Data Analysis and Mathematical Models
 Size is usually designated
as N (total number of
individuals)
 Density – total number
of individuals per area or
volume
 Dispersion – how
individuals in a
population are
distributed
 Age structure – is a description of the abundance of
individuals of each age
 Rapid growth – many young, few elderly; developing
countries
 Slow growth – larger at the bottom that slowly narrow; the
US
 Zero growth – tiers of equal width; Italy
 About 1,000 years ago
the human population
began population
growth thanks to
increasing the carrying
capacity of our
environment
 Increase in food
supply
 Reduction in disease
 Reduction in human
waste
 Expansion of habitat
 Survivorship Curves
describe how mortality
of individuals in a
species varies during
their lifetimes
 3 types of curves
 Type 1
 Type 2
 Type 3
 Type 1 Survivorship
describe species in which
most individuals live to
middle age; after that
mortality is high
 Examples: Humans,
Elephants
 Type 2 Survivorship
describes organisms in
which the length of
survivorship is random,
that is, the likelihood of
death is the same at any
age – constant death rate
 Examples: Rodents and
invertebrates
 Type 3 Survivorship
describe species in which
most individuals die
young, with only a
relative few surviving to
reproductive age and
beyond
 Examples: oysters,
plants, free-swimming
larvae, frogs
 Biotic Potential is the
maximum growth rate of a
population under ideal
conditions
 Take into consideration the
following:
 Age at reproductive




maturity
Clutch size
Frequency of reproduction
Reproductive lifetime
Survivorship of offspring
to reproductive maturity
 Limits to Growth
 Density-Dependent
factors are those factors
whose limiting effect
becomes more intense
as the population
density increases
 Examples – parasite &
disease transmission;
competition for
resources; predation
 Limiting Growth Factors
 Density-Independent
factors occur
independently of the
density of the
population
 Examples – natural
disasters such as fires,
earthquakes, volcanic
eruptions; extreme
climates such as storms
and frosts
 Exponential Growth in a
population occurs
whenever the reproductive
rate is greater than zero.
 Producing a J shaped curve
 G=rN
 G stands for growth, r
stands for the per capita
rate of increase, and N
stands for the population
size
 Logistic Growth occurs when limiting factors restrict the size
of the population to the carrying capacity of the habitat
 Producing a S shaped curve
 G=rN*(K-N)/K
 K stands for the carrying capacity; as N approaches K the
growth rate is slowed, eventually reaching zero growth
 Exponential and logistic growth patterns are
associated with two kinds of life-history strategies:
 R-selected species
 K-selected species
 R-selected species –
 Rapid growth (J shaped
curve)
 Opportunistic species –
grasses and insects
 Quickly invade a habitat
and reproduce
immediately (after
reproducing they die)
 Produce many offspring
that are small, mature
quickly and require little if
any parental care
 K selected species
 Population size remains
relatively constant at
carrying capacity, K – s
shaped curve
 Produce few offspring
that are larger in size
and require extensive
parental care
 Reproduction occurs
repeatedly during their
lifetime