《数学建模》美赛优秀论文：01C（点评）Judge’s Commentary

Judge's Commentary 415 Judge's commentary: The Outstanding Zebra Mussel Papers Gary Krahn Dept of Mathematical Sciences United States Military Academy West Point NY 10996 ag2609@usma. edu Introduction The papers were assessed on their ability to transform the data into useful information the application of an appropriate modeling process; and the integration of environmental science to render appropriate recommen dations The judges appreciated the effort and valued the results of the papers. It was a very difficult problem that required a blend of science, mathematics, and conviction to solve a complex interdisciplinary problem during the four-day contest. It was clear that a solution was not going to jump out of the 40 pages of data; rather, it had to be pulled out skillfully The Problem Zebra mussels were introduced to North America in 1980. They are an eco logical"dead end, "since native fish do not eat them. Researchers are currently attempting to identify environmental factors that may influence the popula tion of zebra mussels within our waterways. Zebra mussels are now spread throughout the eastern waterways of the United States, causing tremendous problems for the ecosystem and the regional economies The UMAP Journal 22 (4)(2001)415-420. Copyright 2001 by COMAP, Inc. Allrights reserved Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial dvantage and that copies bear this notice. Abstracting with credit is permitted, but copyrights for components of this work owned by others than COMAP must be honored. To copy otherwise to republish, to post on servers, or to redistribute to lists requires prior permission from COMAP

Judge’s Commentary 415 Judge’s Commentary: The Outstanding Zebra Mussel Papers Gary Krahn Dept. of Mathematical Sciences United States Military Academy West Point, NY 10996 ag2609@usma.edu Introduction The papers were assessed on • their ability to transform the data into useful information; • the application of an appropriate modeling process; and • the integration of environmental science to render appropriate recommen￾dations. The judges appreciated the effort and valued the results of the papers. It was a very difficult problem that required a blend of science, mathematics, and conviction to solve a complex interdisciplinary problem during the four-day contest. It was clear that a solution was not going to jump out of the 40 pages of data; rather, it had to be pulled out skillfully. The Problem Zebra mussels were introduced to North America in 1980. They are an eco￾logical “dead end,” since native fish do not eat them. Researchers are currently attempting to identify environmental factors that may influence the popula￾tion of zebra mussels within our waterways. Zebra mussels are now spread throughout the eastern waterways of the United States, causing tremendous problems for the ecosystem and the regional economies. The UMAP Journal 22 (4) (2001) 415–420.
c Copyright 2001 by COMAP, Inc. All rights reserved. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice. Abstracting with credit is permitted, but copyrights for components of this work owned by others than COMAP must be honored. To copy otherwise, to republish, to post on servers, or to redistribute to lists requires prior permission from COMAP

416 The UMAP Journal 22.4(2001) The data in the problem statement are real: Prof. Nierzwicki-Bauer of Rens selaer Polytechnic Institute, a leading researcher of zebra mussels, provided data from several lakes in New York. Several population models appear in the literature however. the collection of environmental factors that influence the rate of population growth of the zebra mussel is still unknown. This is a genuine interdisciplinary problem that confronts North America today The data The data appear to have created an"uncomfortable"feeling in the hearts and minds of the modelers. It was difficult for many to digest all of the data and either incorporate all of it into a model or else justify eliminating portions of the data. Often, teams did not address how they managed"missing"data or why they accepted or refuted data that appeared to be erroneous. In most cases teams had done a significant amount of work in an attempt to understand the data. Most teams categorized the population data by month in order te synthesize the data into a more useful form. Similarly, they attempted to aligi the chemical data by averaging several time periods into a single data point Many teams had difficulty describing their analysis and the interpretation of their results. The successful teams discussed how they transformed data and how they confronted missing or confusing data. Tables 1 and 2 show portions of the data, the zebra population of one lake from 1994-2000 and the chemical information on the same lake for 1999. Confusing-yes, but real The entire set of data included the following categories: stratum, total phos horus, dissolved phosphorus, calcium, magnesium, total nitrogen, tempera- ture, chlorophyll, alkalinity chloride, iron, potassium, sodium, pH, secchi disk transparency, and population levels. It was essential to explain how the data would be organized for analysis. The judges expected teams to describe why they selected certain data to remain in their analysis and why other chemicals were eliminated. It was clear that contestants had to make several decisions to transform the data into a useful form. This problem, like last years problem, was not clear-cut. Once again, we found that as the contestants formulated and refined their assumptions, they confronted the complexities typically asso- ciated with an open-ended problem. Last year they had reasonably clean data while this year they had some dirty "data The characteristic of a strong paper was the ability to uncover the uncertain- ties of the population growth of zebra mussels due to chemical concentrations using science and mathematical models. Insome cases, the incomplete data and large unexplainable fuctuations in the population obscured the affect of spe cific chemicals. The data alone cannot reveal the complete interaction among the chemicals affecting population growth. For that reason, successful teams had to take an interdisciplinary problem-solving approach

