BISC 102 Chapter Notes - Chapter 52: Exponential Growth

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Read Chapter 52: pages 1147-1152
Population Growth
Quantifying the growth rate
a population’s growth rate is the change in the
number of individuals in the population per
unit time
if no immigration or emigration is occurring,
the an population’s growth rate is equal to the
number of individuals (N) in the population
times the dierent between the birth rate per
individual (b) and the death rate per individual
(d). The dierence between the birth rate and
the death read per individual is called the per
capita rate of increase, and is symbolized
if the per capita birth rate is higher than the
per capita death rate then r is positive and the
population is growing
the opposite is also true
when conditions are optimal for a particular
species - meaning birth rates per individual are
as high as possible and death rates aper
individual are as low as possible - then r
reachers a maximal value called the intrinsic
rate of increase rmax
each species has a characteristic r-max, that
does not change. But any specific time, a
population has an instantaneous growth rate,
or per capita rate of increase
Exponential Growth
exponential population growth occurs when r
does not change with population size or
density
the key point about exponential growth is that
the growth rate does not depend on the
number of individuals in the population
this type of population growth is called
density dependant
in nature exponential growths observed in two
circumstances
1. a few individuals found a new
population in a new habitat
2. a population has been devastated by a
storm or some other type of catastrophe
and then begins to recover, starting with
a few starting individuals
many populations in unstable or unfavourable
environments have periods of exponential
growth, but it is not possible for exponential
growth to continue indefinitely
population density refers to the number of
individual per unit area - gets very high, the
population’s per capita death rate will
increase, causing r to decline
Logistic Growth
to analyze when growth is density dependant,
biologists use a parameter called carrying
capacity
carrying capacity (k) is defined as the
maximum number of individuals in a
population that can be supported in a
particular habitat over a sustained period of
time
the carrying capacity of a habitat depends on
a large number of factors; food, space, water,
soil quality, and resting or nesting sites.
carrying capacity can change from year to
year, depending on conditions
The Logistic Growth Equation
if a population of size N is below the carrying
capacity K, then the population should
continue to grow
a populations growth rate is proportional to (K-
N)/K:
when N is small, then (K-N)/K is closer to 1
and the growth rate should be high
as N gets larger (K-N)/K gets smaller
when N is at carrying capacity - meaning that
K-N then (K-N)/K is equal to 0 and growth
stops
Graphing Logistic Growth
1. initially, growth is exponential - meaning that r
is constant
2. with time, N increases to the point where
competition for resources of other density-
dependant factors begins to occur. As a result,
the growth rate begins to decline
3. when the population is at the habitat’s carrying
capacity, the growth rate is 0 - the graph of
population size versus time is flat
What Limits Growth Rates and Population Sizes?
population sizes change as a result of two
general types of factors
density indépendant factors alter birth
rates and death rates irrespective of the
number of individuals in the population
and usually involve changes in the
abiotic environment
density dependant factors change in
intensity as a function of population size
and are usually biotic in nature. When
trees crowd each other, they have less
water, nutrients, and sunlight at their
disposal and make fewer seeds
A Closer Look at Density Dependance
density-dependant changes in survivorship
and fecundity cause logistic population growth
in this way, density-dependant factors define a
particular habitat’s carrying capacity
Carrying Capacity is NOT Fixed
its important to recognize that K varies
between species and populations.
k varies in space, it also varies with time, as
conditions in some years are better than in
others
these observations help to explain the
variation in total population size that exists
among species and among populations of the
same species
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