Ecology-Duckweed Population Growth
Introduction
Reproduction is a fundamental characteristic of living things. All organisms are capable of
population growth under some set of possible conditions. Depending upon their life history,
some organisms are capable of much more rapid population growth than others. Ecologists
study population growth, to understand how the biology of organisms interacts with
environmental conditions to produce periods of population growth, stability, and decline, and to
understand the factors that ultimately limit the growth of populations.
Exponential growth
For a continuously reproducing population, exponential growth is an excellent first
approximation of population growth. When resources are not limiting, and interspecific
competition is at a minimum, many populations of organisms grow exponentially. This generally
occur when populations are at densities far below their environmental carrying capacity (see
below), although some populations, especially birds and mammals, may actually decline if
densities are too low, because individuals cannot find mates or engage in other social behaviors
necessary for their reproduction. This is called the Alee effect.
In exponential growth models, births and deaths take place continuously. In calculus terms:
DN/DT=bN-dN
• Where:
• b is the per capita birth rate
• d is the per capita death rate
 N is the population
 T is time
 D is delta (change)
This model ignores immigration and emigration for the time being.
Thus:
dN/dT=rN
r, the instantaneous population growth rate,=b-d)
• You can integrate this to get the exponential growth formula that follows...
N(t)=N0rt
• Where r is the rate of growth
• N is the starting population
• t is the time elapsed
0
Note: if r=0 if the population is constant, r>0 if population is increasing, r<0 if the population is
decreasing.
Limits to Growth
No population can continue growing forever. Even organism that reproduces very slowly, such
as elephants, rhinos, whales, and humans, would outstrip their resources if they reproduced
indefinitely. Populations grow until one or several limiting resources become rare enough to
inhibit reproduction so that the population no longer grows (or, more rarely, until parasites or
predators inflict enough density dependent mortality to halt population growth). The limiting
resource can be light, water, nesting sites, prey, nutrients or other factors. Eventually, every
population reaches its carrying capacity; this is the maximum number of individuals a given
environment can sustain.
Logistic Growth Model
The logistic growth model accounts for carrying capacity. It states that:
dN/dT=[rmaxN(K-N)]/K
• K= Carrying Capacity, this is the maximum number of individuals that the population can
sustain.
• N=The Number of individuals in the population at a given time
• rmax is the maximum population growth rate
For laboratory populations of Paramecia, crustaceans, etc., the logistic provides a pretty good
fit. For actual populations, the logistic does not provide such a good fit.
There are usually other factors involved. One factor: lag time is the time it takes between
reaching carrying capacity and the slowdown in reproduction. Other factors include parasites
and pathogens, which may exhibit population cycles in response to the growth of their prey, and
induce complex dynamics into the system.
In this laboratory exercise, you will observe population growth in a small, notoriously fastgrowing vascular plant, in a laboratory. You will test the validity of the exponential and logistic
growth equations and attempt to identify what, if any, factors limit population growth.
The Laboratory Exercise
This is the kind of lab where you set it up at the beginning of the semester, check
on it periodically, and come back to it weeks later.
Part 1. Set up your duckweed.
Do this on day 0. Record the date so that you know how many days have elapsed between
measurements of population size.
1) Take a single, glass finger bowl and fill it to the top with duckweed medium. This medium is
simply tap water with a few drops of Miracle Gro per liter. The Miracle Gro provides the
Nitrogen, Phosphorus, Iron, Magnesium, and other nutrients plants need to grow. Using a
forceps, remove four duckweed and float them in your fingerbowl. Label the side with tape,
including your names, lab section, and table.
Place it under the lights in the back of the room.
Part 2. Count your duckweed.
Every lab section that this experiment runs;
1) Record the date, the number of days elapsed since the start of the experiment, and the
number of duckweed in your finger bowl. Duckweed have a somewhat modular growth form,
making the definition of an individual rather arbitrary.
Call a duckweed an individual if you can easily separate it from the others.
2) Add enough distilled water to your fingerbowl to top it off. (Question, why distilled water this
time?)
Record your data in the table below.
Date
Days Elapsed
Number of Plant
Date Days Elapsed Number of Individuals
Part 3. On the last day of this exercise, do the following
1) Graph your duckweed on the figure below. Remember to label the axes and title the figure.
2) Answer the following questions
A) Has this population reached carrying capacity?
B) If so, what was the factor limiting population growth? What is the carrying capacity, K, of your
fingerbowl?
If not, what factor might ultimately limit population growth?
C) Look at your figure and mark the last count before the population seemed to slow its rate of
growth (if it never stopped, this will be your last count). What were t (the elapsed time in days),
and Nt, (the population at that day?). Given that N0=4, calculate r max.