416 The UMAP Journal 22.4 (2001) The data in the problem statement are real: Prof. Nierzwicki-Bauer of Rens￾selaer Polytechnic Institute, a leading researcher of zebra mussels, provided data from several lakes in New York. Several population models appear in the literature; however, the collection of environmental factors that influence the rate of population growth of the zebra mussel is still unknown. This is a genuine interdisciplinary problem that confronts North America today. The Data The data appear to have created an “uncomfortable” feeling in the hearts and minds of the modelers. It was difficult for many to digest all of the data and either incorporate all of it into a model or else justify eliminating portions of the data. Often, teams did not address how they managed “missing” data or why they accepted or refuted data that appeared to be erroneous. In most cases, teams had done a significant amount of work in an attempt to understand the data. Most teams categorized the population data by month in order to synthesize the data into a more useful form. Similarly, they attempted to align the chemical data by averaging several time periods into a single data point. Many teams had difficulty describing their analysis and the interpretation of their results. The successful teams discussed how they transformed data and how they confronted missing or confusing data. Tables 1 and 2 show portions of the data, the zebra population of one lake from 1994–2000 and the chemical information on the same lake for 1999. Confusing—yes, but real. The entire set of data included the following categories: stratum, total phos￾phorus, dissolved phosphorus, calcium, magnesium, total nitrogen, tempera￾ture, chlorophyll, alkalinity chloride, iron, potassium, sodium, pH, secchi disk transparency, and population levels. It was essential to explain how the data would be organized for analysis. The judges expected teams to describe why they selected certain data to remain in their analysis and why other chemicals were eliminated. It was clear that contestants had to make several decisions to transform the data into a useful form. This problem, like last year’s problem, was not clear-cut. Once again, we found that as the contestants formulated and refined their assumptions, they confronted the complexities typically asso￾ciated with an open-ended problem. Last year they had reasonably clean data, while this year they had some “dirty” data. The characteristic of a strong paper was the ability to uncover the uncertain￾ties of the population growth of zebra mussels due to chemical concentrations using science and mathematical models. In some cases, the incomplete data and large unexplainable fluctuations in the population obscured the affect of spe￾cific chemicals. The data alone cannot reveal the complete interaction among the chemicals affecting population growth. For that reason, successful teams had to take an interdisciplinary problem-solving approach

Judge's Commentary 417 able 1 Zebra mussel population of one lake Date Population 8/1/94 10/1/94 11/1/94 1.045 7/12/95 10/1/95 11/1/95 200.385 8/1/96 4.843 9/1/96 10/1/96 949,433 11/1/96 49.333 7/1/97 9/1/97 10/1/97 345.555 11/1/97 8/1/98 84,132 9/1/98 599,432 10/1/98 454.93 11/1/98 7/1/99 8/1/99 9/1/99 83 10/1/99 539,229 11/1/99 8/1/00 9/1/00 9.483 10/1/00 11/1/00 467,876

Judge’s Commentary 417 Table 1. Zebra mussel population of one lake. Date Population 7/1/94 100 8/1/94 70 9/1/94 50 10/1/94 248 11/1/94 1,045 7/12/95 222 8/1/95 50 9/1/95 70 10/1/95 40,000 11/1/95 200,385 7/1/96 39 8/1/96 4,843 9/1/96 30,033 10/1/96 949,433 11/1/96 49,333 7/1/97 0 8/1/97 20,456 9/1/97 44,678 10/1/97 345,555 11/1/97 98,789 7/1/98 605 8/1/98 84,132 9/1/98 599,432 10/1/98 454,932 11/1/98 49,332 7/1/99 93 8/1/99 45 9/1/99 83,962 10/1/99 539,229 11/1/99 30,012 7/1/00 0 8/1/00 50 9/1/00 9,483 10/1/00 592,339 11/1/00 467,876

