Populations and our place in the Biosphere
To begin understanding populations, remember the
definition of ecology:
Ecology is the study of the distribution and
abundance of species (or populations).
It is also the study of causes of those
distributions and abundances.
What kinds of distributions are typically seen in
natural populations?
Three kinds represent pigeonholes along what is
really a continuous distribution of kinds:
1) random
2) regular (or overdispersed)
3) clumped (or contagious)
1) Randomly - one example is the distribution of
trees of a single species in the diverse and
complex tropical forest.
2) Regular - (or uniform or overdispersed) One example of this distribution include the
penguins shown below on nesting territories.
Each one is just beyond the reach of its
neighbors. Another is the spacing of creosote
bushes, each poisoning the ground around it.
3) clumped - organisms ‘gather’ where conditions
are better for them. When you measure
population density, it is higher where conditions
are better. This is, especially when viewed from
a larger perspective, the most common pattern.
With that background about distribution, what about
abundance?
Populations are dynamic. They grow in size
(number).
Growth seems to follow two different patterns:
1) Exponential (or density-independent) growth
2) Logistic (or density-dependent) growth
If a real population grew indefinitely, it would
eventually follow the logistic pattern (because the
resources supporting it are not infinite, but some
species (like insects) grow seasonally, and during
their growing season, grow essentially exponentially.
Exponential growth
-Limits to exponential growth are set by abiotic
factors, e.g. weather
-The same proportion of population is affected by
abiotic factors, whatever the size or density of the
population (that’s why it’s described as density
independent.
-The slope of the growth curve (rate of growth)
increases as population grows, and in direct
proportion to the size. Mathematically:
dN
 rN
dt
Graphically:
The 1.0 and 0.5 are values of r, the growth rate per
unit of time. N is the population size.
Populations that seem to grow exponentially still
have a carrying capacity - a population size that
can be supported by prevailing conditions and
resources.
Some populations growing exponentially can,
due to their rapid rates of increase, temporarily
exceed the carrying capacity. Those populations
then crash to sizes well below carrying capacity.
Think of this as boom and bust.
carrying capacity, K
#
time
Logistic growth
-Limits to growth are set by biotic factors, e.g.
food,
interactions with other species like competition
or predation
-The growth curve at low density looks like the
exponential, but slope and growth rate decline
as numbers increase, until there is no further
growth when population size reaches K, the
carrying capacity.
-The proportion affected increases with density (so
this growth pattern is called density-dependent.
Mathematically:
dN
K  N

 rN 

 K 
dt
Graphically:
The data points are a real growth curve for Paramecium in
a culture flask.
Biological interactions influence growth rate:
a) predation, parasitism (and disease, which is
a form of parasitism) reduce growth rate
b) predators and parasites are more likely to
encounter and attack members of a population
as its density increases
c) competition, both between species and among
members of this population, has greater
impact as density increases
d) stresses in the denser population also increase
the likelihood that members will emigrate
e. Thus, the growth rate slows as the carrying
capacity is approached. In theory, growth
ceases, and the population reaches an equilibrium
at the carrying capacity.
f. Due to the shape of the growth curve (basically
S-shaped), logistic growth is sometimes described
as ‘sigmoid’.
What processes determine the changes in population
size?
Birth - adds new individuals to a population
Death - removes the dying from the population
Immigration - brings new individuals into it
Emigration - individuals leave, decreasing the
population
We usually disregard immigration and emigration
in simple models of population growth.
Instead we study the demography of the population.
Demography is the study of the age-specific
survivorship and reproduction of individuals in a
population. From these we can predict whether a
population is going to grow, remain stable, or decline.
There are two approaches: numerical and quantitative
or descriptive and graphical.
First the graphical approach:
a “demographers curve” plots the fractions of a
population in each age class, separating males
and females
Note the differences in shapes of demographers’
curves for Sweden, Mexico, and the U.S.
What do the differences tell us?
1. The ‘curve’ or histogram is divided into 3 regions:
pre-reproductive (ages < puberty)
reproductive (ages from puberty to menopause)
post-reproductive
2. The shape tells us about population growth:
If the curve is wider (a larger fraction) in the
young ages then more will be becoming
reproductive than ceasing reproduction - more
babies means a growing population.
If the curve is straight along the edges, a
similar number is beginning and stopping
reproduction; population size will remain
constant, called zero population growth.
3. When there’s a ‘hump’ in the curve (go back and
look at the curve for the U.S.), it indicates a
transient increase in the number of babies - a
“baby boom”. These data clearly show the postWWII boomers.
Now the quantitative approach: structure and use of a
life table.
In a life table we follow a cohort (a group of organisms
born at the same time), recording how many are alive
at each time interval, and how many young each female
has during the interval.
The numbers in the life table are:
a) age structure - the age classes
b) survivorship - how many from the cohort
(what fraction?) are still alive at age x?
c) age specific natality - how many young are
born to females of each age?
Here’s what a life table looks like:
fraction
fecundity
alive
Age #alive lx
#dying
mx
0
1000 1
500
0
1
500
.5
250
2
2
250
.25
125
4
3
125 .125
62
4
4
62 .0625
62
1
From it many things can be calculated:
1) population growth rate (r) - combines survivorship
and natality (births) into an instantaneous growth
rate. It is analogous to the interest rate on your bank
account (if the bank compounded instantaneously).
However, no bank compounds instantaneously; the
best available is daily compounding.
2) how much longer is an organism already x years
old likely to live? This is what your insurance
needs to know. It is called ex (or life expectancy).
There are typical patterns for a curve of survivorship
over the lifespans of organisms. There are 3 patterns
representing a continuum of possibilities:
Type I - organisms live out a very large fraction of
their genetically programmed maximum
lifespan. Humans and other large mammals
have this survivorship pattern.
Type II - organisms suffer a constant proportional
mortality over time, e.g. the sample life table.
Perching birds and bats are good examples of
this survivorship.
Type III - suffer very high mortality in initial periods
of life, but have high survivorship thereafter.
A maple tree, oyster, or salmon are good
examples here.
There are also characteristic patterns of natality, and
they are associated with the survivorships. In sum,
patterns in survivorship and natality are called:
Life History Patterns
Again there is a continuum, but we recognize
differences between the extremes:
opportunistic (r-selected, weedy) species typically capable of rapid growth when
conditions are good
versus
equilibrial (K-selected, climax) species - grow
only slowly, but maintain populations near
carrying capacity, K.
Characteristics
Opportunistic
Age of 1st
early, low
reproduction
litter size
large
size of offspring small
parental care
no
organism size
population size
growth pattern
typically small
variable - small
frequently looks
exponential
Equilibrial
later, older
small
large
variable,
some yes
typically large
stable - high
logistic