Modeling herbivorous consumer consumption in the Great Bay Estuary, New Hampshire

Ecological Modelling 143 (2001) 71 – 94 www.elsevier.com/locate/ecolmodel

Modeling herbivorous consumer consumption in the Great Bay Estuary, New Hampshire Pamela M. Behm *, Roelof M.J. Boumans Institute for Ecological Economics, Chesapeake Biological Laboratory, Uni6ersity of Maryland Center for En6ironmental Studies, PO Box 38, Solomons, MD 20688, USA

Abstract Herbivores play a vital role in eelgrass-based estuaries. They have been shown to alter plant productivity, distribution, and overall community structure. Epiphyte grazers are especially important as epiphytes compete with eelgrass for light and nutrients. For these reasons, a herbivorous consumer sector was constructed for a spatial ecosystem model developed for the Great Bay Estuary in New Hampshire (the Great Bay Model). There are three classifications used for consumers in the new sector: fast movers, slow movers, and sedentary. Defining this classification structure is the time needed to travel from one location to another. Criteria that determine movement include food availability and competition. Consumer ingestion is limited by metabolic activity, food preference, and food availability. Unit model results indicate that metabolic activity has a significant impact on consumption. Spatial results show an aggregation of consumers in areas of high food biomass. Travel time also appears to have a significant impact on the rate of growth of consumers. Future improvements to the model will incorporate bay competition between consumer groups as well as predator influence on herbivore behavior. The consumer sector should only be used as a framework for future development, pending available data. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Herbivores; Eelgrass meadows; Epiphyte grazers

1. Introduction The Great Bay Estuary in New Hampshire is historically known for its abundant eelgrass meadows. These meadows provide the largest spatial habitat distribution within Great Bay (Short, 1992). A map of the estuary, showing the main waterways, is provided in Fig. 1. Eelgrass health is both a factor in and an * Corresponding author.

indicator of the overall health of bays and estuaries (Short, 1992). The production of eelgrass provides food, shelter, and nursery areas for many marine animals (Bach, 1993; Connolly, 1994). Eelgrass communities help stabilize bottom sediments and filter suspended sediments. Their leaves act as dampers and reduce water motion. Eelgrass meadows also act as a filter, removing dissolved nutrients, which are taken up by the leaves for growth (Short, 1992). However, in the Great Bay Estuary, too many nutrients from wastewater

0304-3800/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 3 8 0 0 ( 0 1 ) 0 0 3 5 5 - 6

72

P.M. Behm, R.M.J. Boumans / Ecological Modelling 143 (2001) 71–94

effluent and fertilizers can produce algal blooms that shade and destroy eelgrass ecosystems (Short, 1992). Direct grazing of eelgrass can have a profound effect on eelgrass communities. Grazing of aboveground eelgrass biomass has been shown to alter plant productivity, distribution, and overall community structure (Thayer et al., 1984). There are claims that few species use living eelgrass as a direct food source and impact is minimal (Thayer et al., 1984). However, there is a surprising lack of studies assessing spatial and temporal variability in herbivorous impact to support these claims (Nienhuis and Groenendijk, 1986). Research has not exposed any recent studies to settle the debate regarding the importance of direct eelgrass grazing.

Eelgrass meadows support herbivores that feed on epiphytes, which compete with the eelgrass for light and nutrients (Hootsmans and Vermaat, 1985). Previous research has shown that epiphytes can reduce photosynthesis of eelgrass by 31% (Hootsmans and Vermaat, 1985). Both eelgrass and epiphytes are nutritious food sources containing organic matter easily assimilated by herbivores (van Montfrans et al., 1984). Therefore, when examining the productivity of eelgrass, it is essential to take into account the grazers that feed upon the light competitors as well as the herbivores that feed on the eelgrass itself. A significant decline in eelgrass beds in the Great Bay Estuary was noticed in the late 1980s. To understand what caused the decline (in order to prevent future declines), a spatial ecosystem-

Fig. 1. Great Bay Estuary showing important waterways.

P.M. Behm, R.M.J. Boumans / Ecological Modelling 143 (2001) 71–94

level model is under development for the portion of the Great Bay Estuary that is dedicated as a National Estuarine Research Reserve (Short et al., 1997). This is equivalent to the area shaded gray in Fig. 1. A conceptual diagram of the unit model (now referred to as the Great Bay Model) is provided in Fig. 2. Key sectors in the Great Bay Model include: eelgrass (above- and below-ground biomass), epiphytes, detritus, phytoplankton, suspended sediments, and herbivores. The Great Bay Model is formulated to simulate the annual as well as the spatial distribution of eelgrass habitats. The spatial simulation model is constructed of a spatial grid with each grid cell containing an entire functioning Great Bay Model (Short et al., 1997). Each grid cell is approximately 100×100 m. The five major food sources of the herbivorous consumers are the eelgrass shoots (above ground material), the eelgrass roots and rhizomes (below ground material), wrack (free-floating eelgrass litterfall), epiphytes, and phytoplankton. There are many consumers that feed on the various food sources. The original Great Bay Model only took into account a ‘general’ consumer with constant preferences for food sources and a constant rate of travel. Research has shown that preference for various food sources may change based on food availability (Nienhuis and Groenendijk, 1986). Further development of the consumers sector included examining the impact of varying food preference by available biomass as well as varying consumer travel time. The purpose of this paper is to examine the impact travel time has on herbivorous consumption found within Great Bay as well as the associated impacts on herbivorous food sources. This investigation will aid in the further understanding of causes of eelgrass decline in Great Bay, specifically those that are consumption related. Therefore, only the consumers sector will be presented in this paper. Additional information on the Great Bay Model (including detailed descriptions of the other sectors) can be found at http://iee.umces.edu/GrBay.

