Waging War Against the Zebra Mussel 399 Waging War Against the Zebra Mussel Nasreen ilias Marie C spong James f. tucker Lewis and Clark College Portland, or 97219 Advisor: Robert w. owens Summary We design a mathematical model that accounts for ph, calcium concentra tion, and food availability, the most important factors in zebra mussel repro- duction and in growth and survival of juvenile mussels. Our model can predict whether a given site is likely to be a suitable environment for a zebra mussel population as well as its potential density. Our model corresponds well with the population data provided and with the threshold values of ph (7. 4)and calcium(12 mg/L) for zebra mussel viability We recommend to the community of lake b that they limit their use of de icing agents containing calcium, because our model predicts that an increase in The UMAP Journal 22 (4)(2001)399-413. 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
Waging War Against the Zebra Mussel 399 Waging War Against the Zebra Mussel Nasreen A. Ilias Marie C. Spong James F. Tucker Lewis and Clark College Portland, OR 97219 Advisor: Robert W. Owens Summary We design a mathematical model that accounts for pH, calcium concentration, and food availability, the most important factors in zebra mussel reproduction and in growth and survival of juvenile mussels. Our model can predict whether a given site is likely to be a suitable environment for a zebra mussel population as well as its potential density. Our model corresponds well with the population data provided and with the threshold values of pH (7.4) and calcium (12 mg/L) for zebra mussel viability. We recommend to the community of Lake B that they limit their use of deicing agents containing calcium, because our model predicts that an increase in The UMAP Journal 22 (4) (2001) 399–413. 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
400 The UMAP Journal 22. 4(2001) the calcium concentration in the lake will significantly enhance its suitability as zebra mussel habitat We find that using the goby fish to reduce zebra mussels is not a feasible op tion if the community is concerned with ecological impact, due to the invasive nature of the goby. Environmental Factors in the Spread of Zebra mussels We first discuss the characteristics of a suitable breeding habitat and then address how the population is unintentionally introduced to new areas opulation growth depends on successful reproduction and survival to adulthood. Veligers, zebra mussel larvae, are more sensitive to stress in their surrounding environment and therefore have more stringent survival require ments. Hence, we examine environmental conditions that can cause stress for the zebra mussel, especially in the larval and juvenile stages Ion Concentrations and ph Calcium is required for the viability of zebra mussel populations because it is a major component in their shells. Alkalinity, which is directly linked to calcium concentrations, is an important variable in determining habitat suit- ability for zebra mussels. Calcium concentrations of 12 mg/L and alkalinity corresponding to 50 mg CaCO3/L are required for adult zebra mussel popula tions [Heath 1993]. A calcium concentration of 12 mg/L is also the minimum required for embryo survival, though higher concentrations enhance egg fer tilization and embryo survivorship [ Sprung 1987] Phosphorous and nitrogen are significant factors to zebra mussel population growth because they are critical nutrients for the freshwater phytoplankton that comprise the primary food source of the zebra mussel. Thus, they are an indirect measure of food availability Baker et al. 1993 The pH of the water is another critical factor. Adults require a pH of about 7. 2; in lower pH environments, they experience a net loss of calcium, sodium, and potassium ions, and in very acidic waters adult zebra mussels eventu- ally die because of ion imbalance [Heath, 1993]. Adults can survive in pH 7 environments, but eggs survive only between pH 7.4 to 9.4 [Baker et al. 1993 Temperature Adult mussels can survive temperatures from 0C to 32C, but growth oc curs only above 10C [Morton 1969] and breeding is triggered only in temper atures of at least 12C [Heath 1993]. Higher temperatures increase overall egg
