BIO205H5 Lecture Notes  Whooping Crane, Intraspecific Competition, Endangered Species
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Intraspecific Population Regulation
Density independent growth
Density dependent growth
Logistic Model
Intraspecific competition
Types of intraspecific competition
Intraspecific competition affects:
 growth/development
 reproduction
stress
 social behavior
Outline
A) Discrete(geometric)growth
–Populationsthatbreedoverdiscretetime
intervals(eg.oneyearperiod)
–Allbirthsoccurinspring;doacensusoneyear
laterafterreproductioniscomplete
N(t)=N(0)t
1.DensityIndependentGrowth
 populations increase and discrete growth has time intervals.
 step graph where breeding occurs in time. if birds breed only in may
then they breed, wait till next year and we see how many are breeding.
look at pops from one year to the next.
A) Discreteorgeometricpopulationgrowth
N(t)=N(0)t
N(1)=N(0)1
Eg.,ifnumberoffemalesbreedinginspringof2009=41
Andifnumberoffemalesbreedinginspringof2010=49
=49/41
=1.2
1.DensityIndependentGrowth
B)Exponentialorcontinuouspopulationgrowth
–Ifreproductioniscontinuous,thenitismore
appropriatetolookattheinstantaneousrateof
increase=r
–Independentoftimeperiods:smoothcurve
N(t)/N(0)=
=erorr=ln
•Example:graysquirrelpopulation:r=ln(1.2)=0.18
1.DensityIndependentGrowth
Whatisr?
b=instantaneousbirthrateperindividual
d=instantaneousdeathrateperindividual
dN/dt =(b‐d)N =rN
dN/dt =rN
r=intrinsicrateofincrease
=rateatwhichapopulationgrowsunderidealconditions
1.DensityIndependentGrowth

 not all organisms have a discrete breeding period and have a
continuous period  curve. more appropriate to look at
instantaneous rate of growht (r). we know that a change in
pop can give us lambda and can be rearranged to give us e^r
the ln of which will give us the pop at instantaneous slope.
 use this in life table to figure out the exponential pop growth.
 density independent growth  density has no affect on the growht
so the population has no affect on density and vice versa 
r = birth rate  death rate based on pop size that we have.
“r”
‐variesamongspecies
‐variesamongpopulations
‐dN/dt =(b‐d)N =rN
‐Rateofchangeofapopulationovertime,dN/dt,
isafunctionofpopulationsizeN(inrN)
Trend:asyougofromsmalltowardslargeanimals,theintrinsic rateof
increasedeclineswithincreasingsize
PopulationGrowthReflectstheDifferencebetween
RatesofBirthandDeath
•WewantanequationtopredictpopulationsizeN(t)under
conditionsofexponentialgrowth
N(t)=N(0)ert
•N(t)=numberattimet
•N(0)=initialpopulationsizeatt=0
•e=baseofnaturallogarithm=2.72
•r=intrinsicrateofincreaseinyoung/timeinterval
•t=numberoftimeintervals(days,years)
GrowthRatesCanBeUsedtoPredictPopulation
Sizes
Whooping crane
Endangered species: 15 whooping cranes remained in 1941
Calculating Exponential Growth Rate
 Whooping cranes were near extinction due to
overhunting and habitat destruction
Characteristics of population:
small population size
protected from hunting
abundant resources
N = 15 birds in 1941
Q1. If there are 425 birds alive in 2004, what is r?
N(t) =N(0)ert
425 = 15er(63)
425/15 = 28.33 = er(63)
r = ln(28.33)/63
= 3.34/63
= 0.053
 r is not going to be the same among species and among
populations.
 as you go from small to larger animals, the rate of increase
declines with increase in size. a very indicative general trend
that the larger you are for animals, intrinsic rate of ___ declines with
size.
 equation predicts a population size under a certain time under
exponential growth.
 a population is endangered and we can introduce it to an env
that will help it increase in number. take a look at what we can find
out from the data of the population.
 protection laws are put against predators etc and put it in an area
with abundant resources.
start with1 5 birds  intro to habitat and monitor it.
 if there are 425 birds in 2004 what is the rate of increase?
 equation of pop at certain period = pop at certain time * e^rt
time difference = 63

Document Summary
What is r? b = instantaneous birth rate per individual d = instantaneous death rate per individual dn/dt = (b d)n = rn dn/dt = rn r = intrinsic rate of increase. N(t) = n(0)ert: n (t) = number at time t, n(0) = initial population size at t = 0 e = base of natural logarithm = 2. 72 r = intrinsic rate of increase in young/time interval t = number of time intervals (days, years) Whooping cranes were near extinction due to overhunting and habitat destruction. 2 = e(0. 053)t ln 2 = 0. 053t t = 0. 693/0. 053. Endangered species: 15 whooping cranes remained in 1941. Density independent growth: birth and death rates are influenced by density independent factors, regardless of the number of individuals, abiotic factors. The logistic model of population growth dn/dt = rn(1 n/k: when n is low relative to k, the term (1 n/k) is close to.