418 The UMAP Journal 22.4(2001) Chemical profiles of the same lake TN Temp Chl-a mg/L mg/L mg/L oC 4/15/9923.205.070.44 8.504.72 5/17/99 0.3215.50727 /18/9927.506.710.45 6/1/99 0.4918.2010.18 6/9/99 0.42 6/14/99 0.4721.0011.64 7/1/99 7/19/9926806.720.8621.0010.18 7/20/9927.206.610.56 7/29/99 0.4421.8013 8/4/99 8/11/99 0.51 8/23/99 0.4421.00509 8/25/99 9/7/99 0.3822.0012.12 9/13/99 0.38 9/24/9924805.670.8916 10/7/99 0.7313.503.64 The Science 4 If science is defined to be the knowledge and study of"what is, "then most of the teams got half of the science-the knowledge part. Almost every team was able to find an enormous amount of information from the open literature by using the Internet. The stronger teams not only gathered information, but they also explained the impact of specific environmental conditions on the life-cycle process of the zebra mussel. If chemicals such as nitrate and magnesium were eliminated without explaining why, the grader immediately suspected that the student did not know why. Likewise, if variables such as chlorophyll, pHlevel and calcium were kept in the model, the outstanding teams explained why, from both a modeling and a scientific perspective. An explanation of the model using both science and mathematics was a characteristic of an outstanding paper. An understanding of the ecological fabric of the waterways was important the design of an outstanding solution to this problem. Environmental science was the thread that related the data to the model and the model to a"realistic olution The model It was important that the modeling process be well formulated and that the rationale of the selected model be clearly explained. The definition of variables, identification of simplifying assumptions, and a discussion of the

418 The UMAP Journal 22.4 (2001) Table 2. Chemical profiles of the same lake. Date Ca Mg TN Temp Chl-a mg/L mg/L mg/L ◦C 4/15/99 23.20 5.07 0.44 8.50 4.72 5/17/99 0.32 15.50 7.27 5/18/99 27.50 6.71 0.45 6/1/99 0.49 18.20 10.18 6/9/99 0.42 6/14/99 0.47 21.00 11.64 7/1/99 0.52 20.80 9.45 7/19/99 26.80 6.72 0.86 21.00 10.18 7/20/99 27.20 6.61 0.56 7/29/99 0.44 21.80 13.58 8/4/99 0.52 8/11/99 0.51 6.30 8/23/99 0.44 21.00 5.09 8/25/99 0.41 9/7/99 0.38 22.00 12.12 9/13/99 0.38 9/24/99 24.80 5.67 0.89 16.00 1.09 10/7/99 0.73 13.50 3.64 The Science If science is defined to be the knowledge and study of “what is,” then most of the teams got half of the science—the knowledge part. Almost every team was able to find an enormous amount of information from the open literature by using the Internet. The stronger teams not only gathered information, but they also explained the impact of specific environmental conditions on the life-cycle process of the zebra mussel. If chemicals such as nitrate and magnesium were eliminated without explaining why, the grader immediately suspected that the student did not know why. Likewise, if variables such as chlorophyll, pH level, and calcium were kept in the model, the outstanding teams explained why, from both a modeling and a scientific perspective. An explanation of the model using both science and mathematics was a characteristic of an outstanding paper. An understanding of the ecological fabric of the waterways was important in the design of an outstanding solution to this problem. Environmental science was the thread that related the data to the model and the model to a ”realistic” solution. The Model It was important that the modeling process be well formulated and that the rationale of the selected model be clearly explained. The definition of variables, identification of simplifying assumptions, and a discussion of the

Judge's Commentary 419 ramifications of these assumptions were important ingredients in the paper Finally, it was important that the model developed was used to answer the question regarding the expected growth of the mussels in lakes B and C. An interdisciplinary discussion of the ramification of the de-icing policy required in Part e was also directly tied to the model. Surprisingly, many teams did not take advantage of their model to address follow-on questions The explanations of the modeling process varied tremendously. Some pa pers contained models that were well designed with results that were analyzed and interpreted. The teams also recognized their models to be both predictive and descriptive. Unfortunately, other papers had wonderful models that uti lized a commercial package or constructed models, but they never explained how the model functioned. It appeared that providing the details of the model's underpinnings impacted the entire paper Groups who had good explanations of their models also related these models nicely to the environmental science of the zebra mussel rate of growth The analysis of the data tied in nicely to how the students performed their modeling. Some students saw the problem as fitting a growth differential equation, and others as fitting a multivariable regression. The approach did not affect the assessment of the paper. Furthermore, whether a team used a discrete dynamical system, curve fitting, or simulation, or adapted the logistic model, a correlation analysis was very important. The stronger papers tended to perform this analysis graphically. Those groups providing useful graphs and explanations of these graphs faired quite well The analysis The problem was an interdisciplinary endeavor. Teams that did great math- ematics but revealed little knowledge on environmental science could not cap- ture the relationships required to solve this problem. Since the data were not clean, it was impossible to use only the data to uncover the essential relations ffecting population growth. Similarly, teams that had a tremendous knowl edge of the science but little mathematics were not able to create an appropriate predictive model. A thorough explanation of the implication of each variable on the growth of the mussel population was essential. Good teams shared modeling process that was well thought out and justified the rationale of the selected model. In Part C (adjustment of the model)a clear explanation of the process involved in modifying the model was important. Finally, in Part D it was important that the analysis of the model was used to answer the question regarding the expected growth of the mussels in Lakes B and c Aninterdisciplinary discussion of the ramification of the de-icing policy was directly tied to the model. Those students who answered all the requirements had a significantly greater chance of going forward than those groups who either did not answer the requirements or who only addressed one or more requirements superficially