73

2. Model overview The consumers unit sector was developed using STELLA™ modeling software. The spatial model was run using the Spatial Modeling Environment (SME) software developed by Thomas Maxwell at the University of Maryland (http://iee.umces.edu/ SME3/). The unit sector represents one cell of the spatial model. There are three consumer ‘types’ modeled in the consumers sector, classified by the time needed to travel from one cell to another. The three types are: “ fast moving consumers— travel from one cell to the next in about 1 day, “ slow moving consumers— travel from one cell to the next in about 10 days, and “ sedentary consumers— travel from one cell to the next in about 100 days. A detailed ecological survey (Short, 1992) provided information regarding the types of herbivores found in Great Bay. Fast movers include waterfowl, amphipods, and crustaceans. Slow movers include snails and small fish. Sedentary consumers include clams, mussels, and oysters. The basic model structure followed by each type is shown in Fig. 3.

3. Fast moving consumers section The fast moving consumers type model structure is provided in Fig. 4. Equations for the fast moving consumers type is provided in Appendix A. As noted above, each type follows the same basic arrangement. The following subsections will discuss the equations in relation to the fast movers, but the same principles were applied to the other types.

3.1. General The general subsection ‘sums up’ all of the interactions for the fast consumer. The fast consumer (in units of kilograms per cell) is defined as:

CONSUMERS – 1 (t) =CONSUMERS – 1 (t − dt) + (cons1 – in – X+ cons – ingest – 1 − cons – egest – 1 − cons – mortality – 1 −cons – respiration – 1 − cons1 – out – X)*dt

P.M. Behm, R.M.J. Boumans / Ecological Modelling 143 (2001) 71–94

Fig. 2. Conceptual Great Bay Model, with major sectors noted.

74

P.M. Behm, R.M.J. Boumans / Ecological Modelling 143 (2001) 71–94

Fig. 3. Conceptual structure of key components incorporated into each section of the consumers sector.

Fig. 4. Fast moving consumers section.

75

P.M. Behm, R.M.J. Boumans / Ecological Modelling 143 (2001) 71–94

76

Table 1 Parameter values used to run the model Parameter Assimilation efficiency Mortality rate Respiration rate Ingestion rate Fast movers travel time Slow movers travel time Sedentary travel time

Symbol

Units

Value

’C egest eff – –

No units

’C mort rt – – ’C resp rt – –

Per h Per h

1×10−6 1.25×10−5

’Ingestion rt – ’tt 1 –

Per h m/day

0.00125 10

’tt 2 –

m/day

1

’tt 3 –

m/day

0.1

See Table 1 for parameter values and Appendix A for more detail. Respiration is a function of both metabolic activity and the rate of respiration:

0.75

where CONSUMERS – 1 =fast moving consumers; cons1 – in – X= consumers that moved into current cell; cons – ingest – 1 =amount of ingested material; cons – egest – 1 =amount of egested material; cons – mortality – 1 =consumer mortality; cons – respiration – 1 = consumer respiration and cons1 – out – X=consumers that moved out of current cell.

cons – respiration – 1 = CONSUMERS – 1 *Acti6ity – 1* ’C – resp – rt. where Acti6ity – 1 = metabolic activity and ’C resp rt=respiration rate. – – Metabolic activity is represented in the model as an index (ranging in value from zero to one, where one is the maximum activity rate). Metabolic activity by consumer type is shown in Fig. 5. Previous studies have shown that metabolic activity is a function of water temperature and varies by consumer (Hochachka, 1983; Vernberg and Vernberg, 1983; Omori and Ikeda, 1984). For this model, metabolic activity was estimated for each consumer type through detailed discussions with experts of the ecology of Great Bay. However, more research regarding the metabolic activity for the consumer types used in this model will need to take place to obtain a

Fig. 5. Metabolic activity expressed as a ratio from 0 to 1, where Activity 1 = fast moving consumers, Activity 2 = slow moving consumers and Activity 3 =sedentary activity.

P.M. Behm, R.M.J. Boumans / Ecological Modelling 143 (2001) 71–94

better understanding of the metabolic activity of these unique consumer types. Egestion is modeled as a constant proportion of consumption: cons – egest – 1 =cons – ingest – 1* ’C – egest – eff where C – egest – eff=egestion efficiency. Mortality is modeled as a constant proportion of fast consumers: cons – mortality – 1 = CONSUMERS – 1* ’C – mort – rt

where C – mort – rt=mortality rate. Consumers moving into and out of the cell are only considered when running the model on a spatial scale. The basic equations defining spatial movement are provided below and discussed further in Section 3.3. Consumers moving into cell: cons1 – in – X =Cons1toE@W + Cons1toS@N +Cons1toW@E +Cons1toN@S where Cons1toE@W = consumers moving into cell from western cell; Cons1toS@N =consumers moving into cell from northern cell; Cons1toW@E =consumers moving into cell from eastern cell and Cons1toN@S = consumers moving into cell from southern cell. Consumers moving out of cell: cons1 – out – X =Cons1toE + Cons1toN + Cons1toS + Cons1toW where Cons1toE = consumers moving out of current cell into eastern cell; Cons1toN =consumers moving out of current cell into northern cell; Cons1toS = consumers moving out of current cell into southern cell and Cons1toW = consumers moving out of current cell into western cell. Ingestion of food sources is discussed in detail in Sections 3.2 and 3.4. The basic equation defining ingestion is: cons – ingest – 1 =Ingest – 1

77

where Ingest – 1 = the total amount of food ingested by fast moving consumers.

