population characteristicspeople.cst.cmich.edu/swans1bj/lect2.pdf · female offspring produced per...

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Population Characteristics

• Population– A group of organisms of a single

species with equal probability ofbreeding with any otherindividual.




• Community– A group of species living in a

given area




• Community– A group of species living in a

given area

• Ecosystems– The community and abiotic

factors.

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• Species– A group of organisms

capable of interbreedingand producing fertileoffspring.

– Isolated gene pools

• Isolation– Temporal

– Spatial

– Mechanical

– Behavioral


• Species

Equus caballus Equus asinus


• Species– A group of

organisms capableof interbreeding

A cross between a male donkey(jack) and a female horse (mare)produces a mule. A cross between afemale donkey (jennet or jenny) anda male horse (stallion) produces ahinny.

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• Species– A group of organisms

capable ofinterbreeding andproducing fertileoffspring.

– Isolated gene pools

• Isolation– Temporal– Spatial– Mechanical– Behavioral

Genes go in but they don’tCome out!

Population Characteristics• Vital Rates

– Birth rate (Natality)• The number of offspring

produced per unit time

• Crude birth rate– Number of individuals born

relative to the population size

– Realized birth• Number of young recruited into

adulthood

– Natality vs. Growth rate• Natality - number of offspring

produced per unit time

• Growth rate - net change inpopulation size (+ or -)

n

noffspring

adults


• Vital Rates– Death rate (Mortality)

• The number of individualsdying per unit time

• Crude birth rate– Number of individuals dying

relative to the population size

– 33% of juvenile male black-footed ferrets die beforereaching adulthood.

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Population Characteristics• Life Tables• lx = nx/n0

– # individuals alive out ofthe original population atthe beginning of age x

• dx = nx/n0– # individuals dying

between age x and x+1.

• qx = dx/nx– Proportion of individuals

of age x that die beforereaching x+1

• ex = Tx/nx

Tx=Σ{(nx+nx+1)/2}– Life expectancy of

individuals of age x

Age nx lx dx qx ex

1 100 0 1 88 0.0 88 7.2 92 91 2 0.9 12 51 0.0 56 6.9 43 86 1 0.8 61 55 0.0 64 6.3 24 80 6 0.8 06 41 0.0 51 5.7 15 76 5 0.7 65 49 0.0 64 56 71 6 0.7 16 70 0.0 98 4.3 17 64 6 0.6 46 85 0.1 32 3.7 28 56 1 0.5 61 94 0.1 68 3.2 19 46 7 0.4 67 86 0.1 84 2.7 5

10 38 1 0.3 81 10 2 0.2 68 2.2 611 27 9 0.2 79 98 0.3 51 1.912 18 1 0.1 81 73 0.4 03 1.6 613 10 8 0.1 08 56 0.5 19 1.4 414 52 0.0 52 28 0.5 38 1.4 415 24 0.0 24 13 0.5 42 1.5 416 11 0.0 11 4 0.3 64 1.6 417 7 0.0 07 4 0.5 71 1.2 918 3 0.0 03 0 0.0 00 1.3 319 3 0.0 03 3 1.0 00 0.2 5


• Survivorship Curves– Graph of log(lx) vs. Age

• Type I– Low juvenile and adult

mortality, high olderadult mortality

• Type II– Constant mortality

across all ages

• Type III– High juvenile mortality,

low mortality afterAge

Frequency ofSurviving (lx)


• Productivity– Birth rate

• Average number of femaleoffspring produced per femaleof age x.

• Net Reproductive Rate– Average number of female

offspring produced over afemale’s life time

Rl m

nx x

00

= ∑

5


• Productivity– Birth rate

• Average number offemale offspringproduced per female ofage x.

• Net Reproductive Rate– Average number of female

offspring produced over afemale’s life time

Rl m

nx x

00

= ∑

Age lx dx qx mx lxmx0 1 0 0 0 2 0 0 0.200 0 01 8 0 0 1 0 0 0.125 0 .3 2 4 02 7 0 0 1 0 0 0.143 0 .4 2 8 03 6 0 0 2 0 0 0.333 0 .3 1 8 04 4 0 0 3 0 0 0.750 0 .1 4 05 1 0 0 1 0 0 1.000 0 0

R00 240 280 180 40 0

10000 74= + + + + + = .