Judge’s Commentary 419 ramifications of these assumptions were important ingredients in the paper. Finally, it was important that the model developed was used to answer the question regarding the expected growth of the mussels in lakes B and C. An interdisciplinary discussion of the ramification of the de-icing policy required in Part E was also directly tied to the model. Surprisingly, many teams did not take advantage of their model to address follow-on questions. The explanations of the modeling process varied tremendously. Some pa￾pers contained models that were well designed with results that were analyzed and interpreted. The teams also recognized their models to be both predictive and descriptive. Unfortunately, other papers had wonderful models that uti￾lized a commercial package or constructed models, but they never explained how the model functioned. It appeared that providing the details of the model’s underpinnings impacted the entire paper. Groups who had good explanations of their models also related these models nicely to the environmental science of the zebra mussel rate of growth. The analysis of the data tied in nicely to how the students performed their modeling. Some students saw the problem as fitting a growth differential equation, and others as fitting a multivariable regression. The approach did not affect the assessment of the paper. Furthermore, whether a team used a discrete dynamical system, curve fitting, or simulation, or adapted the logistic model, a correlation analysis was very important. The stronger papers tended to perform this analysis graphically. Those groups providing useful graphs and explanations of these graphs faired quite well. The Analysis The problem was an interdisciplinary endeavor. Teams that did great math￾ematics but revealed little knowledge on environmental science could not cap￾ture the relationships required to solve this problem. Since the data were not clean, it was impossible to use only the data to uncover the essential relations affecting population growth. Similarly, teams that had a tremendous knowl￾edge of the science but little mathematics were not able to create an appropriate predictive model. A thorough explanation of the implication of each variable on the growth of the mussel population was essential. Good teams shared a modeling process that was well thought out and justified the rationale of the selected model. In Part C (adjustment of the model) a clear explanation of the process involved in modifying the model was important. Finally, in Part D it was important that the analysis of the model was used to answer the question regarding the expected growth of the mussels in Lakes B and C. An interdisciplinary discussion of the ramification of the de-icing policy was directly tied to the model. Those students who answered all the requirements had a significantly greater chance of going forward than those groups who either did not answer the requirements or who only addressed one or more requirements superficially

420 The UMAP Journal 22.4(2001) Presentation Some papers revealed tremendous analysis but lacked clarity in the pre- sentation. The strong papers presented the problem, discussed the data and explained their analysis, and finally revealed the development of their math- ematical methods/models. The big difference in papers was whether they informed the reader of what they did and, more important, how they did it. A clear presentation allowed the judge to comprehend their logic and reasoning One judge noted that he wished he was a mind reader because there was clearly lots of outstanding work; however, only the result was revealed. The strong papers revealed their analysis, not just the result Very broadly, we saw two types of weak presentations. The first consisted of reports that had a significant narrative, but no support in the form of math- ematical modeling or analysis. In these reports, the groups appeared to rely on qualitative observations and the information from the literature(web sites) to reach conclusions. The other type of poor-quality report was those that had a significant amount of mathematics in the form of tables and graphs, but no modeling or analysis to pull it together. These papers appeared to dump their computer runs into the report but did not really know what to do with them This year we noticed that the stronger teams clearly documented informa- tion they gathered from outside sources. When constructed models aligned very closely with models found in the open literature, it became difficult for judges to determine what was original work. Conclusion The effort and creativity of almost every team was inspiring. It appear however, that most teams can reason better than they can communicate. Often wonderful ideas were not revealed to the reader. The necessity to work with large data sets appeared much more difficult than anticipated. The top papers, however, did an amazing effort of blending and revealing the science research and mathematics. The best teams revealed the power of interdisciplinary prob lem solving About the author Gary Krahn received his Ph D in Applied Mathematics at the Naval Post- graduate School. He is currently the Head of the Dept of Mathematical Sci- ences at the u.s. military academy at West point. his current interests are in the study of generalized de bruijn sequences for communication and coding applications. He enjoys his role as a judge and Associate Director of the ICM