3.2. Food a6ailability Food availability simply turns food sources ‘on and off’. This is done so that if the consumer does not have a preference for a particular food type, that food type will not be considered when allocating consumption.

3.3. Mo6ement criteria The movement criteria subsection determines whether or not consumers will move into the surrounding cells. In STELLA, this is not a factor because the unit model represents only one cell. The basic equation used to calculate consumer movement (shown here for movement to the east cell) is: Cons1toE = (Density1 – X – E+ Food1 – X – E) *CONSUMERS – 1 where Cons1toE = consumers moving to east cell; Density1 – X – E= fast moving consumer density in the east cell ratio to density in current cell and Food1 – X – E= total amount of food sources in the east cell ratio to food in current cell. As can be seen in the above equation, the two factors determining movement out of the current cell are food density and competition. For example, if there are more ‘fast movers’ in the current cell than in the east cell and if there is more food in the east cell, then fast movers will move into the east cell. The same conditions are used for movement to the north, south, and west cells. Note that this model does not have diagonal movement. Travel time dictates the speed at which consumers move into the next cell (values provided in Table 1).

3.4. Food selection The basic equation for determining consumption is as follows:

P.M. Behm, R.M.J. Boumans / Ecological Modelling 143 (2001) 71–94

78

Table 2 Food Preference by food source and consumer type Food source

Fast moving

Slow moving

Sedentary

Shoots Roots and Rhizomes Wrack Epiphytes Phytoplankton

3 3

1 2

0 2

3 1 0

3 4 1

0 0 8

Ingest – 1 = Cons – Ingest – Ep1 +Cons – ingest – Ph1 +Cons – ingest – RR1 +Cons – ingest – Sh1 +Cons – Ingest – Sw1 +Cons – ingest – Wr1 where Cons – Ingest – Ep1 =amount of epiphytes consumed by fast movers; Cons – ingest – Ph1 = amount of phytoplankton consumed by fast movers; Cons – ingest – RR1 =amount of roots and rhizomes consumed by fast movers; Cons – ingest – Sh1 =amount of shoots consumed by fast movers and Cons – ingest – Wr1 =amount of wrack consumed by fast movers. The equation for the amount of epiphytes eaten is calculated by: Cons – Ingest – Ep1 = Min(Epiphytes*Ep – need – 1 /Ep – need, (Ep – need – 1 /Need – Total – 1 )*Con – pot – ingest – 1 ) where Epiphytes= total amount of epiphytes; Ep – need – 1 =the total need for epiphytes by fast consumers; Ep – need=the total need for epiphytes by all consumers; Need – Total – 1 =the total need for food by fast consumers and Con – pot – ingest – 1 = the maximum total that fast consumers can ingest. Ingestion of the remaining food sources was derived in the same manner. ‘Need’ is determined not only by whether or not the fast mover has a preference for a particular food source, but also by how much of a particular food source is available. For instance, if the fast consumer has a high preference for wrack, but there is not a lot of wrack available and they have a lower preference

for shoots, but shoots are more abundant, the need for wrack might actually be lower than the need for shoots. This is shown by the following epiphytes ‘need’ equation: Ep – need – 1 = (’Ep – Pref – 1 /pref – tot – 1 ) +Ep – supply – 1 where ’Ep – Pref – 1 = the preference the fast movers have for epiphytes; pref – tot – 1 = total preferences of fast consumers and Ep – supply – 1 = ratio of epiphytes to the total food sources available to fast movers. Note that supply is calculated only if preference is greater than zero. Consumer preferences for all food sources are shown in Table 2. Preferences were determined by correspondence with various experts in the field of eelgrass communities and specifically, the Great Bay area. Several references also provided insight into the type of foods that various herbivores consume in eelgrass communities (Owen, 1972; Fralick et al., 1974; Zimmerman et al., 1979; van Montfrans et al., 1982; Kitting, 1984; Thayer et al., 1984; Hootsmans and Vermaat, 1985; Percival et al., 1996). The potential amount of food that could be consumed is determined by: Con – pot – ingest – 1 = MIN(Pot – food – 1, (’Ingestion – rt*Acti6ity – 1*CONSUMERS – 1 )) where Pot – food – 1 = total amount of food available to fast consumers; ’Ingestion – rt= ingestion rate and Acti6ity – 1 = metabolic activity (described above in Section 3.1). The potential amount of food available to fast movers is calculated by: Pot – food – 1 = (Epiphytes*Ep – need – 1 /Ep – need) +(Phytoplankton*Ph – need – 1 /Ph – need) +(RootsRhy*RR – need – 1 /RR – need) +(Shoots*Sh – need – 1 /Sh – need) + (wrack*Wr – need – 1 /Wr – need)