• What values of R0 for– Increasing population

– Stable population

– Decreasing population


• Age Structure

– Three shapes• Rapid growth

• Slow growth

• Negative growth

Habitat• Habitat

– Basic Needs• Food

• Shelter

• Water

• Peregrins– Endangered due to

DDT

– Habitat loss

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Habitat

• Habitat is notalways what youthink– Peregrins require

• Food - birds

• Shelter - highcliffs

• Water

Niche

• Multiple definitions– Job based

• The role of the organism inthe habitat

• Pileated woodpecker– Insect eater

– Cavity maker

– n-DimensionalHypervolume

• Requirements for aorganism to persist

Niche

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Niche

• Conditions canallow for– Survival

– Growth

– Reproduction

Temperature

Fitness

Niche

• n-DimensionalHypervolume– Interaction of all the

variables whichinfluence survival of anorganism

• Precipitation

• Temperature

• Altitude

• Size of preyNiche Variable

Fitness

Population Growth

Fundamental Equation:

N(t+1) = N(t) + B – D + I – E

N(t+1) - N(t) = B – D + I – E= ∆N = B – D + I – E

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Population Growth

• Types of Population growth– Exponential

• Continuous increase

– The rate of increase can stayconstant but more and moreindividuals are added as timegoes on.

– Example

» growth rate = 10%

» N = 10: + 1 kids

» N=100: + 10 kids

» N=1000: + 100 kids

» N=10000 + 1000 kids

Reindeer on St. George Is.

Population Growth

• Types of Population growth– Exponential

• Continuous increase

– Can’t occur forever!!

Reindeer on St. George Is.

Population Growth

• Exponential Growth– Growth across generations– Nt = R0 Nt-1

• Nt = population size at time t• Nt = population size at time t-1• R0

t = net replacement rate• Nt-1 = R0 Nt-1

– >Nt = R0 R0 Nt-1

– Nt = R0 t N0

– Assumes• Animals only breed once per

year• Generations do not overlap

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Population GrowthdN

dtrN

dN

dtb d N

N N etrt

=

= −( )

=

0 0

0

• Exponential Growth– Doesn’t assume single

reproductive event per year

– Doesn’t assume generations donot overlapping

• r = Intrinsic rate of increase– r = ln(R0)

• N = number of individuals

• b0 = Average birth rate perunit time

• d0 = Average death rate perunit time

What values of r equate to - Increasing population size? - Stable population size? - Decreasing population size?

Population Growth

• Why don’t populations experience continuous exponentialgrowth? Or how fast is fast?

Number of grains of rice

0

2E+18

4E+18

6E+18

8E+18

1E+19

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61

Square number

Nu

mb

er o

f g

rain

s o

f ri

ce

•Rice example–922,370,000,000,000,000,000

PopulationGrowth

• Why don’t populationsexperience continuousexponential growth?

• Mice example– R0 = 2, N0 = 2

– After 95 generations wewould have …

190000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000mice

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Population Growth

• Doubling time– Exponential growth is repeated

doubling

– Every time you doublesomething you currently havemore than every previouslyexisted!

N N e

N N e

e

rt

tr r

t ort

ort

rt

double

=

=

==

= =

2

2

2

2 0 7

0

ln( )

ln( ) .

Population Growth

• What limits population Growth?– Density Independent Factors

• Floods

• Fires

• Weather

– Density Dependent Factors• Competition

• Predation

• Parasitism

• Disease

Population Growth

• Logistic Growth– Population size can’t

exceed the size for whichresources are available.

– Results in a carryingcapacity (k)

• Maximum population sizewhich can be sustained witha given resource base

– Food– Space– Water– Shelter

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Intraspecific Competition

Population Growth

• Logistic Growth

– r = intrinsic rate ofincrease

– K = carrying capacity• Determined by intraspecific

competition

– N = Number of organisms

dN

dtrN

K N

K= −

Density-dependent Effects

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rNdt

dN =

−=

KN

rNdtdN

1

r vs. K Strategy

• r-Strategists– Many small young– Little or no parental care– Rapid development– Long distance dispersers– Early age of 1st reproduction– Poor competitors– Short life span– Small body size– Live in disturbed habitats– Wide fluctuations in

population size

• K-Strategists– Few large young– More parental care– Slower development– Short distance dispersers– Later age of 1st reproduction– Good competitors– Long life span– Larger body size– Live in stable habitats– Relatively constant

population size

Species-o’the-Hour

white-tailed deer (Odocoileus virginianus)

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Species-o’the-hour

white-tailed deer (Odocoileus virginianus)

e.g., N-S variation (often seen in animals)

N: adult males = 100 cm at shoulder

100-150 kg

S: adult males = 90 cm at shoulder

50-100 kg

key deer = 36 kg


Range = S Canada, U.S. (except parts SW),

Mexico to Bolivia & NE Brazil

Their home ranges are generally small, often a square kilometer or less. Whitetail deer yard up in theirown territories during heavy snow.