400 The UMAP Journal 22.4 (2001) the calcium concentration in the lake will significantly enhance its suitability as zebra mussel habitat. We find that using the goby fish to reduce zebra mussels is not a feasible option if the community is concerned with ecological impact, due to the invasive nature of the goby. Environmental Factors in the Spread of Zebra Mussels We first discuss the characteristics of a suitable breeding habitat and then address how the population is unintentionally introduced to new areas. Population growth depends on successful reproduction and survival to adulthood. Veligers, zebra mussel larvae, are more sensitive to stress in their surrounding environment and therefore have more stringent survival requirements. Hence, we examine environmental conditions that can cause stress for the zebra mussel, especially in the larval and juvenile stages. Ion Concentrations and pH Calcium is required for the viability of zebra mussel populations because it is a major component in their shells. Alkalinity, which is directly linked to calcium concentrations, is an important variable in determining habitat suitability for zebra mussels. Calcium concentrations of 12 mg/L and alkalinity corresponding to 50 mg CaCO3/L are required for adult zebra mussel populations [Heath 1993]. A calcium concentration of 12 mg/L is also the minimum required for embryo survival, though higher concentrations enhance egg fertilization and embryo survivorship [Sprung 1987]. Phosphorous and nitrogen are significant factors to zebra mussel population growth because they are critical nutrients for the freshwater phytoplankton that comprise the primary food source of the zebra mussel. Thus, they are an indirect measure of food availability [Baker et al. 1993]. The pH of the water is another critical factor. Adults require a pH of about 7.2; in lower pH environments, they experience a net loss of calcium, sodium, and potassium ions, and in very acidic waters adult zebra mussels eventually die because of ion imbalance [Heath, 1993]. Adults can survive in pH 7 environments, but eggs survive only between pH 7.4 to 9.4 [Baker et al. 1993]. Temperature Adult mussels can survive temperatures from 0◦C to 32◦C, but growth occurs only above 10◦C [Morton 1969] and breeding is triggered only in temperatures of at least 12◦C [Heath 1993]. Higher temperatures increase overall egg
Waging War Against the Zebra Mussel 401 production [Borcherding 1995] but also increase metabolism and demand for dissolved oxygen. Zebra mussels require 25%oxygen saturation(2 mg/L)at 25C [Heath 1993]. Based on these values and the data provided for Lake A we find that neither temperature nor dissolved oxygen is a limiting factor of zebra mussel proliferation there. Saltatory Spread Saltatory spread is the movement of a species in large leaps rather than by gradual transitions. It is believed that zebra mussels were introduced to the great Lakes system in 1986 from larvae discharged in ballast water from a commercial ship [Griffiths et al. 1991. As of 1996, zebra mussels had spread to 18 states in the United States(as far south as Louisiana) and two provinces in Canada, almost entirely within commercially navigated waters Johnson and Padilla 1996]-strong evidence that commercial shipping was the primary vector of initial zebra mussel spread in the United States and canada Most of the united states contains environments suitable for zebra mus sel infestation [Strayer 1991], so the identification and elimination of saltatory spread to inland water systems is key to preventing infestation of the western United States. Transient recreational boating seems to be the most likely candi- date for inland spread of the species. Based on this and other studies, it appears that recreational boating represents a substantial threat to the containment of the zebra mussel infestation in america Advective and Diffusive Spread Zebra mussels live the first few weeks of their lives as planktonic larvae that are easily diffused or carried by moving water. This allows for the widespread dissemination of offspring by diffusion, currents, and wind-driven advection within a lake or watershed Johnson and Carlton 1996], which largely explain the species rapid spread [Martel 1993]. However, veligers have been shown to ave high mortality in turbulent waters, and mussel density in streams flowing out ofinfested lakes has been shown to decrease exponentially with the distance downstream [Horvath and Lamberti 1999]. Post-metamorphic zebra mussels have the ability to secrete long monofilament-like mucous threads that increase hydrodynamic drag and allow for faster advective spread [Martel 1993]. These juveniles can survive turbulence much better than veligers, which implies that they are the primary vector of downstream advective spread Zebra Mussel Population Model for lake a Using our model, we attempt to answer two important questions 1. Given chemical information for a given site . is the site suitable for zebra