P.M. Behm, R.M.J. Boumans / Ecological Modelling 143 (2001) 71–94

where Ep – need – 1 /Ep – need =this ratio (epiphytes used only as an example) distributes the total amount of food available to all consumers so that: Pot – food – 1 + Pot – food – 2 +Pot – food – 3 =Epiphytes+ Phytoplankton + RootsRhy + Shoots+ wrack

4. Model evaluation

4.1. Calibration/confirmation Data on the relative amounts of consumer group activity in Great Bay is not readily available to calibrate the model at the present time. Data required includes: metabolic activity estimates (as discussed above), ingestion rates, group food preference distribution, and mortality rates. Estimates of parameter values currently used were made based on conversations with experts in the field as well as previous calibrations with available eelgrass data. As a result, this model is not confirmed for Great Bay and will be used only as a framework in the future.

5. Unit model simulations The following subsections show results of the unit model run in STELLA™. Recall that the model in STELLA™ is equivalent to one cell in the spatial model. There are no interactions between other cells and therefore, there is no movement into or out of the cell. The consumers sector was run jointly with the Great Bay Model. As mentioned above (Section 1), the purpose for development of the Great Bay Model is to better understand the causes/impacts of eelgrass depletion. Therefore, there were two scenarios modeled: a base scenario and an eelgrass depletion scenario. The base scenario has the same parameters and configurations found in Appendix A. The eelgrass depletion scenario was modeled by disabling eelgrass production to evaluate the impact of eelgrass loss on consumer behavior.

79

5.1. Base run The unit model was run for two calendar years at hourly timesteps using the parameters and configurations listed in Appendix A. Results are shown in Figs. 6–11. All three consumer types gradually increase in biomass over the two years (Fig. 6). Consumer biomass continues to increase for all three types until food sources decline, as shown in Fig. 6a. Both slow moving and sedentary consumers peaked in amount ingested in the late fall (Fig. 7) when shoots and roots are at a maximum, as can be seen in Fig. 8. The amount of each food source ingested by fast moving consumers is shown in Fig. 9. Slow moving consumer ingestion by food source peaks twice each year, in spring and in fall, as shown in Fig. 10. This is when metabolic activity is at its peak, as discussed in Section 3.1. Ingestion of food sources by sedentary consumers is shown in Fig. 11. Only food sources for which the consumer type has a preference are represented in Figs. 9–11.

5.2. Depleted eelgrass An eelgrass depletion scenario was also simulated. This was done by assuming that there was no primary production of eelgrass. Results are shown in Figs. 12–17. Interestingly, varying primary production between zero and the maximum value produced little difference in the biomass of consumers. This implies that there is enough eelgrass production (even at minimal primary production rates) to support herbivore consumption. As can be seen in Fig. 12, consumers that had a high preference for any eelgrass component (shoots, roots and rhizomes, and wrack) did not grow nearly as much over the years as seen in the base run. The sedentary consumers, which mostly consume phytoplankton, did not experience as large a decline as the others. Consumers did not consume nearly as much during this simulation as shown in Fig. 13. Depletion of eelgrass shoots caused depletion of roots and rhizomes, wrack, and epiphytes (Fig. 14). As a result, once the eelgrass components were depleted, the only food source available to the consumers was phytoplankton (Figs. 15–17). Increased phytoplankton ingestion had a fairly significant impact

80

P.M. Behm, R.M.J. Boumans / Ecological Modelling 143 (2001) 71–94

Fig. 6. (a) Consumer biomass (kg/cell) over 2 years where consumers – 1 = fast movers, consumers – 2 = slow movers, and consumers – 3= sedentary consumers. (b) Decline in consumer biomass (kg/cell) only after decline in total food biomass (kg/cell).

P.M. Behm, R.M.J. Boumans / Ecological Modelling 143 (2001) 71–94

81

Fig. 7. Total ingestion (kg/h per cell) by consumer types where cons – ingest – 1 = ingestion by fast movers, cons – ingest – 2 =ingestion by slow movers, and cons – ingest – 3 =ingestion by sedentary consumers.

Fig. 8. Food source biomass (kg/cell).

P.M. Behm, R.M.J. Boumans / Ecological Modelling 143 (2001) 71–94

82

Fig. 9. Ingestion (kg/h per cell) of specific food sources by fast moving consumers.

on phyto plankton biomass, as seen when comparing Figs. 8 and 14. 6. Spatial dynamics Spatial modeling results are shown in Figs. 18 and 19. The spatial model is currently being run for one year. Results shown represent one cell chosen in an area of the bay where food biomass is readily abundant throughout the year. As can be seen in Fig. 18, growth of fast moving consumers follows the same general pattern as food biomass for the particular cell, shown in Fig. 19. Slow moving consumers increase more rapidly in the spring and fall, even though available food biomass is nearly identical to food available to fast consumers. There is a very slow increase in biomass of sedentary consumers as they are more confined to cells due to a slow travel time. 7. Discussion The purpose of this analysis was to obtain a

better understanding of the impacts herbivores can have on an eelgrass-based estuary. As can be seen from the results of this study, the amount of food ingested by each consumer type is dependent on several variables including preference, amount of food available, and metabolic activity. The results of the base run scenario suggest that with the current parameters and distributions, food abundance and metabolic activity have the greatest impact on consumption. In late fall and winter, fast and sedentary consumer consumption is at a maximum while slow consumers peak in ingestion in both spring and fall, as seen in Fig. 7. Fast consumers ingest more shoots and roots and rhizomes than other food sources (Fig. 9). Waterfowl dominate the fast consumer section due to a much larger biomass and primarily feed on the shoots and roots and rhizomes within this system (Thayer et al., 1984). As can be seen in Fig. 8, shoots and roots and rhizomes constitute the major biomass of food sources. Therefore, with a high preference and high food abundance, ingestion will be at a maximum for these two food sources. Previous research has shown that the heaviest waterfowl grazing in eel-

P.M. Behm, R.M.J. Boumans / Ecological Modelling 143 (2001) 71–94

Fig. 10. Ingestion (kg/h per cell) of specific food sources by slow moving consumers.

