conducted in “Quantitative Ecology of

PURPOSE OF ACTIVITY The following summary outlines a combined computer and laboratory exercise conducted in “Quantitative Ecology of Marine Systems,” a class I developed at the Shannon Point Marine Center, Western Washington University. The purpose of the laboratory exercise presented here is to familiarize students with the basic variables that drive biological encounter rates: organism speed, size, and abundance. In this inquiry-based exercise, students progress from developing a conceptual model to empirically testing predictions generated by a quantitative model. The learning objectives, beyond the subject matter, include sampling design, quantitative skills, and the association of conceptual and quantitative models.


BACKGROUND
Many biological rates and processes are determined by individual-level interactions or encounters between organisms and their biotic or abiotic environments.
Even abiotic processes, such as chemical reactions and asteroid collisions, are encounter-rate dependent.All of these seemingly disparate processes can be understood within a single framework that considers three variables: organism abundance, size (e.g., organism diameter or perception distance), and motility.
The interplay among these three variables provides a quantitative predictor of organism encounter rates with, amongst others, suitable mates (sexual reproduction), suitable prey (predation), and suitable habitat (colonization).Understanding biological encounter rates is therefore fundamentally important to understanding a wide range of ecological phenomena that affect oceanographic rates and processes.

RESEARCH QUESTIONS
How does organism encounter rate vary with varying abundance, motility, and size?Which biological processes are encounter-rate dependent?Which are the important variables in these processes?

APPROACH
Students will have some intuition how the aforementioned variables will affect biological encounter rates.The approach taken in this laboratory is to allow students to explore and build upon their intuition.This laboratory consists of two discrete sections: (1) an interactive computer exercise in which students generate hypotheses about factors that could affect encounter rates and (2) a laboratory exercise that tests some of these hypotheses.To allow students to draw on their own intuition, I intentionally do not precede this exercise with a lecture.I offer students Gerritsen and Strickler (1977) for background.
The model simulates random organism movements in two dimensions and keeps track of each organism's encounters with indestructible targets (i.e., targets remain available after they are encountered).Students record the en-An Integrated Model Simulation and Empirical Laboratory on counter rates given a set of initial values and then, using a graphical interface (Figure 1), modify those values to identify the quantitative signifi cance of each variable.In the process, the class discuss-

MECHANICS
Each of the two segments can take between 1-3 hours, depending on how intensely the material is discussed and how much students are guided in their exploration.To decrease the total time required, the computer exercise can be replaced by a guided discussion, or homework exercise that asks students to speculate on the important factors driving encounter rates.The data analysis will be done as an independent or homework exercise.
For the model simulation, students are provided with computer code (to download the model simulation code, go to http://www.tos.org/hands-on/index. html) that displays the model variables in an editable user interface (Figure 1).
Upon pressing the "Run Model" button, the simulation displays the positions of targets and searchers in a two-dimensional arena (Figure 2).The time elapsed is displayed on the top of the screen.At the end of the simulation, the average encounter rate is displayed on the screen.

ACTIVITY
The written instructions given to students are as follows (go to www.tos.org/hands-on to download an MS Word fi le of these instructions):

Computer Simulations
You should treat the computer simulations just like any other experiment.
That is, you should make ample notes on your set-up and results.You will be asked to write a laboratory report about both segments of the lab.In your discussion, include answers to at least some of the questions stated below.This laboratory also provides a wonderful opportunity to introduce students to the value of exploiting theory and model simulations to generate testable hypotheses.Students will benefi t from a discussion of the differences and similarities between theoretical and empirical work.It will be particularly useful to help students understand the need to verify assumptions and to discover why models are simplifi ed characterizations of complex processes.

HANDS ON OCE ANOGR APHY
Hands-On Oceanography provides peer-reviewed activities appropriate for undergraduate and/or graduate classes in oceanography.Hands-on is broadly interpreted as those activities that actively engage students (i.e., activities where students have to make decisions, record results, and interpret results).Hands-on activities include, but are not limited to, computer-based models and laboratory demonstrations.Chlorophyll analysis presents some diffi culties, and instructors concerned about these may prefer to substitute another analyte such as salinity, dissolved oxygen, or a nutrient.One limitation of the method used here is the need to shorten the recommended 2 to 24 hour extraction period (Arar and Collins, 1997;Clesceri et al., 1998) to fi t within a two-or three-hour lab.Other potential limitations are the need for a fume hood and seawater.

