MAR 580: Models for Marine Ecosystem Based Management

Multispecies models, �estimating species interactions, multispecies policy advice

27 September 2022

This week’s Outline

• Tuesday:
• Multispecies modeling
• Minimal Realistic Models
• Roles for MRMs
• Multispecies policy advice
• Thursday:
• Species distribution modeling, sdmTMB
• Guest lecture via Zoom: Dr. Eric Ward, NOAA NWFSC

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• Third assignment (deadline changed to 10/13)
• Size-dependent predation
• Introduction to MARSS package in R

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A spectrum of tools, a spectrum of uses

Stock/Single Species

Ecosystem

Aggregate Biomass

Single stock models

Multiple stock assessments integrated

Stock assessments with add-ons: explicit M2 or habitat or climate considerations

Multi-species assessments

Functional group models

Whole system models

Integrated ecosystem assessments

Multi-species

Economic assessments, social impacts

(almost) all you ever need to �know for Population Modeling

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Numbers next year = numbers this year

+ births – deaths� + immigrants – emigrants

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Multispecies models

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Effectively a set of single species models with some form of linkage between them, usually species interactions, all modeled simultaneously.

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Image from: http://www.anselm.edu/homepage/jpitocch/genbios/52-19a-PopCycleHareLynxPhot.jpg

Image from bbc.co.uk

Minimal Realistic Models�a.k.a. Models of Intermediate Complexity

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Plagányi et al. (2014)

Objective of these models is to consider the interactions among a small number of species and components.

• Focus on ‘key’ system properties/components relevant to the research or management questions.
• May include a suite of model types for each component.
• Perhaps statistically estimate model parameters using data similar to single-species models.

Multispecies models

• Models of multispecies dynamics have been around for a long time (e.g. Lotka 1910).
• Add species interactions to simultaneous sets of population dynamics.

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Lotka-Volterra Predator-Prey

Adding interactions to the logistic model

Competition

Predation

We can add interaction terms to ‘simple’ production models.

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e.g. Lotka-Volterra competition terms to the logistic model. Here the α’s are positive.

(representing negative effects of species on eachother)

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There are a myriad of ways for including these terms – choices should ideally be driven by some understanding of the system.

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Here we model a Type II functional response in the consumption of prey N by predator P.

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This is more realistic than the Lotka-Volterra equations as it implies saturation in the per capita predator consumption.

A simple multispecies model

Channel Islands: introduced feral pigs allowed golden eagles to establish and increase, greatly increasing predation (hyperpredation) on native foxes. Low fox numbers allowed competitively inferior skunks to flourish.

Multispecies equations

No pigs

Pigs

Roemer, G.W., Donlan, C.J., and Courchamp, F. 2002. Golden eagles, feral pigs, and insular carnivores: How exotic species turn native predators into prey. Proc. Natl Acad. Sci. U.S.A. 99(2): 791-796.

From Branch

Choice of functional response can greatly influence model behavior, yet not always be easy to identify.

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Models sensitive to form of functional response describing predator-prey dynamics.

Kinzey & Punt (2009) Multispecies and single-species models of fish population dynamics: comparing parameter estimates. Natural resource modeling 22: 67-104.

Multispecies Fisheries Production Models

• Several instances of these models being applied.
• Pooled biomass dynamics versions have not tended to be fit to data (but see WGSAM in a couple of weeks!), rather rely on auxiliary information for parameterization.
• Length structured versions have.

Gamble, R.J. and J.S. Link. 2009. Analyzing the tradeoffs among ecological and fishing effects on an example fish community: A multispecies (fisheries) production model. Ecol. Mod. 220: 2570-2582.

Stage-structured multispecies models

• Like their single-species counterparts, these models include population structure such as age and/or length.
• Species interactions can then be length or age dependent.
• More realistic, big fish eat small fish….
• The focus of these models has primarily been on trophic interactions.
• Predation mortality
• Prey-dependent growth largely not included.

Stage-structured multispecies models

• Modeling predation via M2
• M2 essentially treated as another fishing fleet, but with functional response replacing selectivity.

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Modeling predation mortality

• Size-based approaches (e.g. Hall et al. 2006)
• Take advantage of scaling relationships associated with growth, consumption, and size ratios between predator and prey species.
• Dramatically reduces number of parameters

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• Alternative is to estimate functional�response parameters based on �stomach contents data
• Ration can be derived from growth�curve, or a function of covariates.
• Require ‘other food’ component.

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Hall et al. (2006)

Multispecies Virtual Population Analysis (MSVPA)

Other Food

Consumption = Predator BM * %DR

P_prey = (Suitable Biomass)_prey / Total Suitable Biomass

C_prey = Consumption * P_prey

M2_prey = C_prey / BM_prey

M2_age

Single Species VPA

BM_age

BM_age

BM_age

BM_age

BM_age

Diet Data

Suitability

Parameters

Other

Predators

Adapted from Garrison et al.

Multispecies statistical catch-at-age models

Simultaneous stock assessments of multiple species fitted to numerous data, including diet information.

e.g. Aleutian Islands groundfish fishery (Kinzey & Punt 2009).

Walleye pollock, Atka mackerel, and Pacific cod interact as predators and prey.