Fig. 11. Ingestion (kg/h per cell) of specific food sources by sedentary consumers.

83

84

P.M. Behm, R.M.J. Boumans / Ecological Modelling 143 (2001) 71–94

Fig. 12. Consumer biomass (kg/cell) with eelgrass depletion.

Fig. 13. Eelgrass depletion scenario: total ingestion (kg/h per cell) by consumer types where cons – ingest – 1 = ingestion by fast movers, cons – ingest – 2 =ingestion by slow movers, and cons – ingest – 3 =ingestion by sedentary consumers.

P.M. Behm, R.M.J. Boumans / Ecological Modelling 143 (2001) 71–94

Fig. 14. Eelgrass depletion scenario: food source biomass (kg/cell).

Fig. 15. Eelgrass depletion scenario: ingestion (kg/h per cell) of specific food sources by fast moving consumers.

85

86

P.M. Behm, R.M.J. Boumans / Ecological Modelling 143 (2001) 71–94

Fig. 16. Eelgrass depletion scenario: ingestion (kg/h per cell) of specific food sources by slow moving consumers.

Fig. 17. Eelgrass depletion scenario: ingestion (kg/h per cell) of specific food sources by sedentary consumers.

P.M. Behm, R.M.J. Boumans / Ecological Modelling 143 (2001) 71–94

Fig. 18. Growth of consumers (in kg) in one cell of the spatial model.

Fig. 19. Growth of available food biomass (in kg) in one cell of the spatial model.

87

88

P.M. Behm, R.M.J. Boumans / Ecological Modelling 143 (2001) 71–94

grass meadows primarily occurs during fall and winter (Thayer et al., 1984), which is accurately portrayed in this model. Ingestion by slow moving consumers seems to be far more dependent on metabolic activity as can be seen when comparing Figs. 5 and 10. This implies that food is readily abundant to slow consumers and consumption is at the maximum that metabolic activity will allow. Sedentary consumer ingestion also appears to be more dependent on metabolic activity than food abundance (Fig. 11). A possible explanation for consumption independence to food abundance is the relatively low ingestion rate. The eelgrass depletion scenario was an attempt at determining the effects depleted food sources had on food selection and consumer growth. Eelgrass depletion in Great Bay in the 1980s resulted from an outbreak of the ‘wasting disease’ caused by the pathogenic organism Labyrinthula zosterae (Short et al., 1993). In this scenario, the depletion of eelgrass caused the mortality of epiphytes (Fig. 14) resulting in a decline of consumers with a preference for both eelgrass and/or epiphytes. As all consumers had a preference for phytoplankton, consumers did not immediately leave the system or die from starvation. Rather, increase in biomass was greatly reduced over the year (Fig. 12). As shown in Figs. 15–17, phytoplankton ingestion was dominant for all consumer groups. Spatial modeling results provided further insight into consumer behavior in the bay. As shown in Fig. 18, fast moving consumers increase in biomass throughout the year, which is consistent with the growth in food biomass (Fig. 19). This validates the model constraints which force consumers to move from areas of low food abundance to areas of high abundance. In fact, consumer density seems to play a lesser role in determining consumer distribution as consumers aggregate in areas of high biomass. For waterfowl in particular, previous studies have shown that abundance is greater in areas of denser plant material (Thayer et al., 1984). Fast-moving consumers have the highest travel times, so they can move to areas of greater food sources more rapidly, thereby making more food available to them than the slow or sedentary consumers. As shown in Figs. 18 and 19, fast moving consumers increase in biomass at a much

faster rate in the presence of a rapid increase in food biomass. Sedentary consumers, on the other hand, slowly increase in biomass throughout the year (Fig. 18), enforcing the conclusion that travel time can significantly impact the growth of consumers throughout the year. These conclusions can easily be tested in Great Bay through an analysis of spatial distribution of herbivores (including observations of the cause of movement patterns). Slow-moving consumers increase in biomass consistent with metabolic activity constraints shown in Fig. 5. That is, during the spring and fall, when metabolic activity is at a maximum, slowmoving consumers experience the greatest increases in biomass. In fact, biomass tends to level off during the summer months as shown in Fig. 18, regardless of available food biomass. This indicates that metabolic activity limits consumption rather than available food supply.

