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Optimality in Biology: A Cost-benefit Analysis of Feeding in Painted Lady Butterflies
Optimization is the process of attaining the best possible compromise between minimizing costs and maximizing benefits. When shopping, consumers trade off price and quality. For a given price range, it makes sense to look for the highest quality product currently available. For a given quality level of product, the strategy is to find the lowest price. Evolution by natural selection is a process of optimization. In an evolutionary context, natural selection trades costs and benefits in ways that move phenotypes in the direction of optimality. An example of an important trait in the life of a bird is the porosity of its egg shell. Shells have microscopic pores that permit exchanges of gases between the atmosphere and the respiring embryo. Pores that are excessively small will limit respiration, but very large pores will desiccate the embryo by promoting evaporative water loss. Natural selection has favored an optimal pore size that represents a compromise: pores of a size sufficient for aerobic respiration but not large enough to upset the egg’s water budget. Animal behaviors often have associated costs and benefits and can therefore be viewed in terms of optimality. Baleen whales obtain energy by straining microorganisms out of the water column as they swim. Suppose that in waters near the surface there are very high densities of small plankton whereas in a deeper strata the plankton are less abundant but of greater size and energy content. Where should the whales swim? Natural selection will favor choices and behaviors that promote efficient acquisition and processing of food energy and nutrients. In times of food scarcity, efficiency could mean the difference between living and dying. During times of food abundance, efficiency could permit an animal to make a very large investment in personal reproduction. Butterflies feed on nectar produced by flowers. Nectar is a complex solution of sugars and amino acids. The butterfly has a proboscis (see sketch) that allows it to reach nectaries deep inside the flower. When feeding, the uncoiled proboscis pulls nectar upward by a process called siphoning. The ease with which the nectar rises in the proboscis depends
on several factors including solution viscosity and proboscis size. This is a special case of fluid flow through tubes which has been described in general terms by the Poiseuille equation: FLOW = ΔP π r4 8 L η where ΔP = pressure difference across
the length of the tube r = radius of tube L = length of tube
η = fluid viscosity
What are some of the important relationships that relate to foraging on nectar? The Poiseuille equation indicates that the rate of fluid flow decreases as viscosity increases. As sugar concentration of nectar increases, so does viscosity ... but so does energy content. Is low flow of energy-rich nectar preferable to a high flow of energy-poor nectar? This seems like a problem in optimality. The picture gets even more complex if water in the nectar is considered to be a potential resource. In this lab we will investigate the ingestion of sucrose solutions by the painted lady butterfly (Vanessa cardui). Our test solutions of 8.75%, 17.5%, 35%, 50%, and 80% will therefore represent varying concentrations, viscosities, and energy and water contents.
MEASURING INGESTION Each group will have a small collection of butterflies. Each butterfly will be used in our experiment only one time. Butterflies are relatively delicate insects and anything that
we can do to reduce mechanical damage and general stress will be to our advantage. Butterflies should be gently picked up by grasping the folded wings between your index and middle fingers. Don’t be alarmed if a butterfly gets away from you. Once they come to rest they can be easily captured. Our strategy will be to determine the volume of ingested solution by weighing butterflies before and after feeding. Weights will be measured on an analytical balance to four decimal places. Place a butterfly in a weighing container and allow it to become inactive before taking the reading. After weighing, remove the butterfly from the container and present the sugar solution. Allow the tarsi (last segment) of the walking legs to touch the solution. Tasting the sugar in this way should cause the proboscis to uncoil. You may find that if you hold the butterfly near the bench top, it will extend its legs. You can then walk the butterfly into the sugar solution. It may help ergonomically to brace your elbow or wrist on the lab bench. If the proboscis will not uncoil naturally, you may have to use a small probe to help it reach the fluid. IMPORTANT: Do not dunk the body of your butterfly into the sugar solution. A wet body will distort your estimates of ingestion weights. Feeding will be assumed to occur between the time that the proboscis enters the fluid and the time that it leaves the fluid. Carefully record this interval with a stopwatch. It is preferable but not necessary that feeding bouts are continuous. Stopping and restarting the stopwatch is OK (avoid accidentally zeroing your stopwatch!). During a typical feeding session, a butterfly may consume 30-40 uL of sugar solution. In order to attain this, try to measure ingestion over the following intervals: 8.75 % sucrose - 2 min, 17.5 % - 2.5 min, 35 % - 3 min, 50 % - 4 min, and 80 % - 5 min. When feeding stops, reweigh the butterfly and then place it in the holding tank for used subjects. Repeat this entire process with other butterflies and concentrations according to your research design.
