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Population Growth and Regulation (more chapter 10)
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Terms in this set (56)
Population
a group of individuals of the same species living in the same place
Population Growth Rate
the number of new individuals produced per unit of time minus the number that die
Population Ecology
critical for conservation of threatened species, control of over-abundant pest and invasive species, responsible management of natural populations
Exponential Functions
tell you the result of raising a base number to a given power
Log Functions
reverse exponential functions, tell you what power is needed to achieve a result form a base number
Expnential Growth Model
how a population will grow under ideal conditions
Relative growth rate is constant
Nt=N0e^rt
Nt
future population size
N0
current population size
e
Euler's number ~2.718
r
intrinsic per capita growth rate (instantaneous)
t
time
d
change in
Population's growth at a specific point in time
dN/dt=rN
Intrinsic Growth Rate
R=b-d
2 percent per year
The population of Utopia grows exponentially with a birth rate of 3 percent per year and a death rate of 1 percent per year. What is the per capita growth rate for the Utopian population?
Geometric Growth Model Equation
Nt=N0λ^t
Geometric Growth Model
compares population size at regular time intervals
λ
discrete population growth rate (Nt/Nt-1)
Doubling Time
the time required for a population to double in size, useful measure of population growth
Continuos Exponential Growth
T2=(loge2)/r
Discrete Growth
T2=(loge2)/logeλ
Density Independent
exponential and geometric models because assumes constant birth and death rate
Indefinite Growth is Not Possible
resource limitation, epidemics and other natural enemies, environmental change and natural disasters
Density Independent Factors
not related to the population's density, often abiotic
Density Dependent Factors
related to density, often biotic
Negative Density Dependence
high population size, intraspecific competition, disease, birth rate decrease
Positive Density Dependence
low population size, inability to find mates or forage successfully
Population Regulation
involves positive and negative density dependence
Low Density
few individuals available to breed, low growth
Increased Densities
with abundant resources, more individuals for breeding
Carrying Capacity
K, the maximum population supported by the environment
Above K
low reproduction and survival cause negative population growth
Logistic Model of Population Growth
describes slowing growth of populations at high densities
dN/dt=rN(1-N/K)
Inflection Point
the point of fastest growth after which growth begins to slow
Experimental Evidence
many organisms show evidence of logistic population growth, protists raised with two different food supplies, both leveled off just at different Ks
Predictions of the Logistic Model
rarely fulfilled, environmental variability, populations overshoot K, complex dynamics: cycles and chaos
Density Independence
birth and death rates unaffected by population size, does not mean infinite growth, many factors can prevent populations from reaching K (disturbance, climate, fire, specialist predation)
Age Structure
population growth rate is influenced by the proportions of individuals in different age class
Life Table Analysis
growth in a structured population-females only
X
time/age
Nx
number of individuals surviving to age x
Sx
age specific survival (from x to x+1)
Bx
age specific fecundity, births
Calculating Survivorship
l2=l1s1
Calculating Net Reproductive Rate
multiply survivorship lx, by the fecundity bx for each age class, add new values together
After Many Generations
population will grow geometrically at a stable rate of increase, the population will reach a stable age distribution, after initial fluctuations number per age class may go up or down but proportion remains the same
Survivorship
lx, the probability of surviving from birth to any later age class
Type 1 Survivorship
high mortality late in life
Type II Survivorship
constant mortality
Type III Survivorship
high mortality early in life
Net Reproductive Rate
R0, average number of female offspring per female over her lifetime
Cohort Approach
follow a group of same-aged individuals throughout lives, easy to apply to organisms that are sessile or easily tracked throughout lives, results can be confounded with environmental change
Static Approach
all individuals at a particular point in time, can be applied to more mobile individuals, but requires a way to identify age, age not confounded with time but year selected may not be representative
Cohort Survivorship
lx=nx/n0
Human Population Growth
has been growing exponentially, don't know if we have already overshot K
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