420 The UMAP Journal 22.4 (2001) Presentation Some papers revealed tremendous analysis but lacked clarity in the pre￾sentation. The strong papers presented the problem, discussed the data and explained their analysis, and finally revealed the development of their math￾ematical methods/models. The big difference in papers was whether they informed the reader of what they did and, more important, how they did it. A clear presentation allowed the judge to comprehend their logic and reasoning. One judge noted that he wished he was a mind reader because there was clearly lots of outstanding work; however, only the result was revealed. The strong papers revealed their analysis, not just the results. Very broadly, we saw two types of weak presentations. The first consisted of reports that had a significant narrative, but no support in the form of math￾ematical modeling or analysis. In these reports, the groups appeared to rely on qualitative observations and the information from the literature (web sites) to reach conclusions. The other type of poor-quality report was those that had a significant amount of mathematics in the form of tables and graphs, but no modeling or analysis to pull it together. These papers appeared to dump their computer runs into the report but did not really know what to do with them. This year we noticed that the stronger teams clearly documented informa￾tion they gathered from outside sources. When constructed models aligned very closely with models found in the open literature, it became difficult for judges to determine what was original work. Conclusion The effort and creativity of almost every team was inspiring. It appears, however, that most teams can reason better than they can communicate. Often, wonderful ideas were not revealed to the reader. The necessity to work with large data sets appeared much more difficult than anticipated. The top papers, however, did an amazing effort of blending and revealing the science, research, and mathematics. The best teams revealed the power of interdisciplinary prob￾lem solving. About the Author Gary Krahn received his Ph.D. in Applied Mathematics at the Naval Post￾graduate School. He is currently the Head of the Dept. of Mathematical Sci￾ences at the U.S. Military Academy at West Point. His current interests are in the study of generalized de Bruijn sequences for communication and coding applications. He enjoys his role as a judge and Associate Director of the ICM

Author 's co Author's Commentary: The Outstanding Zebra Mussel Papers Sandra a. nierzwicki-Bauer Darrin fresh Water institute Rensselaer Polytechnic Institute TroV. ny 12180 nierzs@rpi. edu Introduction One cannot underestimate the potential impact of exotic aqu In particular, the zebra mussel, a small, fingernail-sized freshwater mollusk that was unintentionally introduced to North America via ballast water from a transoceanic vessel, has caused havoc to say the least! Zebra mussels have significantly impacted electrical power generation stations, drinking water treatment plants, industrial facilities, navigation lock and dam structures, and recreational water bodies. In fact. zebra mussels cause an estimated s5 billion in economic damage annually, with this amount continuing to escalate. The zebra mussel problem is a national one, which impacts over half of the fifty states. In light of the ecologically devastating and costly consequences of ze bra mussels, it is imperative that there is increased education, research, and science-based policy As revealed in this years contest the use of real data sets means work ing with numerous variables and sometimes incomplete information. Addi tionally, the facts that need to be considered when trying to address issues surrounding the success or failure of zebra mussels to spread and survive are complex. Many important and complex environmental problems lie at the in terface of disciplines and therefore require interdisciplinary approaches to be addressed. Interdisciplinary training is more than learning and acquiring the ability to talk different languages across disciplinary boundaries. It is an ap- proach that promotes teamwork, innovation, creativity, and" out-of-the-box thinking for solving"real-world"issues and problems. The interdisciplinary problem contest plays a vital role in this experiential training bringing together The UMAP 22 (4)(2001)421-425. Copyright 2001 by COMAP, Inc. Allrights reserved Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice. Abstracting with credit is permitted, but copyrights for components of this work owned by others than COMAP must be honored. To copy otherwise to republish, to post on servers, or to redistribute to lists requires prior permission from COMAP

