e.g. hunting) survival

decreases

• Compensatory mortality– As more mortality factors are added, survival remains the

same (up to a point).– Rationale to justify hunting

• Would have died anyway, why not from hunting?

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

Additive vs. Compensatory

Harvest rate

Survival

rate

Compensation

Additive

Num

ber

of s

urvi

vors

Percent of maximum life span

Survivorship Curves

Survivorship Curves

BioEd Online

Survivorship Curves

Life Tables

• Actuarial tables

Life Tables

x Lx Dx qx = dx/lx Ex

1 1000 54 54/1000=0.054 7.1

2 1000-54=946

145 145/946=0.153 ------

3 946-145= 801

12 12/801=.015 7.7

Table 5.4

Life 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• 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 Data

• Two problems in estimating N– First observability

• Proportion of animals seen p is observability• C = count

C pN

N Cp

Estimating N

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

N C

p

N 43

0.1430

Population Data

• Problems in estimating N– Second sampling

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

Population 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 Stamps

• Migratory Bird Harvest Information System– HIP (Harvest Information Program) certification on

hunting license– Used to sample hunters of doves, woodcock, and other

webless migratory birds• Duck Stamps

– All duck, geese, swan hunters purchase– 1934 drawn by “Ding” Darling– $750mm for refuges ($.98/$1.00)– Used to sample hunters

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 Banding

• Amateur and professionals• Federal bird banding lab

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

Patuxent Wildlife Res. Center• 1936• USGS

• Patuxent

• BBL, BBS, zoo curators, scientists, toxicologists• Whooping cranes• Video• Ultralight

Metapopulations• 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 exacerbate• Model