Waging War Against the Zebra Mussel 401 production [Borcherding 1995] but also increase metabolism and demand for dissolved oxygen. Zebra mussels require 25% oxygen saturation (2 mg/L) at 25◦C [Heath 1993]. Based on these values and the data provided for Lake A, we find that neither temperature nor dissolved oxygen is a limiting factor of zebra mussel proliferation there. Saltatory Spread Saltatory spread is the movement of a species in large leaps rather than by gradual transitions. It is believed that zebra mussels were introduced to the Great Lakes system in 1986 from larvae discharged in ballast water from a commercial ship [Griffiths et al. 1991]. As of 1996, zebra mussels had spread to 18 states in the United States (as far south as Louisiana) and two provinces in Canada, almost entirely within commercially navigated waters [Johnson and Padilla 1996]—strong evidence that commercial shipping was the primary vector of initial zebra mussel spread in the United States and Canada. Most of the United States contains environments suitable for zebra mussel infestation [Strayer 1991], so the identification and elimination of saltatory spread to inland water systems is key to preventing infestation of the western United States. Transient recreational boating seems to be the most likely candidate for inland spread of the species. Based on this and other studies, it appears that recreational boating represents a substantial threat to the containment of the zebra mussel infestation in America. Advective and Diffusive Spread Zebra mussels live the first few weeks of their lives as planktonic larvae that are easily diffused or carried by moving water. This allows for the widespread dissemination of offspring by diffusion, currents, and wind-driven advection within a lake or watershed [Johnson and Carlton 1996], which largely explain the species rapid spread [Martel 1993]. However, veligers have been shown to have high mortality in turbulent waters, and mussel density in streams flowing out of infested lakes has been shown to decrease exponentially with the distance downstream [Horvath and Lamberti 1999]. Post-metamorphic zebra mussels have the ability to secrete long monofilament-like mucous threads that increase hydrodynamic drag and allow for faster advective spread [Martel 1993]. These juveniles can survive turbulence much better than veligers, which implies that they are the primary vector of downstream advective spread. Zebra Mussel Population Model for Lake A Using our model, we attempt to answer two important questions: 1. Given chemical information for a given site, is the site suitable for zebra mussels?
402 The UMAP Journal 22. 4(2001) 2. If a site is determined to be a suitable habitat, will it support a low-or a high-density zebra mussel population? Rather than focusing on developing a complicated model that would predict le exact size of the population, we devised a simple, comprehensive model that answers these questions The inspiration for our model was derived from Ramcharan [1992 Assumptions The density of juveniles collected on the settling plates is proportional to the size of the adult population; this assumption allows us to use the provided data to predict the severity of the zebra mussel infestation. significantly vary with changes in the size of the zebra mussel population The chemical composition and concentrations(such as calcium levels)do no Examining the first data set from Lake A, we find that pH and calcium oncentration are the two most important factors in determining whether zebra mussel population is viable in a given site. This is reasonable, conside that the zebra mussels are very sensitive to ph and they need calcium to br their shells when developing from veligers to juveniles and onto adults We do not include temperature, because although it is important to the ife cycle of the zebra mussel, as long as the temperature is high enough to signal spawning, reproduction will occur. All 10 sites in Lake A had suitable temperatures for spawning We developed a model equation(Model 1)utilizing the values provided for pH and calcium concentration for the 1992 to 1999 period that give a simple measure to predict the viability(v) of a zebra mussel invasion at a particular site. The coefficients of the two variables (ph and [Ca)are used to weight the relative importance of the two factors. The range of values for pH for the ten sites is smaller than the range of values for calcium concentration, thus the coefficients function to equalize the importance of these two factors. The exact values of the coefficients were determined by successively modifying and refining the values until an equation was found that accurately reflected whether the lake site was a suitable habitat or not based on the population data We chose the threshold value of 10. 4 for viability because there appears to be a break there between the sites where zebra mussels survived and the sites where they were absent, and because 10. 4 is close to the value from the equation with 7. 4 for pH and 12 mg/L for calcium concentration. =10pH+0.2la If V >10.4. the site is a suitable habitat for zebra mussel Applying Model 1 to sites 1-10 in Lake A produces Table 1