8. Conclusion The results of this analysis should serve as an excellent guide for future field experiments. Several testable hypotheses have been formulated as a result of this analysis. First, results suggest that under normal conditions, food sources are readily abundant in eelgrass meadows to support herbivores. However, as seen in the eelgrass depletion scenario, depletion of food sources causes a rapid die-off of herbivores. This indicates that food availability only becomes the limiting factor in herbivore consumption during a die-off episode. Second, spatial analysis indicates that fast-moving consumers have the ability to move to food sources quicker than other types, therefore allowing for a rapid increase in biomass. As mentioned above, an analysis of spatial distribution of herbivores as well as an analysis of the cause of movement would provide more information to support this hypothesis. Finally, an analysis of the consequences of eelgrass depletion for herbivores would provide support for the eelgrass depletion scenario results. There are several modifications that would improve the viability of this model. First, carnivores

P.M. Behm, R.M.J. Boumans / Ecological Modelling 143 (2001) 71–94

can have significant impacts on the feeding behavior of herbivores in several ways (Sogard and Olla, 1993). They introduce a stress, influence habitat selection, and can deplete herbivore populations. Second, competition between consumer types is currently not included in the model. Finally, the Great Bay Model is still a ‘work in progress’. As such, the consumers sector is only as valid as it relates to the structures in the other sectors determining food source magnitude. In conclusion, the model framework provided in this paper provides an excellent basis for modeling consumer food consumption in an eelgrass-based

estuary. Further data is needed to calibrate and confirm the model for Great Bay. Acknowledgements We would like to extend sincere gratitude to F. Short and D. Burdick, whose expertise with the Great Bay Estuary (as well as eelgrass dynamics) has been extremely useful. R. Costanza provided invaluable instruction in the area of model development. We would also like to thank three anonymous reviewers who provided excellent feedback for this paper.

Appendix A. Consumers sector equations using fast moving consumers as an example A.1. Fast mo6ing consumers

89

90

P.M. Behm, R.M.J. Boumans / Ecological Modelling 143 (2001) 71–94

A.2. General fast mo6ing consumers CONSUMERS – 1(t)=CONSUMERS – 1(t − dt) + (cons1 – in – X+ cons – ingest – 1− cons – egest – 1− cons – mortality – 1− cons – respiration – 1 −cons1 – out – X)*dt INIT CONSUMERS – 1 = ’ic – consumer* ’cell – size*.3 INFLOWS: cons1 – in – X =Cons1toE@W +Cons1toS@N + Cons1toW@E+ Cons1toN@S cons – ingest – 1 = Ingest – 1 OUTFLOWS: cons – egest – 1=cons – ingest – 1* ’C – egest – eff cons – mortality – 1=CONSUMERS – 1* ’C – mort – rt cons – respiration – 1=CONSUMERS – 1*Activity – 1* ’C – resp – rt cons1 – out – X = Cons1toE +Cons1toN +Cons1toS + Cons1toW Activity – 1=((H2O – Temp + 10) ‚6)/((12 ‚ 6) + ((H2O – Temp + 10)‚ 6)) Consdens1 = CONSUMERS – 1/’cell – size ’C egest eff = 0.75 – – ’C mort rt= 1× 10 − 6 – – ’C resp rt= 1.25× 10 − 5 – – ’ic consumer = ’ic mac PhBio*0.01 – – – A.3. Food a6ailable to fast consumers OMtotBio – 1=Ep – Total – 1+ Ph – Total – 1 + RR – Total – 1+ Sh – Total – 1+ Wr – Total – 1 Ep – Switch – 1=if ’Ep – Pref – 1 \0 then 1 else 0 Ep – Total – 1=Epiphytes*Ep – Switch – 1 Ph – Switch – 1 =if ’Ph – Pref – 1 \0 then 1 else 0 Ph – Total – 1=Phytoplankton*Ph – Switch – 1 RR – switch – 1= if ’RR – Pref – 1 \0 then 1 else 0 RR – Total – 1=RootsRhy*RR – switch – 1 Sh – switch – 1= if ’Sh – Pref – 1 \0 then 1 else 0 Sh – Total – 1= Shoots*Sh – Switch – 1 Wr – Switch – 1=if ’Wr – Pref – 1 \0 then 1 else 0 Wr – Total – 1=wrack*Wr – Switch – 1