Author’s Commentary 421 Author’s Commentary: The Outstanding Zebra Mussel Papers Sandra A. Nierzwicki-Bauer Darrin Fresh Water Institute Rensselaer Polytechnic Institute Troy, NY 12180 nierzs@rpi.edu Introduction One cannot underestimate the potential impact of exotic aquatic species. In particular, the zebra mussel, a small, fingernail-sized freshwater mollusk that was unintentionally introduced to North America via ballast water from a transoceanic vessel, has caused havoc to say the least! Zebra mussels have significantly impacted electrical power generation stations, drinking water treatment plants, industrial facilities, navigation lock and dam structures, and recreational water bodies. In fact, zebra mussels cause an estimated $5 billion in economic damage annually, with this amount continuing to escalate. The zebra mussel problem is a national one, which impacts over half of the fifty states. In light of the ecologically devastating and costly consequences of ze￾bra mussels, it is imperative that there is increased education, research, and science-based policy. As revealed in this year’s contest, the use of real data sets means work￾ing with numerous variables and sometimes incomplete information. Addi￾tionally, the facts that need to be considered when trying to address issues surrounding the success or failure of zebra mussels to spread and survive are complex. Many important and complex environmental problems lie at the in￾terface of disciplines and therefore require interdisciplinary approaches to be addressed. Interdisciplinary training is more than learning and acquiring the ability to talk different languages across disciplinary boundaries. It is an ap￾proach that promotes teamwork, innovation, creativity, and “out-of-the-box” thinking for solving “real-world” issues and problems. The interdisciplinary problem contest plays a vital role in this experiential training bringing together The UMAP Journal 22 (4) (2001) 421–425.
c Copyright 2001 by COMAP, Inc. All rights reserved. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice. Abstracting with credit is permitted, but copyrights for components of this work owned by others than COMAP must be honored. To copy otherwise, to republish, to post on servers, or to redistribute to lists requires prior permission from COMAP

422 The UMAP Journal 22. 4 (2001) teams of students that are focused for four days on"solving" a complex prob lem. The breadth of approaches that were used by the teams this year was truly Impressive. Basis for Contest Question: Queen of the American Lakes, Lake George, NY Until recently, it was thought that zebra mussels had not invaded Lake George, New York, the home of the Darrin Fresh Water Institute DFWD) Since 1995, the DFWI had carried out a zebra mussel monitoring program in Lake George where zebra mussel larvae had been observed in only two of the years In 1997, larval zebra mussel numbers at 1 of 11 locations were comparable to those observed in the Hudson River, an area of high zebra mussel colonization Despite the presence of larvae, no adult zebra mussels or settled juveniles had been observed. In December of 1999, the situation changed when two divers from the Bateaux Below Inc, a nonprofit organization dedicated to underwater archaeology, found adult zebra mussels at the southern end of lake george In response to the discovery of these mussels, the dFWI has been working intensively at the site to determine why adult zebra mussels were able to survive and reproduce, ways in which they could have been introduced to this location and an appropriate action to eradicate them from this location The discovery of zebra mussels in Lake George was particularly surpris ing given the low calcium content and low pH of the lake; laboratory tank experiments had previously shown that zebra mussel larvae would not sur vive under these conditions. However, water chemistry analyses conducted at the site where the mussels were found revealed calcium and ph levels higher than that characteristic of the majority of Lake George. Further investigation revealed that water entering the lake from a nearby culvert was introducing stormwater runoff and groundwater into the lake with calcium levels four times higher than that characteristic of the rest of the lake. In addition, the site contains numerous concrete and rock aggregates that are likely sources of additional calcium. Finally, there is potential contribution of calcium from a concrete boardwalk that was built approximately a year before the discovery of zebra mussels at this location troduction of zebra mussels may have occurred when boats contaminated from other lakes entered Lake george at the boat launch adjacent to the site Introduction could also have occurred during the construction of the nearby boardwalk via contaminated equipment. The exact mechanism(s) by which they were introduced may never be known After discovering zebra mussels in Lake George, the dFWI and Bateaux Be low scuba divers carried out an extensive survey of the location to determine the size of the affected area. The mussels were confined to a 15, 000 square foot area. After consultation with state and local agencies, it was agreed that

