Why include species interactions?

Ignore predation at your peril: results from multispecies state-space modeling (Trijoulet, et al., 2020a)

Ignoring trophic interactions that occur in marine ecosystems induces bias in stock assessment outputs and results in low model predictive ability with subsequently biased reference points.

EBFM Objectives in the Northeast US

• EBFM Objective 1: what happens with all the species in the region under a certain management regime?

  • Apply a full system model to assess "side effects" of target species management
  • Ability to implement fishing and biological scenarios
  • Hypothesis testing and MSE framework desirable

• EBFM Objective 2: how well do multispecies models perform for assessment?

  • Consider alternative model structures
    • Biomass dynamics
    • Size structured
    • Age structured
  • Evaluate data availability for each structure
  • Evaluate estimation performance of each structure
  • Evaluate uncertainty and sensitivity
  • Evaluate feasibility of developing and using multi-model inference

Place-based approach

Objective 1: evaluate system responses to management

Rpath (Lucey, et al., 2020a) with MSE capability (Lucey, et al., 2021)

Food web: Rpath in collaboration with AFSC

Food web: Rpath in collaboration with AFSC

Objective 2: evaluate multispecies assessment tools

Multispecies production (Gamble, et al., 2009a)

Multispecies catch at length (Gaichas, et al., 2017a)

(and eventually)

Multispecies catch at age (Curti, et al., 2013a)

Multispecies production simulation: Kraken and estimation FIT: MSSPM

Species interactions:

• Predation: Top down (predation decreases population growth of prey, predator population growth independent of prey)
• Competition: Within and between species groups

Based on Shaefer and Lotka-Volterra population dynamics and predation equations

• Species have intrinsic population growth rate $r_i$
• Full model has
  • Carrying capacity $K$ at the species group level $K_G$ and at the full system level $K_\sigma$
  • Within group competition $\beta_{ig}$ and between group competition $\beta_{iG}$ slow population growth near $K$
  • Predation $\alpha_{ip}$ and harvest $H_i$ reduce population

$$\frac{dN_i}{dt} = r_iN_i \bigg(1 - \frac{N_i}{K_G} - \frac{\sum_g \beta_{ig}N_g}{K_G} - \frac{\sum_G \beta_{iG}N_G}{K_\sigma - K_G} \bigg) - N_i\sum_p\alpha_{ip}N_p - H_iN_i$$

• Simpler version used in most applications has interaction coefficient $\alpha$ that incorporates carrying capacity $$B_{i,t+1}=B_{i,t} + r_iB_{i,t} - B_{i,t}\sum_j\alpha_{i,j}B_{j,t} - C_{i,t}$$

Multispecies catch at length simulation model: Hydra

Species interactions:

• Predation: Top down only (predators increase M of prey, predators grow regardless of prey)

Based on standard structured stock assessment population dynamics equations, Same MSVPA predation equation as MSCAA (but length based), same dependencies and caveats

• First, split $M$ for species $i$ size $j$ into components: $$M_{i,j,t} = M1_i + M2_{i,j,t}$$
• Calculate $M2$ with MSVPA predation equation, which applies a predator consumption:biomass ratio to the suitable prey biomass for that predator.
• Suitability, $\rho$, of prey species $m$ size $n$ for a given predator species $i$ size $j$ a function of size preference and vulnerability {0,1}.
• Food intake $I$ for each predator-at-size is temperature dependent consumption rate times mean stomach content weight.
• Also sensitive to "other food" $\Omega$.

$$M2_{m,n,t} = \sum_i \sum_j I_{i,j,t} N_{i,j,t} \frac{\rho_{i,j,m,n}}{\sum_a \sum_b \rho_{i,j,a,b} W_{a,b} N_{a,b} + \Omega}$$

Model life cycle

(NRC, 2007)

What makes a good model?

• Differs by life stage

• Each builds on the next

• Common themes

This week: constructed model (framework) review

For each model, reviews should evaluate:

1. Spatial and temporal resolution
2. Algorithm choices
3. Assumptions (scientific basis, computational infrastructure; adequacy of conceptual model)
4. Data availability/software tools
5. Quality assurance/quality control (code testing)
6. Test scenarios
7. Corroboration with observations
8. Uncertainty/sensitivity analysis
9. Peer review (previous)

Common attributes across models

A common dataset for 10 Georges Bank species has been developed, as well as a simulated dataset for model performance testing. The mskeyrun data package holds both datasets. All modeling teams used these datasets. Group decisions on data are also documented online.

Datasets: real and simulated

ms-keyrun real biomass and catch data

ms-keyrun real diet data

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ms-keyrun simulated data

References

Additional resources

Hydra: past use as simulation model

Next: Multispecies catch at age estimation model: seeking catchy name FIT: MSCAA

Species interactions:

• Predation: Top down only (predators increase M of prey, predators grow regardless of prey)

Based on standard age structured stock assessment population dynamics equations

• First, split $M$ for species $i$ age $a$ into components: $$M_{i,a,t} = M1_i + M2_{i,a,t}$$
• Calculate $M2$ with MSVPA predation equation, which applies a predator consumption:biomass ratio to the suitable prey biomass for that predator.
• Suitability is a function of predator size preference (based on an age-specific predator:prey weight ratio) and prey vulnerability (everything about the prey that isn't size related).
• Also sensitive to "other food"

$$M2_{i,a,t} = \frac{1}{N_{i,a,t}W_{i,a,t}}\sum_j \sum_b CB_{j,b} B_{j,b,t} \frac{\phi_{i,a,j,b,t}}{\phi_{j,b,t}}$$