RESEARCH QUESTION
The emphasis in this activity is on context.The instructor needs to convey that context can be established even for a single data point such as measured here.The research question, then, begins with, "What is the concentration?" and leads to, "Is the datum oceanographically consistent?" Follow-up questions could include: Could the procedural modifi cations have contributed error?How does sampling location/depth/technique/time infl uence the result?Are direct comparisons of this measurement to other data valid?Students usually assume the online data are "better" than their measurements and this too could lead to further questions and discussion (Tomczak, 2006).

PURPOSE OF ACTIVITY
The purpose of this activity is to familiarize students with how a particle's size, shape and orientation affects its settling at low Reynolds numbers.This activity can also be used to teach statistical skills (e.g., replication of measurements, propagation of error, type I vs. type II regressions).

AUDIENCE
Components of this activity have been used in a variety of classes, including an advanced graduate class on particle dynamics, a junior-senior undergraduate class on organism design, and a sophomore undergraduate class on physics for marine sciences at the School of Marine Sciences of the University of Maine (more information available at http:// misclab.umeoce.maine.edu/education.htm).Students should be familiar with the concepts of Reynolds number and drag prior to the lab.

BACKGROUND
Settling of particles is the primary transport mode for carbon from the surface oceans to depth and is the physical process behind the "biological pump" that incorporates dissolved inorganic carbon into particulate structures of phytoplankton that later sink.Material that does not sink will eventually get remineralized or otherwise dissolved in the upper ocean.Settling is also an integral part of the life of planktonic organisms, regulating their vertical position relative to light, nutrients, prey, and predators.It plays an important role in sediment dynamics by, among other consequences, sorting the material arriving to the seabed and providing one mechanism for aggregation.The settling of small marine particles (phytoplankton, larvae, fi ne sediments) is a case of low-Reynoldsnumber fl ow.Humans have developed intuition for high (turbulent)-Reynoldsnumber fl ows, based on our own experience, but have very little intuition for the world of low Reynolds numbers.Yet, this is the world inhabited by the majority of planktonic organisms.

RESEARCH QUESTION
How does settling velocity depend on size, shape, and orientation at low Reynolds numbers?Does Stokes' solution hold, and over what range of Reynolds numbers?

HYPOTHESIS
Stokes' solution is applicable for settling at low Reynolds numbers (Re << 1).When particles are not spherical, deviations from that solution are expected; in general, the larger the cross-sectional area perpendicular to the settling direction, the slower the particle settles.

APPROACH
Students will measure settling velocities of a series of small beads of varying sizes, but which are all made of the same three materials (e.g., clay, steel, glass) in a highly viscous fl uid before comparing results in water.The student will explore the effect of shape on settling by constructing models of non-spherical particles and measuring how their settling changes with orientation.

Settling of Particles in Aquatic Environments
Low Reynolds Numbers

AUDIENCE
The target audience is undergraduates.
The content can easily be modifi ed to satisfy graduate students, through intensifying the students' interactions with the theoretical and modeling aspects.
Non-majors will benefi t from this exercise through emphasis on the many biological processes that are driven by encounter rates.

1.
Measure encounter rates given the model-supplied values.Make sure that the two fi les "encounter.m" and "enc_ code.m" are in the same folder.From within Matlab open and execute the code: "encounter.m."A user interface will pop up with some preset values (Figure 1).(Should you ever accidentally "lose" the interface, just run "encounter.m"again.)Click on the "Run Model" button.What happens?What do you see?If your simulation results in an encounter rate, a second graph appears.What does it show?Keep in mind that your results might differ from your fellow students' because there is a considerable random element in each model simulation.It will be useful to keep track of the group results.Close all open graphs and return to the user interface.2. In sequence, vary each of the following variables: concentration of searchers and targets, target size, swimming speed of searcher and target.What is the biological meaning of each change you made: are the changes realistic?Should you only use realistic values?Keep track of the effects these variations have on changes in encounter rate.For some variables, small changes in values will change encounter rates much more than large changes in other values.Why is that?Note that changes in target size will not be visible.