422 The UMAP Journal 22.4 (2001) teams of students that are focused for four days on “solving” a complex prob￾lem. The breadth of approaches that were used by the teams this year was truly impressive. Basis for Contest Question: Queen of the American Lakes, Lake George, NY Until recently, it was thought that zebra mussels had not invaded Lake George, New York, the home of the Darrin Fresh Water Institute (DFWI). Since 1995, the DFWI had carried out a zebra mussel monitoring program in Lake George where zebra mussel larvae had been observed in only two of the years. In 1997, larval zebra mussel numbers at 1 of 11 locations were comparable to those observed in the Hudson River, an area of high zebra mussel colonization. Despite the presence of larvae, no adult zebra mussels or settled juveniles had been observed. In December of 1999, the situation changed when two divers from the Bateaux Below Inc., a nonprofit organization dedicated to underwater archaeology, found adult zebra mussels at the southern end of Lake George. In response to the discovery of these mussels, the DFWI has been working intensively at the site to determine why adult zebra mussels were able to survive and reproduce, ways in which they could have been introduced to this location, and an appropriate action to eradicate them from this location. The discovery of zebra mussels in Lake George was particularly surpris￾ing given the low calcium content and low pH of the lake; laboratory tank experiments had previously shown that zebra mussel larvae would not sur￾vive under these conditions. However, water chemistry analyses conducted at the site where the mussels were found revealed calcium and pH levels higher than that characteristic of the majority of Lake George. Further investigation revealed that water entering the lake from a nearby culvert was introducing stormwater runoff and groundwater into the lake with calcium levels four times higher than that characteristic of the rest of the lake. In addition, the site contains numerous concrete and rock aggregates that are likely sources of additional calcium. Finally, there is potential contribution of calcium from a concrete boardwalk that was built approximately a year before the discovery of zebra mussels at this location. Introduction of zebra mussels may have occurred when boats contaminated from other lakes entered Lake George at the boat launch adjacent to the site. Introduction could also have occurred during the construction of the nearby boardwalk via contaminated equipment. The exact mechanism(s) by which they were introduced may never be known. After discovering zebra mussels in Lake George, the DFWI and Bateaux Be￾low SCUBA divers carried out an extensive survey of the location to determine the size of the affected area. The mussels were confined to a 15,000 square￾foot area. After consultation with state and local agencies, it was agreed that

Author 's co hand-harvesting of the relatively low-density mussels was the best solution Diving at the site to remove all visible zebra mussels began and has been ongo- ing since April 2, 2000. This approach has been extremely labor intensive and while hopefully effective, would not be feasible if multiple sites were found throughout lake geor Currently, a number of activities are being continued at Lake George, in- cluding monitoring and removal of any remaining zebra mussels at this site Removal of any remaining zebra mussels is critical to reduce the likelihood of successful reproduction. In addition, mussels that are not removed may adapt to the lower calcium and ph conditions and spread into surrounding areas Water samples are continuing to be checked for microscopic larvae and chem- ical parameters. This information will be used to evaluate success of removal efforts, determine whether to extend the monitoring area beyond the present site and better understand the local water chemistry. As can be seen from the abovestory, the questions asked in this years contest-examining environmental factors that could influence the spread of zebra mussels and the potential impacts of human activities and policy issues are real ones. I read with great interest the solutions provided by this years teams. In fact, i plan to reread a number of them as we continue to work on these research questions Proactive vs. Reactive There are many ways in which we can be proactive against the potential threat and spread of zebra mussels. Perhaps of primary importance is education of individuals, through which it is hoped that the spread of zebra mussels can be reduced. The primary mode by which zebra mussels are transported to new bodies of water or to new locations within single water bodies is by human activities: mussels attached to boat bottoms or veligers hitching a ride in bait buckets or scuba gear, for example. Therefore education can be viewed preventive measure for the spread of zebra mussels A second critical activity is monitoring for the first appearance of zebra mussel larvae(veligers), young juvenile mussels and adult zebra mussels Of course, the earlier the detection, the better the opportunity to minimize widespread colonization. Thus, monitoring programs are paramount in being proactive about zebra mussel infestations Third, and to the point of the contest question, there is a need for develop ment of mathematical models that can be made robust using the numerous data sets that already exist for water bodies that either have or lack zebra mussels These models may then be used to predict possible new infestations within wa ter bodies potentially in jeopardy of zebra mussel introductions. At the time of the contest only three such models had been published in the scientific lit- erature. To have interdisciplinary student teams and worldwide focus on this important issue was a fantastic opportunity