402 The UMAP Journal 22.4 (2001) 2. If a site is determined to be a suitable habitat, will it support a low- or a high-density zebra mussel population? Rather than focusing on developing a complicated model that would predict the exact size of the population, we devised a simple, comprehensive model that answers these questions. The inspiration for our model was derived from Ramcharan [1992]. Assumptions • The density of juveniles collected on the settling plates is proportional to the size of the adult population; this assumption allows us to use the provided data to predict the severity of the zebra mussel infestation. • The chemical composition and concentrations (such as calcium levels) do not significantly vary with changes in the size of the zebra mussel population. Examining the first data set from Lake A, we find that pH and calcium concentration are the two most important factors in determining whether a zebra mussel population is viable in a given site. This is reasonable, considering that the zebra mussels are very sensitive to pH and they need calcium to build their shells when developing from veligers to juveniles and onto adults. We do not include temperature, because although it is important to the life cycle of the zebra mussel, as long as the temperature is high enough to signal spawning, reproduction will occur. All 10 sites in Lake A had suitable temperatures for spawning. We developed a model equation (Model 1) utilizing the values provided for pH and calcium concentration for the 1992 to 1999 period that give a simple measure to predict the viability (V ) of a zebra mussel invasion at a particular site. The coefficients of the two variables (pH and [Ca]) are used to weight the relative importance of the two factors. The range of values for pH for the ten sites is smaller than the range of values for calcium concentration, thus the coefficients function to equalize the importance of these two factors. The exact values of the coefficients were determined by successively modifying and refining the values until an equation was found that accurately reflected whether the lake site was a suitable habitat or not based on the population data. We chose the threshold value of 10.4 for viability because there appears to be a break there between the sites where zebra mussels survived and the sites where they were absent, and because 10.4 is close to the value from the equation with 7.4 for pH and 12 mg/L for calcium concentration. V = 1.0 pH + 0.2 [Ca] If V > 10.4, the site is a suitable habitat for zebra mussels. Applying Model 1 to sites 1–10 in Lake A produces Table 1
Waging War Against the Zebra Mussel 403 Calculated viability values for sites 1-10 in Lake A using model 1 g 176826813.04 28002231246 3|7.7417611.26 16.511.14 58.0216.91140 67.5913.410.27 7|7.6616.911.04 87.8216.61114 79515.711.09 10 8612.010.26 The model predicts that sites 6 and 10 should not be suitable habitats, while the other eight sites should be. Figure 1, which plots date vs. juveniles/day for each of the sites, shows that the data agree well with our model. Sites 6 and 10 have virtually no zebra mussel population growth, and sites 1, 2, 3,4,5 and 9 all show evidence of infestation. Although it is predicted that sites 7 and 8 should be susceptible to invasion, enlargement of Figure 1 shows that these two sites are not supporting large populations; correspondingly, V for sites 7 and 8 is relatively low. Also, the source of the zebra mussel invasion was site 1 hence the more southerly sites have had longer to form stable populations than the northern sites 7 and 8. With threshold ph of 7. 4 and threshold calcium level of 12 mg/L, the model-which predicts that sites 6 and 10, whose values border on the threshold, are not likely to be habitable-is consistent with the literature Graph 1. Relative Population of Locat NE三 60000 3 40000 7120/95 12/1/96 4/15/98 8/28/99 Figure 1. Relative populations at sites 1-10
Graph 1. Relative Population of Locat 0 20000 40000 60000 80000 100000 120000 140000 7/20/95 12/1/96 4/15/98 8/28/99 1/9/01 Date Juveniles/day/m^2 Location 1 Location 2 Location 3 Location 5 Location 9 Waging War Against the Zebra Mussel 403 Table 1. Calculated viability values for sites 1–10 in Lake A using model 1. Site pH [Ca] V mg/L 1 7.68 26.8 13.04 2 8.00 22.3 12.46 3 7.74 17.6 11.26 4 7.84 16.5 11.14 5 8.02 16.9 11.40 6 7.59 13.4 10.27 7 7.66 16.9 11.04 8 7.82 16.6 11.14 9 7.95 15.7 11.09 10 7.86 12.0 10.26 The model predicts that sites 6 and 10 should not be suitable habitats, while the other eight sites should be. Figure 1, which plots date vs. juveniles/day for each of the sites, shows that the data agree well with our model. Sites 6 and 10 have virtually no zebra mussel population growth, and sites 1, 2, 3, 4, 5, and 9 all show evidence of infestation. Although it is predicted that sites 7 and 8 should be susceptible to invasion, enlargement of Figure 1 shows that these two sites are not supporting large populations; correspondingly, V for sites 7 and 8 is relatively low. Also, the source of the zebra mussel invasion was site 1, hence the more southerly sites have had longer to form stable populations than the northern sites 7 and 8. With threshold pH of 7.4 and threshold calcium level of 12 mg/L, the model—which predicts that sites 6 and 10, whose values border on the threshold, are not likely to be habitable—is consistent with the literature. Figure 1. Relative populations at sites 1–10