Figure 2 .
Figure 2. Screen shot of a model simulation showing targets (green stars) and searcher (red circles) in a two-dimensional arena.Encountered targets change color to white.At the end of the simulation, the average encounter rate (per time step and searcher) is displayed.Th e length units for the sea urchin example are microns (i.e., the shown area is 1 mm 2 ); each model time step equals 3 seconds.Dimensions of length and time are relative to the particular system modeled.During the lab, students are asked to identify the spatial and temporal units of their model system.

Figure 1 .
Figure 1.Screen shot of the user interface that allows students to modify the variables in the model.Any combination of values, except negative numbers, are permissible.No units are given, to allow students to relate the simulation to a variety of organisms.
3. Based on your model variations, develop a set of predictions specifying the relative importance of each variable for organism encounter rates.4. Develop an experimental protocol to test those predictions using sea urchin sperm and eggs.Which variables can you change?What should you measure?How?What sample sizes should you gather?Note that the model simulates a hypothetical case and does not provide you with units for and time dimensions.What will the dimensions of your model system be? 5.For your write-up, think about the model assumptions.What are some shortcomings of this simulation?(For example, targets remain available after they are encountered, feeding or fertilization would 'remove' the target from the pool.)Think of biological manifestations of your model manipulations: how can organisms change their size or speed?What strategies could organisms use to conceal themselves or advertise their presence?Laboratory Exercise Because students are supposed to develop the protocol, I do not supply them with written instructions.I let each student develop a protocol, which we discuss prior to the experiment.The methods suggested here will result in rough estimates of the necessary data.Students are typically very good at recognizing limitations in their methodology.Often, they will suggest very elaborate fi xes (e.g., need three-dimensional, high-speed video to measure swimming speeds and a fl ow cytometer to measure cell-cyclespecifi c organism densities).I use these discussions to ask students to incorporate logistic constraints in their modifi ed procedures.Together, all students then develop one common protocol.I particularly stress bench skills, sample size, and labeling.As a result of the computer exercise or group discussion, students will have arrived at the conclusion that size, speed, and concentration are all important variables.They typically recognize that they can only alter concentration and that organism swimming speed and size are fi xed variables that need to be measured.Using microscope slides (depression or clay-feet raised), students measure size and swimming speeds of sperm and egg (I alert students to the fact that unless they know eggs are non-motile, they need to verify it).Both sperm and eggs are highly concentrated and can be counted with a hemocytometer.With students that had worked with hemocytometers before, this process took about 30 minutes.Then students prepare a 0.02 to 20 percent dilution series of the sperm.The number of dilutions depends on the number of students.I ask each student to conduct at least three fertilization replicates (e.g., three independent trials exposing eggs to a specifi c concentration of sperm).Using a microscope, students score percent fertilization on 100 eggs per experiment.Provided eggs are dense, scoring of 100 eggs takes less than 10 minutes.With a sample size of at least 12 independent fertilizations, one should see some discussable results (Figure 3).