Author’s Commentary 423 hand-harvesting of the relatively low-density mussels was the best solution. Diving at the site to remove all visible zebra mussels began and has been ongo￾ing since April 2, 2000. This approach has been extremely labor intensive and, while hopefully effective, would not be feasible if multiple sites were found throughout Lake George. Currently, a number of activities are being continued at Lake George, in￾cluding monitoring and removal of any remaining zebra mussels at this site. Removal of any remaining zebra mussels is critical to reduce the likelihood of successful reproduction. In addition, mussels that are not removed may adapt to the lower calcium and pH conditions and spread into surrounding areas. Water samples are continuing to be checked for microscopic larvae and chem￾ical parameters. This information will be used to evaluate success of removal efforts, determine whether to extend the monitoring area beyond the present site and better understand the local water chemistry. As can be seen from the above “story,” the questions asked in this year’s contest—examining environmental factors that could influence the spread of zebra mussels and the potential impacts of human activities and policy issues— are real ones. I read with great interest the solutions provided by this year’s teams. In fact, I plan to reread a number of them as we continue to work on these research questions. Proactive vs. Reactive There are many ways in which we can be proactive against the potential threat and spread of zebra mussels. Perhaps of primary importance is education of individuals, through which it is hoped that the spread of zebra mussels can be reduced. The primary mode by which zebra mussels are transported to new bodies of water or to new locations within single water bodies is by human activities: mussels attached to boat bottoms, or veligers hitching a ride in bait buckets or scuba gear, for example. Therefore education can be viewed as a preventive measure for the spread of zebra mussels. A second critical activity is monitoring for the first appearance of zebra mussel larvae (veligers), young juvenile mussels and adult zebra mussels. Of course, the earlier the detection, the better the opportunity to minimize a widespread colonization. Thus, monitoring programs are paramount in being proactive about zebra mussel infestations. Third, and to the point of the contest question, there is a need for develop￾ment of mathematical models that can be made robust using the numerous data sets that already exist for water bodies that either have or lack zebra mussels. These models may then be used to predict possible new infestations within wa￾ter bodies potentially in jeopardy of zebra mussel introductions. At the time of the contest only three such models had been published in the scientific lit￾erature. To have interdisciplinary student teams and worldwide focus on this important issue was a fantastic opportunity

424 The UMAP Journal 22.4(2001) Another aspect of this year's question related to policy. Too often policy development is the result of being reactive. The most beneficial outcomes are likely to occur if we are proactive and policy decisions are put into place before rather than after there is a serious and sometimes uncorrectable problem. In order to facilitate this scientists must accept the responsibility of effectively conveying scientific findings and results in"layman,s" terms. It is only then that policy can be an informed decision influenced by the scientific fact finders Data Sets for Competition Just as the students in the contest worked in teams the collection of data for this years problem was also an example of collaboration and teamwork. The sharing of scientific information is critical when working on complex problems where the saying that"the whole is greater than the individual parts"is truly the case. Data were kindly provided for the contest by Cathi Eliopoulos of the Vermont Department of Environmental Conserva tion, for Lake A Lake Champlain) Larry Eichler of the Darrin Fresh Water Institute, Rensselaer Polytechnic Institute, for Lake B Lake George, NY); and Scott Kishbaugh of the New York Dept of Environmental Conservation, for Lake c Zebra mussels were discovered in Lake Champlain in 1993 and have since continued to expand in their distribution throughout the lake. In 1999, adult zebra mussels were found for the first time at the southern end of lake george This remains the only location in that lake where they have been observed to date, although the search for additional colonies continues. No zebra mussels have been found in Lake C, and this is likely to remain the case unless there are significant increases in calcium concentrations within the lake Acknowledgment I would like to thank Chris Arney and gary Krahn for their invaluable contributions in brainstorming and the development of this years problem

424 The UMAP Journal 22.4 (2001) Another aspect of this year’s question related to policy. Too often policy development is the result of being reactive. The most beneficial outcomes are likely to occur if we are proactive and policy decisions are put into place before, rather than after there is a serious and sometimes uncorrectable problem. In order to facilitate this scientists must accept the responsibility of effectively conveying scientific findings and results in ”layman’s” terms. It is only then that policy can be an informed decision influenced by the scientific fact finders. Data Sets for Competition Just as the students in the contest worked in teams, the collection of data for this year’s problem was also an example of collaboration and teamwork. The sharing of scientific information is critical when working on complex problems, where the saying that “the whole is greater than the individual parts” is truly the case. Data were kindly provided for the contest by • Cathi Eliopoulos of the Vermont Department of Environmental Conserva￾tion, for Lake A (Lake Champlain); • Larry Eichler of the Darrin Fresh Water Institute, Rensselaer Polytechnic Institute, for Lake B (Lake George, NY); and • Scott Kishbaugh of the New York Dept. of Environmental Conservation, for Lake C. Zebra mussels were discovered in Lake Champlain in 1993 and have since continued to expand in their distribution throughout the lake. In 1999, adult zebra mussels were found for the first time at the southern end of Lake George. This remains the only location in that lake where they have been observed to date, although the search for additional colonies continues. No zebra mussels have been found in Lake C, and this is likely to remain the case unless there are significant increases in calcium concentrations within the lake. Acknowledgment I would like to thank Chris Arney and Gary Krahn for their invaluable contributions in brainstorming and the development of this year’s problem