Whitetail deer are generally considered solitary, especially in summer. The basic social unit is a femaleand her fawns, although does have been observed to graze together in herds of up to hundreds ofindividuals.

Females generally follow their mothers for about two years, but males leave the group within the firstyear. Bucks may form transient groups of 2-4 in the summer, but these disband prior to the matingseason. Males begin rutting as early as September, and at this point become entirely preoccupiedwith obtaining matings. They do not guard harems (as with elk) but rather fight each otherindividually, clashing antlers to gain access to a particular female.

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Mating - Males mate at age 2, females can mate as young as 7 months. - Bucks are polygamous although they may mate guard a doe for several days or even weeks until oestrus. - Does are seasonally polyoestrous and usually come into heat in November for a 24 hour period. - If a doe is not mated, a second oestrus occurs approximately 28 days later. - Mating occurs from October to December and gestation is approximately 200 days. - First year breeders generally have 1 fawn, after, 2 per litter (occasionally 3 or 4). - Fawns are precocious and nibble on vegetation only a few days after birth. - They are weaned at approximately six weeks. Life span inthe wild is 10 years.

Whitetail does keep their offspring hiddenfrom predators. When foraging, femalesleavetheir offspring in dense vegetationforupto four hours at a time.

While waiting for the female to return,fawns lay flat on the ground with theirnecks outstretched, well camouflagedagainst the forest floor.

Fawns withhold their feces and urine until the mother arrives, at which point sheingests whatever the fawn voids to denypredators any sign of the fawn.

Bovine Tuberculosis

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Diet: Catholic diet depending on what is available in their habitat. In Michigan forests, buds and twigs ofmaple, sassafras, poplar, aspen and birch (to name a few) are consumed, as well as many shrubs. Conifers are often utilized in winter when other foods are scarce. Whitetail deer are crepuscular, feedingmainly from before dawn until several hours after, and again from late afternoon until dusk.

Competition

• Intraspecific– Between individuals of

the same species

• Interspecific– Between individuals of

different species

• Which one isstronger?

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Interspecific Competition

Competition

dN

dtr N

K N N

K

dN

dtr N

K N N

K

11 1

1 1 12 2

1

22 2

2 2 21 1

2

= − −

= − −

α

α

• Interspecific competiton– Convert individuals of

species 1 into species 2equivalents.

-α12 Amount of spp.1’s nicheoverlapped by spp 2’s niche- α21 Amount of spp.2’s nicheoverlapped by spp 1’s niche

Competition

• What happens tospecies 1 in thepresence of species 2?

K1N1

N2

K1/α12

dN1/dt =0

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Competition


K1N1

N2

K1/α12

dN1/dt =0

Competition


K2

N1

N2

K2/α21

dN2/dt =0

Competition


K2

N1

N2

K2/α21

dN2/dt =0

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Competition

K2

N1

N2

K2/α21

dN2/dt =0

K1N1

N2

K1/α12

dN1/dt =0

Competition

K2

N2

K2/α21K1N1

K1/α12

Species 2 wins

Competition

K2

N2

K2/α21K1N1

K1/α12 K2

N2

K2/α21 K1N1

K1/α12

Species 2 wins Species 1 wins

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Competition

K2

N2

K2/α21 K1N1

K1/α12

Unknown who winsBut somebody loses

Competition

K2

N2

K2/α21 K1N1

K1/α12

K2

N2

K2/α21 K1N1

K1/α12

Unknown who winsBut somebody loses

Both species winCoexistence

Competition

• What are the requirements forcoexistence?

– K1/α12 > K2

• K1 > α12 K2

– K1 > K2/α21

• K2 > α21 K1

K2

N2

K2/α21 K1N1

K1/α12

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Competition

• Competition betweentwo species ofparamecia results inthe extinction of thespecies with the lowercarrying capacity


eastern cottontail (Sylvilagus floridanus)

Habitat

Old fields, brushy forestedges, suburbs

Food

Herbivorous --grasses/forbs, woodyplants (winter) --caprophagy

Reproduction

Late winter to fall

2-3 mo. sexual mature

litter size = 3-5, 28 g.p.

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Behavior

solitary

crepuscular & nocturnal

Status

game species

Michigan Regs

Season mid Sept-late Mar

Bag limit = 5

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