See also:

Holsman et al. (2016) [CEATTLE]�Curti et al. (2013)�ICES (2010) - (SMS model)�Van Kirk et al. (2010, 2012)

Barents Sea Minke Whales-Cod-Capelin EXAMPLE

• Several models:
• GADGET,
• BORMICON,
• MULTSPEC, etc.
• Explores tradeoffs among 4 main species interactions.
• Environment and fishing contrasted.

Bogstad, B., Hauge, K. H., & Ulltang, Ø. (1997). MULTSPEC–a multi-species model for fish and marine mammals in the Barents Sea. Journal of Northwest Atlantic Fishery Science, 22(317-341), 1-1.

North Sea SMS model (ICES 2010, etc.)

Estimating parameters

• Previous models require typical stock assessment data, plus either:
• Assumptions about ecological relationships
• Stomach contents data

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• Alternative approaches to estimating parameters for multispecies models are less mechanistic:

Multivariate autoregressive (MAR) models

• Take the form

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• B matrix can be VERY big
• Simplified dynamics
• Estimating parameters is often non-trivial
• MARSS package in R uses EM algorithm to do maximum likelihood estimation.

e.g. Ives et al. 2003 Ecol. Monographs, Holmes et al. 2012. R journal.

Food web models based on metabolic scaling

• Make use of metabolic scaling theory to determine biological dynamics
• e.g. Kleiber’s law
• Used to compare empirical data with theoretical structures (network theory)
• Understand role of structure in behavior of foodweb
• Connectance
• Robustness to perturbation
• Simple rules to connect foodwebs
• e.g. trophic niche model

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e.g. Dunne et al. 2004. MEPS.

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Image produced with FoodWeb3D, written by R.J. Williams and provided by the Pacific Ecoinformatics and Computational Ecology Lab (www.foodwebs.org, Yoon et al. 2004). 

Size spectra models

• Simple metabolic models.
• Feeding ecology based on theoretical size-based relationships
• Focus on size distribution of communities rather than individual species.
• Model evaluation by changes to the slopes of the size spectra.

Hartvig et al. 2011

Minimal Realistic Models�a.k.a. Models of Intermediate Complexity

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(Plagányi et al. (2014)

Objective of these models is to consider the interactions among a small number of species and components.

• Focus on ‘key’ system properties/components relevant to the research or management questions.
• May include a suite of model types for each component.
• Statistically estimate model parameters using data similar to single-species models.

Models of Intermediate Complexity

Plagányi et al. (2014) Multispecies fisheries management and conservation: tactical applications using�models of intermediate complexity. Fish and Fisheries. doi: 10.1111/j.1467-2979.2012.00488.x

The South African Seal-Hake “Minimal Realistic Model”

A.E. Punt

Punt, A. E., & Butterworth, D. S. (1995).�South African Journal of Marine Science, 16(1), 255-285.

Uses of MRMS/MICE

• Most MRMs have been developed as the basis for strategic evaluations.
• But many could be fit to data and also used to provide tactical advice.
• Example: Fay et al. (2013, 2015), used auxiliary information to simulate multispecies dynamics for Georges Bank.
• In principle the parameters can be estimated by fitting to data.
• Well constructed MICE are based on extensive stakeholder consultation.

Challenges with multispecies reference points

• Recall logistic growth model

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• Add single competitor

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• Dependence on biomass of other species.
• Sometimes possible to solve system of equations to obtain maximizing population state vector.
• But, implies decision about what is the ‘right’ population size for other species.

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Reading: Collie and Gislason 2001, Fogarty 2014, Moffit et al. 2016

Fishery interactions with multispecies models

Multispecies Yield-per-recruit (MSYPR)

• These add technical interactions to YPR models.
• Similar to YPR models, but effectively focus on bycatch, mixed species fisheries.

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Simulations: balancing fishery/conservation objectives

Gaichas et al. 2012 MEPS

Yield maximizing biodiversity is ~95% of MMSY

Three

fisheries: selectivity

and catchability

Can an improved mix of gears 🡪 higher yields?

+ ~15%

Simulations to evaluate multispecies fishery performance (Gaichas et al. 2017)

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• Operationalizing EBFM requires strategies that address tradeoffs among species, and balance societal and ecological management objectives.
• Aggregate fishing limits that maximize yield and conserve biomass exist
• Community composition and (likely) value trade off across the range of fishing effort.

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Multispecies Models and MRMs

• Growing use of all types of models.
• Continued development and enhancement of model construction.
• Movement from heuristic to strategic/tactical applications.
• These models are clearly more realistic!
• Cost (data, institutional change) of application/implementation is high.
• Rigorous evaluation of uncertainty / robustness required for general applications.

Advantages

• Focus more specifically on restricted subset of system and problems.
• Account for uncertainty more fully than whole of system models
• Models can be structured to take advantage of available data.
• Flexible nature can tailor model to specific systems and problems.

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Disadvantages

• Lack the detail and realism for evaluating complex systems.
• Possibility of choosing the wrong key species and interactions.
• Custom built, time consuming and labor intensive for individual applications.
• Management not really set up for using them as assessment models

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Functional responses matter

Pinnegar et al.

Multispecies Models

• Questions?