458 Multispecies Models-II (Including Predation In Population Models) Fish 458, Lecture 27.

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Multispecies Models-II

(Including Predation In Population Models)

Fish 458, Lecture 27

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Overview Predators as a fishery Minimal Realistic Models General ecosystem models (EcoPath /

Ecosim)

Note: Each type of model addresses a different set of questions. The choice of modelling framework depends on the question being addressed – there is no “correct” modelling framework.

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Predators As A Fishery-I The objective is to model the

numbers-at-age for a prey species given information on how the numbers of predators has changed over time (e.g. from an assessment of the predator species).

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Predators As A Fishery-II The model of the population

dynamics becomes:/ 2 / 2

1, 1 , , ,( )M My a y a y a y aN N e C P e

' , '/ 2'

, ,/ 2' ' , '

'

Pa y a

May a a a y aM

a a y aa

R NP w N e

w N e

Fishery catch Numbers predated

Predator selectivity

Annual predator rationPredator numbers

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Predators As A Fishery-III(Extensions)

Each predator age-class has a different selectivity pattern (smaller predator age-classes feed on smaller prey).

This model can be used to model cannibalism (i.e. the predator numbers are the prey numbers).

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Predators As A Fishery-IV(Advantages and Disadvantages)

Advantages: Simple - only requires information on

predator numbers and the ration of each predator age-class (in addition to the data for the prey species).

Disadvantages: Ignores the dynamics of the predator species

(the predator numbers are pre-specified). Ignores how the predator diet may change as

the prey numbers change.

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Minimal Realistic Models-I The objective of these models is to

consider the interactions among a small number of species by developing a multi-species model with a small number of predators.

An example of this type of model is that developed to examine the consequences of a cull of Cape fur seals to increase catches and catch-rates of Cape hake.

458Herewith a“hake-centric” food web

Even this web wastoo complex toparameterize!

© Ocean of Life (1989)

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We will reduce theweb to what can befitted to using the existing data.

We remove all “small” links / preyspecies. Over 90%of the identified mortality on hake is still captured.

X X

XXX

X

X

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Management

The Seal-Hake “Minimal Realistic Model”

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ManagementModel Structures andManagement Systems

Catches Fixed F

Cull scenarios

Species-; age-structured

Age-; sex-structured

Delay-difference

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Minimal Realistic Models-II(Advantages and Disadvantages)

Advantages: Limited data requirements (compared to

more complicated models). Can be fitted to data using standard

methods. Restricted to the set of “species of interest”.

Disadvantages: Still highly data intensive. How can you be sure that the correct species

are included in the model without building an even larger / more complicated model?

The models need to be developed from scratch for each new application.

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General Ecosystem Models(EcoPath / EcoSim)

These models: sacrifice detail (e.g. age-structure and

by grouping species) to represent a larger range of species and interactions;

address broad-scale questions related to the structure of the ecosystem.

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A “simplified” food webof the Benguela system!

We need a “simple” modelof each component to capture all the interactions.

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EcoPath / Ecosim - I(EcoPath)

EcoPath is a set of equations that describe trophic relationships among ecosystem components. A typical assumption is that the system is "balanced", i.e., the sum total of trophic interactions, production, and other mortality is zero or another constant.

The EcoPath model provides the initial state of the system for projections into the future using the EcoSim model.

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EcoPath / Ecosim - II The biomass of each component (a

species or group of species) is governed by the differential equation:

( ( ), ( )) ( ) ( ) ( ( ), ( ))jj ij i j j j j j jk j ki k

dBg c B t B t F B t M B t c B t B t

dt

Growth efficiency

Predation byspecies j

Fishing mortality

Othermortality

Predation ofspecies j

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EcoPath / Ecosim - III The Ecosim predation equation can

be parameterized to allow for “top-down” (predator) or “bottom-up” (prey) control.* * * * *

* *

( / ) ( / )( / )

( 1) ( / )ij j j ij i i j j

ijij j j

DC Q B B X B B B Bc

X B B

*

*

*

initial biomassof component ,

( / ) consumption to biomass ratio for component ,

fraction of species in the diet of predator (initialstate)

vulnerability parameter

i

i

ij

ij

B i

Q B i

DC i j

X

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EcoPath / Ecosim - IV Vulernability:

1 – Bottom-up control (amount consumed is linearly proportional to prey biomass and independent of predator biomass).

- Top-down control (amount consumed is proportional to the product of the prey and predator abundances).

3.333 – default value.

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EcoPath / Ecosim - V(Advantages and Disadvantages)

Advantages: Can capture a large number of species and

address whole-ecosystem questions. A software package (EwE) exists that

implements this model. This package is used by many users.

Extensions to the model exist to: allow for predator handling time; include spatial structure (EcoSpace); include age-structure; include forcing functions (e.g. changes over time in

primary production); fit the model to time-series of abundance estimates

(e.g. from surveys.

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EcoPath / Ecosim - VI(Advantages and Disadvantages)

Disadvantages: Highly data intensive - for each component

information is required on: biomass, the production/biomass ratio, the

consumption/biomass ratio, diet, fishing mortality, and “other” mortality.

Although flexible, the predation function does not capture all possible hypotheses for the interaction between prey and predators.

The results are often sensitive to the values assumed for the vulnerability parameters (beware of the default values).

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Final Notes Disagreements between the predictions

of single- and multi-species models can be informative and lead to the generation of hypotheses for system behaviour.

Caution should be exercised in making use of the predictions of multi-species models unless there is substantial agreement across different approaches.

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Readings Punt and Butterworth (1995). Walters et al. (1997).