P.M. Behm, R.M.J. Boumans / Ecological Modelling 143 (2001) 71–94

A.4. Mo6ement criteria Cons1toE=if (Density1 – X – E +Food1 – X – E) \ 1 then CONSUMERS – 1 else (Density1 – X – E + Food1 – X – E)*CONSUMERS – 1 Cons1toN=if (Density1 – X – N +Food1 – X – N) \ 1 then CONSUMERS – 1 else (Density1 – X – N+ Food1 – X – N)*CONSUMERS – 1 Cons1toS =if (Density1 – X – S +Food1 – X – S) \ 1 then CONSUMERS – 1 else (Density1 – X – S + Food1 – X – S)*CONSUMERS – 1 Cons1toW=if (Density1 – X – W+Food1 – X – W) \ 1 then CONSUMERS – 1 else (Density1 – X – W+ Food1 – X – W)*CONSUMERS – 1 Density1 – X – E = IF Consdens1BConsdens1@E OR Consdens1 B 1 THEN 0 ELSE Travel – time – 1*((Consdens1 −Consdens1@E)/Consdens1) Density1 – X – N= IF Consdens1 BConsdens1@N OR Consdens1 B 1 THEN 0 ELSE Travel – time – 1*((Consdens1 −Consdens1@N)/Consdens1) Density1 – X – S= IF Consdens1 BConsdens1@S OR Consdens1 B 1 THEN 0 ELSE Travel – time – 1*((Consdens1 − Consdens1@S)/Consdens1) Density1 – X – W = IF Consdens1 B Consdens1@W OR Consdens1 B 1 THEN 0 ELSE Travel – time – 1*((Consdens1 −Consdens1@W)/Consdens1) Food1 – X – E=IF OMtotBio – 1 \ OMtotBio – 1@E OR OMtotBio – 1 B 1 THEN 0 ELSE (Travel – time – 1)*(OMtotBio – 1@E −OMtotBio – 1)/OMtotBio – 1 Food1 – X – N= IF OMtotBio – 1 \ OMtotBio – 1@N OR OMtotBio – 1 B 1 THEN 0 ELSE (Travel – time – 1)*(OMtotBio – 1@N− OMtotBio – 1)/OMtotBio – 1 Food1 – X – S =IF OMtotBio – 1 \ OMtotBio – 1@S OR OMtotBio – 1 B 1 THEN 0 ELSE (Travel – time – 1)*(OMtotBio – 1@S −OMtotBio – 1)/OMtotBio – 1 Food1 – X – W= IF OMtotBio – 1 \ OMtotBio – 1@W OR OMtotBio – 1 B 1 THEN 0 ELSE (Travel – time – 1)*(OMtotBio – 1@W −OMtotBio – 1)/OMtotBio – 1 Travel – time – 1= ’tt – 1/24 ’tt 1= 96 – Cons1toE@W= 0 Cons1toN@S =0 Cons1toS@N=0

91

92

P.M. Behm, R.M.J. Boumans / Ecological Modelling 143 (2001) 71–94

Cons1toW@E =0 Consdens1@E =0 Consdens1@N =0 Consdens1@S = 0 Consdens1@W = 0 OMtotBio – 1@E = 0 OMtotBio – 1@N =0 OMtotBio – 1@S = 0 OMtotBio – 1@W= 0

A.5. Food selection Ingest – 1= Cons – Ingest – Ep1+Cons – ingest – Ph1+Cons – ingest – RR1+ Cons – ingest – Sh1+ Cons – ingest – Wr1 Cons – Ingest – Ep1=Min(Epiphytes*Ep – need – 1/Ep – need, (Ep – need – 1/Need – Total – 1)*Con – pot – ingest – 1) Cons – ingest – Ph1=Min(Phytoplankton*Ph – need – 1/Ph – need, (Ph – need – 1/Need – Total – 1)*Con – pot – ingest – 1) Cons – ingest – RR1=Min(RootsRhy*RR – need – 1/RR – need, (RR – need – 1/Need – Total – 1)*Con – pot – ingest – 1) Cons – ingest – Sh1=Min(Shoots*Sh – need – 1/Sh – need, (Sh – need – 1/Need – Total – 1)*Con – pot – ingest – 1) Cons – ingest – Wr1=Min(Wrack*Wr – need – 1/Wr – need, (Wr – need – 1/Need – Total – 1)*Con – pot – ingest – 1) Con – pot – ingest – 1=MIN(Pot – food – 1, (’Ingestion – rt*Activity – 1*CONSUMERS – 1)) Need – Total – 1=Ep – need – 1+Ph – need – 1 +RR – need – 1 +Sh – need – 1 +Wr – need – 1 Pot – food – 1=(Epiphytes*Ep – need – 1/Ep – need)+(Phytoplankton*Ph – need – 1/Ph – need)+ (RootsRhy*RR – need – 1/RR – need)+ (Shoots*Sh – need – 1/Sh – need)+ (wrack*Wr – need – 1/Wr – need) pref – tot – 1= ’Ep – Pref – 1+ ’Ph – Pref – 1 + ’RR – Pref – 1+ ’Sh – Pref – 1+ ’Wr – Pref – 1 Ep – need – 1=(’Ep – Pref – 1/pref – tot – 1)+Ep – supply – 1 Ep – supply – 1=if OMtotBio – 1= 0 then 0 else Ep – Switch – 1*Epiphytes/OMtotBio – 1 ’Ep Pref 1=1 – – Ph – need – 1=if ’Ph – Pref – 1=0 then 0 else (’Ph – Pref – 1/pref – tot – 1) + Ph – supply – 1 Ph – supply – 1=if OMtotBio – 1=0 then 0 else Ph – Switch – 1*Phytoplankton/OMtotBio – 1 ’Ph Pref 1=1 – – RR – need – 1=if ’RR – Pref – 1=0 then 0 else (’RR – Pref – 1/pref – tot – 1)+ RR – supply – 1 RR – supply – 1=if OMtotBio – 1=0 then 0 else RR – switch – 1*RootsRhy/OMtotBio – 1 ’RR Pref 1=3 – – Sh – need – 1=Sh – supply – 1+(’Sh – Pref – 1/pref – tot – 1) Sh – supply – 1=if OMtotBio – 1= 0 then 0 else Sh – switch – 1*Shoots/OMtotBio – 1 ’Sh Pref 1=3 – – Wr – need – 1=if ’Wr – Pref – 1=0 then 0 else (’Wr – Pref – 1/pref – tot – 1) +Wr – supply – 1

