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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