|Measuring Duckweed Growth|
Growth curves for populations of many organisms, including duckweeds, can be divided into different phases (labeled A - D), as shown in the graph.
For natural populations, there may be fluctuations in the availability
of nutrients over the course of the growing season. For example, nutrients
may be diluted after heavy rains. Applications of fertilizers in nearby
fields and subsequent runoff may result in periodic bursts of nutrients into
Why measure growth curves?
Growth curves must be drawn from a series of growth measurements at different times during the growth curve. This is much more time-consuming than just measuring a single end-point. Why go to the trouble?
Using total growth end-point measurements in bioassays is misleading. There are two reasons for this:
Are duckweed growth rates exponential?
Equations for Ideal Exponential Growth
Exponential growth, the number of fronds, N, at a given time t is given by Equation 1, where: No= number of starting fronds and k = exponential growth rate constant. This can be re-arranged to give Equations 2 and 3. An estimate of doubling time ( t2 ) can be calculated from Equation 4, where ln(2) = 0.693. A better estimate of k and t2can be obtained from a linear regression analysis using Equation 2. Linear regression analysis is easily done in spreadsheets and many scientific calculators.
Equation 1: N = Noekt
Equation 2: k·t = ln N - ln No
Equation 3: k = ( ln N - ln No ) / t
Equation 4: t2 = ln 2 / k
Keep in mind that these equations are valid only for ideal exponential
growth conditions (Phase B above). For other phases
of growth, different sets of equations must be applied to compensate for
lag phase or to allow for senescence and death.
The most commonly used method of measuring growth of duckweed is to count fronds. Most duckweed research and phytotoxicity tests depend on frond counts. However, counting fronds is deceptively easy. To count the fronds in just a few containers can take considerable time. Frond counts will be proportional to biomass only if fronds in different treatments share the same average measurements (the same geometry) and same density. The effects of the different treatments may negate these assumptions.
When counting fronds, it is the accepted procedure to count every visible frond, even the tips of small new fronds that are just beginning to emerge from the pocket of the mother frond. The "blackboard" drawing shows an example with several fronds in different orientations and stages of growth, and with two plants connected by a stipe (stipule).
A magnifying glass or a stereomicroscope (10x is good) is necessary for good frond counts. Recall how much care is necessary in counting blood cells in a hemocytometer. It is all to easy to miss fronds or count them twice. Placing a square-ruled sheet of paper beneath the culture can help to reduce counting errors. It is also possible to automate frond counting using video image analysis.
This [ growth curve
] was obtained by counting fronds.
Weight, Fresh or Dry
Weight is an obvious measure of plant growth. However, weighing duckweed plants can be a problem. Keep in mind that duckweeds are delicate. Even measuring their fresh weight requires removing the plants from their medium and blotting them. Thigmotropism, the response of plants to mechanical force and vibration, is a possible result of even gentle handling. Thigmotropism is known to cause changes in growth rate or the pattern of growth in many plants. It is unknown if this response occurs in duckweeds, but genes regulating this response have been identified in Arabidopsis.
Fresh or wet weight is measured after blotting the plants very gently with a soft paper towel to remove the free moisture. Then they are weighed immediately. Since duckweed lack a cuticle on their lower surface, waiting even a short time will allow drying. Duckweeds are between 86% and 97%water by weight (Landolt, 1987, page 9), so small variations in drying will have a major impact on results. However, with care, fresh weights are a useful means of estimating the biomass.
Dry weight is a more acceptable means of measuring growth, but is useful only for an end point. Keep in mind that duckweed dry weight is just 3% to 14% of fresh weight (see above), so (for laboratory-scale experiments) an accurate milligram balance will be necessary. According to Landolt (1987, page 69), the dry weight of the largest duckweed fronds (Spirodela) are about 0.6 mg each.
Determine dry weight by blotting the plants and placing them on a pre-weighed and numbered weighing boat. Dry the plants in a hot oven overnight. Unless rigorous research is being done, the temperature need not be very high. It is only necessary that the duckweeds be dried to a uniform condition every time. Since duckweeds have a high surface area and no cuticle on the lower surface, they dry rapidly. It is generally unnecessary to weigh them more than once to show that the weight is constant. However, I do place them in a desiccator to cool before weighing them. A Zip-LocTM bag would also work This method is suited to obtaining weights on very small samples of duckweeds grown in the lab.
To accelerate the process, use a microwave oven and/or a draft of dry air
(a hair dryer) - but don't blow the duckweed away! Also part-way
through the process, fork the still-moist plant material from the bottom
up to the top.
Since duckweeds grow by spreading over the surface of their medium, surface area is a useful means of estimating growth. As with frond counts, surface area measurements will be proportional to biomass only if fronds in different treatments share the same average measurements (the same geometry) and same density.
Surface area can be estimated from enlarged photographs or tracings, or can be calculated using digital image analysis. One simple way of estimating area in enlargements and tracings is to cut out the enlarged duckweeds, place them on graph paper and count the squares covered. Another is to weigh the cutouts. Following such procedures will give students an appreciation for the ease of digital imaging methods.
Surface area measurements are the only reasonable way to measure duckweed
growth on a large scale, as on bayous, ponds and canals. Airborne
false color video analysis has successfully been employed to study the
growth of duckweeds in Dutch canals by Synoptics. For application to
environmental management the results were incorporated into a Geographical
Information System (GIS).
Digital Image Analysis
If a digital video camera or a flat-bed scanner is available, these methods can be used. Photographs can be scanned off-line for later analysis. Commercial software is available from many vendors for all-purpose scientific image analysis, but will require programming for this application. Digital image analysis results (in units of cm2 or percentage of surface covered) can be calibrated against any of the traditional methods for measuring duckweed biomass. Where such a correlation breaks down (for example where growth conditions result in production of smaller fronds), the results (in area/frond) may be interesting in their own right.
LemnaTec, GmbH, a company in
Germany, has commercialized measurement of duckweed growth by digital image
Landolt, E. and Kandeler, R. (1987) The family of Lemnaceae - a monographic
study. Vol. 2, Phytochemistry, physiology, application, bibliography.
Veroff. Geobot. Inst. ETH, Zurich, 638 pp.
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Revised: May 3, 2003