P.M. Behm, R.M.J. Boumans / Ecological Modelling 143 (2001) 71–94

Wr – supply – 1=if OMtotBio – 1 =0 then 0 else Wr – Switch – 1*wrack/OMtotBio – 1 ’Wr Pref 1=3 – – ’Ingestion rt=1.25 ×10 − 3 – A.6. Summation of consumer 6ariables

A.7. Summation of total need Ep – need= Ep – need – 1 +Ep – need – 2 + Ep – need – 3 Ph – need= Ph – need – 1 + Ph – need – 2 + Ph – need – 3 RR – need= RR – need – 1 +RR – need – 2 + RR – need – 3 Sh – need= Sh – need – 1 +Sh – need – 2 +Sh – need – 3 Wr – need =Wr – need – 1 +Wr – need – 2 + Wr – need – 3 A.8. Summation of consumer ingestion Cons – Ingest – Epi = Cons – Ingest – Ep1 + Cons – Ingest – Ep2 + Cons – Ingest – Ep3 Cons – Ingest – Ph = Cons – ingest – Ph1 +Cons – ingest – Ph2 + Cons – ingest – Ph3 Cons – Ingest – RR = Cons – ingest – RR1 +Cons – ingest – RR2 + Cons – ingest – RR3 Cons – Ingest – Sh = Cons – ingest – Sh1 + Cons – ingest – Sh2 + Cons – ingest – Sh3 Cons – Ingest – Wr =Cons – ingest – Wr1 + Cons – ingest – Wr2 + Cons – ingest – Wr3

93

94

P.M. Behm, R.M.J. Boumans / Ecological Modelling 143 (2001) 71–94

References Bach, H.K., 1993. A dynamic model describing the seasonal variations in growth and the distribution of eelgrass (Zostera marina L.). Ecol. Model. 65, 31 – 50. Connolly, R.M., 1994. The role of seagrass as preferred habitat for juvenile Sillaginodes punctata (Cuv. and Val.) (Sillaginidae, Pisces): habitat selection for feeding? J. Exp. Mar. Biol. Ecol. 180, 39 –47. Fralick, R.A., Turgeon, K.W., Mathieson, A.C., 1974. Destruction of Kelp populations by Lacuna 6incta (Montagu). The Nautilus 88 (4), 112 –114. Hochachka, P.W., 1983. The Mollusca, Volume 2, Environmental Biochemistry and Physiology. Academic Press, New York, NY. Hootsmans, M.J.M., Vermaat, J.E., 1985. The effect of periphyton-grazing by three epifaunal species on the growth of Zostera marina L. under experimental conditions. Aquat. Bot. 22, 83 – 88. Kitting, C.L., 1984. Selectivity by dense populations of small invertebrates foraging among seagrass blade surfaces. Estuaries 7 (4A), 276 – 288. Nienhuis, P.H., Groenendijk, A.M., 1986. Consumption of eelgrass (Zostera marina) by birds and invertebrates: an annual budget. Mar. Ecol. Prog. Ser. 29, 29 –35. Omori, M., Ikeda, T., 1984. Methods in Marine Zooplankton Ecology. Wiley, New York, NY. Owen, M., 1972. Some factors affecting food intake and selection in white-fronted geese. J. Anim. Ecol. 41, 79 –92. Percival, S.M., Sutherland, W.J., Evans, P.R., 1996. A spatial depletion model of the responses of grazing wildfowl to the availability of intertidal vegetation. J. Appl. Ecol. 33, 979 – 992.

Short, F.T. (Ed.), 1992. The Ecology of the Great Bay Estuary, New Hampshire and Maine: An Estuarine Profile and Bibliography. NOAA – Coastal Ocean Program Publ., p. 222. Short, F.T., Burdick, D.M., Wolf, J., Jones, G.E., 1993. Eelgrass in Estuarine Research Reserves Along the East Coast, U.S.A., Part I: Declines from Pollution and Disease and Part II: Management of Eelgrass Meadows. NOAA – Coastal Ocean Program Publ., p. 107. Short, F.T., Congalton, R.G., Burdick, D.M., Boumans, R.M., 1997. Modelling Eelgrass Habitat Change to Link Ecosystem Processes with Remote Sensing. Final Report to NOAA Coastal Ocean Program and NOAA Coastal Change Analysis Program. Sogard, S.M., Olla, B.L., 1993. The influence of predator presence on utilization of artificial seagrass habitats by juvenile walleye pollock, Theragra chalcogramma. Env. Biol. Fish. 37, 57 – 65. Thayer, G.W., Bjorndal, K.A., Ogden, J.C., Williams, S.L., Zieman, J.C., 1984. Role of larger herbivores in seagrass communities. Estuaries 7 (4A), 351 – 376. van Montfrans, J., Orth, R.J., Vay, S.A., 1982. Preliminary studies of grazing by Bittium 6arium on eelgrass periphyton. Aquat. Bot. 14, 75 – 89. van Montfrans, J., Wetzel, R.L., Orth, R.J., 1984. Epiphytegrazer relationships in seagrass meadows: consequences for seagrass growth and production. Estuaries 7 (4A), 289 – 309. Vernberg, F.J., Vernberg, W.B. (Ed.), 1983. The Biology of Crustacea, Volume 8, Environmental Adaptations. Academic Press, New York, NY. Zimmerman, R., Gibson, R., Harrington, J., 1979. Herbivory and detritivory among gammaridean amphipods from a Florida seagrass community. Mar. Biol. 54, 41 – 47.