Theoretical Basis of the BASS Bioaccumulation and Aquatic System Simulator

1. Theoretical Basis of the BASS Bioaccumulation and Aquatic System Simulator Craig Barber Ecosystems Research Division NERL/ORD/USEPA Athens, GA October 12, 2005

2. BASS (Bioaccumulation and Aquatic System Simulator)

3. BASS: Bioaccumulation Algorithms • Gill Exchange • Gill exchange is analogous to diffusion through laminar flow between parallel plates (secondary lamellae) • Internal chemical distribution between lipid, non-lipid organic, and aqueous phase is rapid in comparison to gill uptake and excretion • Dietary Exchange • Mass balance of ingested and egested chemical assuming fecal partitioning (i.e., chemical concentrations in the fish’s aqueous phase and in the feces’s aqueous and dry phases have equilibrated) • Dermal Exchange • Assumed negligible

4. BASS: Gill Exchange Algorithms

5. BASS: Gill Exchange Algorithms

6. BASS: Gill Exchange Algorithms • the ventilation volumes can be estimated by

7. BASS: Gill Exchange Algorithms

8. BASS: Dietary Exchange Algorithms • To calculate the fecal concentration Ce assume that • Because the transit time through the gastrointestinal tract is relatively slow, chemical concentrations in the fish's aqueous blood, intestinal fluids, and dry fecal matter are assumed to equilibrate with one another. • Secondary, the fish’s intestinal contents and whole body are osmotically equilibrated.

9. BASS: Dietary Exchange Algorithms • Chemical assimilation efficiencies are not constant; rather they are complex functions of • the fish’s body concentration and composition • the prey’s body concentration and composition • the fish’s food assimilation efficiency

10. BASS: Modeling Temperature Effect on Growth • Traditional Q10 or Arrhenius effects model

11. BASS: Modeling Temperature Effect on Growth Adverse effects of high temperatures can be modeled by multiplying the Arrhenius ODE by a hyperbolic temperature term that approaches unity as temperature decreases below T1, equals zero at T1, and becomes increasingly negative as temperatures approach the fish’s upper thermal tolerance limit TL = T2

12. BASS: Modeling Temperature Effect on Growth

13. BASS: Modeling Temperature Effect on Growth

14. BASS: Modeling Fish Growth • Although diffusion-based bioaccumulation “must” be referenced to wet weight, growth is traditionally modeled based on dry weight or energy. BASS calculates wet weight from dry weight by solving

15. BASS: Modeling Fish Feeding • BASS allows users to model feeding by any combination of the following models • Allometric • Holling-Rashevsky • Clearance (planktivores) • Linear (back-calculated from growth) • Feeding classes defined for age, length, or weight classes

16. BASS: Modeling Fish Feeding • BASS’s allometric model is

17. BASS: Modeling Fish Feeding • BASS’s Holling-Rashevsky model is

18. BASS: Modeling Fish Feeding • BASS’s Clearance model is

19. BASS: Modeling Fish Feeding • BASS’s “Linear” model is

20. BASS: Fish Respiration • Calculated from standard oxygen consumption using Respiratory Quotients and routine to standard respiratory coefficients

21. BASS: Specific Dynamic Action SDA is additional respiration that occurs in association with the assimilation of food. It is generally treated as a constant fraction of feeding or assimilation. In BASS it is assumed

22. BASS: Excretion BASS calculates excretion assuming that fish maintain a constant nitrogen / carbon ratio NC (g(N) / g(C)), i.e.,

23. BASS: Predator-Prey Dynamics • BASS simulates aquatic food webs in which each cohort of a species can feed upon other fish, benthos, incidental terrestrial insects, periphyton / attached algae, phytoplankton, and zooplankton. • The realized feeding of each fish cohort is determined by • the cohort’s estimated maximum individual feeding rate • the cohort's population size, and • the biomass of prey available to the cohort which is the sum of the prey's compartmental biomasses minus the biomass of those components which are expected to be consumed by other cohorts that are more efficient foragers / competitors.

24. BASS: Predator-Prey Dynamics • BASS ranks the competitive abilities of different cohorts using the following assumptions: • The competitive abilities of benthivores and piscivores are positively correlated with their body sizes • Reactive distances, swimming speeds, and territory sizes of fish are positively correlated with their body size. Given two differently sized predators of the same potential prey, such trends suggest that larger predators are more likely to encounter that prey than are the smaller predators. • Handling times tend to be inversely correlated with body size. Thus larger predators can dispatch intercepted prey and resume foraging more quickly than the smaller predators. • The competitive abilities of planktivores are inversely related to their body size due to their relative morphologies. Thus, “large” planktivores only have access to the leftovers of “small” planktivores.

25. BASS: Predator-Prey Dynamics • BASS assumes that a fish’s dietary composition is dependent both on the abundance of prey and on the predator’s preference for those prey. Thus, in general

26. BASS: Predator-Prey Dynamics Predation by piscivores is assumed to be size dependent

27. BASS: Predator-Prey Dynamics Prey sizes are assumed to be distributed as a triangular distribution

28. BASS: Non-Predatory Mortality and Dispersal BASS simulates dispersal and non-predatory mortality is based on the general empirical observation that population densities of most vertebrates can be characterized by the self-thinning power function relationship

29. BASS: Non-Predatory Mortality and Dispersal This self-thinning power function relationship implies that cohort dispersal and total mortality is related to its specific growth rate by

30. BASS: Non-Predatory Mortality and Dispersal Because the preceding equation encompasses a cohort’s predatory mortality, non-predatory mortality, and dispersal, and because BASS explicitly models the cohort's predatory mortality, BASS assumes that the cohort's rate of non-predatory mortality and dispersal is simply a fraction δ of bγ. In particular

31. BASS: Reproduction & Recruitment BASS estimates a species’ recruitment by assuming that each species turns over a fixed percentage of its potential spawning biomass into new young-of-year (YOY). This percentage is referred to as the species’ reproductive biomass investment (rbi). The species’ spawning biomass is defined to be the total biomass of all cohorts whose body length is are greater than or equal to a specified minimum value (tl_r0) marking the species’ sexual maturation. This algorithm is analogous to the spawner’s abundance model for fish recruitment

32. BASS: Nonfish biota BASS assumes that the non-fish components of a community of concern can be treated as 4 lumped compartments • benthos, • periphyton/attached algae, • Phytoplankton • zooplankton. • These compartments can be treated either as community forcing functions or as bona fide state variables. • Also terrestrial insects can be specified as a forcing function

33. BASS: Nonfish biota When benthos, periphyton, phytoplankton, or zooplankton are treated as state variables.

34. BASS: Nonfish biota BASS formulates a compartment's ingestion, photosynthesis and respiration, by first formulating these processes for the individuals that comprise the compartment. In particular, BASS assumes that the ingestion, photosynthesis, and respiration by individuals within these compartments are describe by