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

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.

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).

Predators As A Fishery-II The model of the population dynamics becomes: Fishery catch Numbers predated Annual predator ration Predator numbers Predator selectivity

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).

Predators As A Fishery-IV (Advantages and Disadvantages) 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.

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.

Herewith a“hake-centric” food web Even this web was too complex to parameterize! © Ocean of Life (1989)

X X X X X X X We will reduce the web to what can be fitted to using the existing data. X We remove all “small” links / prey species. Over 90% of the identified mortality on hake is still captured. X

Management The Seal-Hake “Minimal Realistic Model”

Management Model Structures and Management Systems Age-; sex- Cull scenarios Age-; sex- structured Catches Fixed F Species-; age- structured Delay-difference

Minimal Realistic Models-II (Advantages and Disadvantages) 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.

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.

A “simplified” food web of the Benguela system! We need a “simple” model of each component to capture all the interactions.

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.

EcoPath / Ecosim - II The biomass of each component (a species or group of species) is governed by the differential equation: Fishing mortality Predation of species j Growth efficiency Predation by species j Other mortality

EcoPath / Ecosim - III The Ecosim predation equation can be parameterized to allow for “top-down” (predator) or “bottom-up” (prey) control.

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.

EcoPath / Ecosim - V (Advantages and Disadvantages) 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.

EcoPath / Ecosim - VI (Advantages and 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).

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.

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