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Dynamic Mass Balance Simulations

Sean Lucey

Northeast Fisheries Science Center

Models for Marine Ecosystem-based Management – October, 25, 2022

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www.theguardian.com

www.gma.org

www.voanews.com

Consumption (Q)

Production (P)

Unassimilated Food (U)

Respiration (R)

Production (P)

Biomass Accumulation (BA)

Predator Mortality (M2)

Other Mortality (M0)

Emigration (E)

Fishery Yield (Y)

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Mass balance models

  • Identify and quantify major energy flows in the ecosystem
  • Describe ecosystem resources and their interactions
  • Evaluate the ecosystem effects of fishing or environmental changes
  • Explore management policy option

U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 3

Plagányi 2007

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Dynamic simulations

  • Uses mass-balance for initial state
  • Utilizes ‘Foraging Arena Theory’
  • Can includes both biomass and size-structure dynamics

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Mass Balance Master Equations

Production = fishery removals + predation + emigration + biomass accumulation + other mortality

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​

Consumption = production + unassimilated food + respiration

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Biomass dynamics

  • Series of coupled differential equations
  • Based on Ecopath’s master equation for production

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​

​

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Change in biomass = growth efficiency X consumption – predation + immigration – (other mortality + fishing mortality + emigration)

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Predicting consumption

  • Classical food web models assumed “mass action” principles
  • Works for few, weak trophic interactions
  • When applied to whole ecosystems
    • Strong “top-down” control
    • Predictions of dynamic instability
    • Unstable community structure – loss of biodiversity

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Foraging Arenas

U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 8

Pr

Pr

Pr

Pr

z

z

z

z

z

z

z

p

p

p

p

p

p

p

p

p

p

p

P2

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What it explains

  • Empty stomachs
  • High search efficiencies
  • Widespread complex trophic ontogeny
  • Lack of proportional dependence of M on predator abundance
  • Conservation of Z
  • “Bottom up” control patterns
  • High sensitivity of top predators to fishing
  • Higher biodiversity

U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 9

Walters and Martell 2004

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Predicting trophic flow

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Predator

Bj

Unavailable Prey

Bi - Vij

Available Prey

Vij

 

 

 

 

 

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Foraging Arena relationships

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Adding realism

  • Handling time
  • Foraging time adjustment
  • Mediation

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classicjacksonarts.com

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Handling Time

  • Constraint on consumption
    • Pursuit
    • Capture
    • Manipulation

U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 13

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Foraging Time Adjustment

  • Ability to increase/decrease time spent foraging to maintain a stable consumption rate
  • Increase/decrease exposure to predation

U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 14

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Realistic consumption

  • Original consumption

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​

​

​

​

​

​

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  • “Realistic” consumption

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​

​

​

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Size structure

  • Represent ontogenetic shifts
  • Deriso-Schnute delay-difference model
  • Tracks numbers and biomass
  • Can create as many stanzas as necessary

U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 16

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U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 17

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Parameters

  • Length of stanzas (months)
  • Z per stanza
  • Von Bertalanffy K
  • Relative weight at maturity (Wmat/Winf)
  • Only need B and QB for leading stanza

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Keeping track

  • Relative numbers
    • where la is population growth rate-corrected survivorship

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  • Relative biomass

U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 19

 

 

 

 

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Use relative to get actual

  • Calculated total biomass using ‘leading’ stanza

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​

  • Use total biomass to calculate stanza biomass

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​

  • Similar process for consumption

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Recruitment

  • Fecundity assumed proportional to body weight
  • Size-numbers-dependent monthly egg production used to predict changes in recruitment to age 0

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jimdaleywrites.com

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Solving the processes

  • Differential equations solved through numerical integration
    • 4th order Runge-Kutta
    • Adams-Bashforth
  • Requires short time steps (1 month)
  • Split out groups likely to remain at equilibrium

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Speed-splitting

  • Groups with turnover faster than the time step are likely to stay at relative equilibrium

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russmarrs2-rise-of-sqeegee.wikia.com

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Dynamic simulations using rsim

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Remember

  • Difficult to fully represent natural dynamics
  • Should be able to reproduce correct direction/order of magnitude perturbations
  • Values of the predicted outcomes are relative to each other especially those that impact policy choice

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Ecosense

Gaichas et al. 2015

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Increase GOM herring survival 10%

Herring up

Other forage down

Groundfish

High uncertainty

10% increase in production

No change

in production

Marine

mammals

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Decrease GOM herring biomass 50%

High uncertainty

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U.S. Department of Commerce | National Oceanic and Atmospheric Administration | NOAA Fisheries | Page 29