Figure 3 .
Figure 3. Students' results from triplicate measurements of fertilization success using sperm at six diff erent target concentrations, ranging in dilution from 0.02 to 20% of the original sperm extract.Maximum fertilization rate in pure sperm was low at 39%.Error bars shown are +/-one standard deviation.
Visit www.tos.org/hands-on to download activities or submit an activity of your own for consideration.In this activity, students make a single measurement (chlorophyll) for the purpose of interpreting it in a regional, seasonal, and historical context.The activity introduces students to the vast amount of online oceanographic data, builds lab skills, and requires calculations that emphasize basic concepts and unit conversions.AUDIENCEThe activity is one of several analytical labs in Introduction to Marine Science, a course for undergraduate Marine Science and Marine Biology majors at Maine Maritime Academy.The labs teach skills that students will use later on a research cruise.For this activity, students need to be familiar with the concept of density and have basic chemical safety skills.BACKGROUNDWe frequently ask students if their results "make sense."For those new to science, answering this question can be inherently daunting.Even advanced students may have trouble putting their research and lab results in context.Here we encourage students to contextually and quantitatively interpret their data.We choose chlorophyll as the analyte for several reasons: chlorophyll data are available online; the chlorophyll extraction procedure is "hands-on" and easily mastered; and the extraction period provides time to obtain data and do calculations during lab.For our region, the Gulf of Maine Ocean Observing System's (GoMOOS) web site provides near-realtime data from buoys equipped with fl uorometric sensors, and NOAA's Coast-Watch web site provides access to recent surface chlorophyll concentrations derived from satellite observations of ocean color (Figure1).Additionally, we access historical data at NOAA's online World Ocean Atlas.Comparing data among these sites requires unit conversions, another valuable introductory lesson.Lastly, the technique and web resources provide several "teaching moments" depending on the instructor's interests.These can include informal discussions of concentration factors, replication, solubility, fl uorescence, light absorbance, principles of remote sensing, and more.
Finding Context Joceline Boucher (jbouch@mma.edu) is Professor of Marine Chemistry, Corning School of Ocean Studies, Maine Maritime Academy, Castine, ME, USA.Lauren E. Sahl is Professor of Ocean Studies, Corning School of Ocean Studies, Maine Maritime Academy, Castine, ME, USA.BY JOCELINE BOUCHER AND LAUREN E. SAHL Th is article has been published in Oceanography, Volume 19, Number 3, a quarterly journal of Th e Oceanography Society.Copyright 2006 by Th e Oceanography Society.All rights reserved.Permission is granted to copy this article for use in teaching and research.Republication, systemmatic reproduction, or collective redistirbution of any portion of this article by photocopy machine, reposting, or other means is permitted only with the approval of Th e Oceanography Society.Send all correspondence to: info@tos.orgor Th e Oceanography Society, PO Box 1931, Rockville, MD 20849-1931, USA.Oceanography Vol. 19, No. 2, June 2006 151 HANDS ON OCEANOGR APHY

Oceanography
Vol. 19, No. 4, Dec. 2006  187 HANDS ON OCEANOGR APHY PURPOSE OF ACTIVITY The following summary outlines a combined computer and laboratory exercise conducted in "Quantitative Ecology of Marine Systems," a class I developed at the Shannon Point Marine Center, Western Washington University.The purpose of the laboratory exercise presented here is to familiarize students with the basic variables that drive biological encounter rates: organism speed, size, and abundance.In this inquiry-based exercise, students progress from developing a conceptual model to empirically testing predictions generated by a quantitative model.The learning objectives, beyond the subject matter, include sampling design, quantitative skills, and the association of conceptual and quantitative models.

BACKGROUND
Many biological rates and processes are determined by individual-level interactions or encounters between organisms and their biotic or abiotic environments.Even abiotic processes, such as chemical reactions and asteroid collisions, are encounter-rate dependent.All of these seemingly disparate processes can be understood within a single framework that considers three variables: organism abundance, size (e.g., organism diameter or perception distance), and motility.The interplay among these three variables provides a quantitative predictor of organism encounter rates with, amongst others, suitable mates (sexual reproduction), suitable prey (predation), and suitable habitat (colonization).Understanding biological encounter rates is therefore fundamentally important to understanding a wide range of ecological phenomena that affect oceanographic rates and processes.RESEARCH QUESTIONS How does organism encounter rate vary with varying abundance, motility, and size?Which biological processes are encounter-rate dependent?Which are the important variables in these processes?APPROACH Students will have some intuition how the aforementioned variables will affect biological encounter rates.The approach taken in this laboratory is to allow students to explore and build upon their intuition.This laboratory consists of two discrete sections: (1) an interactive computer exercise in which students generate hypotheses about factors that could affect encounter rates and (2) a laboratory exercise that tests some of these hypotheses.To allow students to draw on their own intuition, I intentionally do not precede this exercise with a lecture.I offer students Gerritsen and Strickler (1977) for background.The model simulates random organism movements in two dimensions and keeps track of each organism's encounters with indestructible targets (i.e., targets remain available after they are encountered).Students record the en-An Integrated Model Simulation and Empirical Laboratory on Biological Encounter Rates Susanne Menden-Deuer (smd@eno.princeton.edu) is Lecturer, Shannon Point Marine Center, Western Washington University, Anacortes, WA, USA and is currently Research Fellow, Department of Ecology and Evolutionary Biology, Princeton University, Princeton, NJ, USA.