CALCULATIONS One of our goals is to collect data and make calculations that will lead to two graphs: (1) nanoliters consumed/sec vs. percent sucrose and (2) ug consumed/sec vs. percent sucrose. To make these graphs, we need to calculate the volume of solution consumed by each butterfly based on the measured weight of the consumed solution. To do this, we must know the specific gravities of each of the five sugar solutions. The following example shows how to calculate specific gravity, volume ingestion rates, and sugar ingestion rates for a 35 % sucrose solution. EXAMPLE: 35 % sucrose solution = 35 g 100 mL
DATA: 0.0003 g of a 35 % sucrose solution was consumed in 2 min FACT: pure (dry) sucrose has a specific gravity of 1.588 g/mL
1) To calculate the specific gravity of a 35 % sucrose solution, we must first calculate the weight of the water in the solution (we know the sucrose weighs 35 g).
35 g = 22.04 mL sucrose 1.588 g mL
======> water volume = 77.96 mL ======> water weight = 77.96 g Specific Gravity = 35 g + 77.96 g = 112.96 g = 1.1296 g 100 mL 100 mL mL 2) To calculate volume ingestion rates in nL/sec, divide weight of solution ingested by solution specific gravity:
0.0003 g = 0.0002655 mL = 265.5 nL 1.1296 g mL 265.5 nL = 2.2125 nL 120 sec sec
3) To calculate sugar ingestion rates in ug/sec, first change the units of the sugar solution:
35 g = 0.000035 ug = 0.35 ug 100 mL 0.0001 nL nL Then, 2.2125 nL x 0.35 ug = 0.7744 ug sec nL sec
(collected at the beginning of lab)
Without conferring with class mates, each person should independently submit, on a single piece of paper, the following three items: 1) Hypotheses that will be tested in today’s lab. 2) A graph showing a line that displays your prediction of the relationship between volume ingestion rates of sucrose solutions (nL/sec) and sucrose concentrations (%). 3) A graph showing a line that displays your prediction of the relationship between sucrose ingestion rates (ug/sec) and sucrose concentrations (%).
A copy of your pre-lab page along with similar pages from lab partners should appear in the group’s lab report as an appendix at the end.
AFTER LAB Each group will produce and submit one lab report. The data from your lab group will be pooled with similar data from other lab groups and from other years. You will therefore have reasonably large sample sizes of replicated data at your disposal. Use PRISM to create graphs of (1) volume ingestion rates (nL/sec) vs sucrose concentrations (%) and (2) sugar ingestion rates (ug/sec) vs sucrose concentrations (%). If data appear linear, consider using linear regression and linear correlation. Consider the possibility of statistically evaluating volume and sugar ingestion rates at various sugar concentrations. Your Discussion should interpret the specific outcome of your experiment and the ways in which it relates to the larger idea of natural selection optimizing phenotypes. Are the terms in the Poiseuille equation “optimizable”? Flowers and butterflies are both in this story … which are doing the optimizing? Discuss a possible evolutionary “tension” between flowers “trying” to attract insects and insects “playing the field” when visiting flowers. Sugar consumption may be our focal point, but what about body water content? The use of properly cited and strongly paraphrased primary literature is expected … visit our e-reserves. The lab report will follow the standard IMRAD format as outlined in the handout entitled LAB REPORT FORMAT FOR YCP BIOLOGY COURSES. Please study that handout before beginning your report. See Dr. Rehnberg if questions arise.
Group Writing Description Address the following questions in an appendix at the end of your lab report:
How was participation by group members organized? Which group members were given primary responsibility for writing a specific section of the report? When (date) was a rough draft completed, assembled, and distributed to all group members? When (date) did all group members complete and return their revisions of the rough draft? Who received those revisions and incorporated changes into a new draft? When the new draft was done, did group members reread and make further comments?
Optimal Foraging in Butterflies
Replicate Ingestion Data
Replicate 8.75 % 17.5 % 35 % 50 % 80 % 1
g = sec =