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Fish 458 - Spring 2005Fisheries Stock Assessments

(Models for Conservation)

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Basic Information Instructor:

Dr Andre Punt (FISH 206A; aepunt@u) Office hours:

Class web-site http://courses.washington.edu/fish458/

Prerequisites for this course Fish 456 and Fish 497 (or talk to me) Familiarity with EXCEL and Visual

Basic

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Class Structure Lectures (Room 108): M, W, F

(9.30-10:20) Computer laboratory sessions

(Room 207): T (14:30-16:20) Weekly homework assignments.

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Class Evaluation Submission of homework

assignments. Homework assignments (70%). Mid-term examination (30%).

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Course Overview The purpose of modeling. Developing conceptual and

mathematical models of natural populations.

Fitting models to data / evaluating the plausibility of alternative models.

Exploring different management policies.

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Course Readings(see Web Site for Full

Listing) Burgman, M.A., Ferson, S., Akçakaya, H.R. 1994.

Risk Assessment in Conservation Biology, Chapman & Hall.

Haddon, M. 2001. Modelling and Quantitative Methods in Fisheries. CRC.

Hilborn, R., Mangel, M. 1997. The Ecological Detective. Princeton.

Hilborn, R., Walters, C.J. 1992. Quantitative Fisheries Stock Assessment. Chapman and Hall.

Quinn, T.J., Deriso, R.B. 1999. Quantitative Fish Dynamics. Oxford.

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Example Application Areas Evaluating proposed removal quotas (how

many). Assessing extinction risk (what probability). Designing reserves (where / how large). How to select the data to collect to

improve our understanding.Note: Decisions often have to be made

before we have the data on which to base the decisions (the precautionary approach)!

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Some Example Species Bowhead whales

Long-lived, small population size, could have gone extinct but recovering.

South African hake Fast growing, overfished, recovering.

Northern Cod Fast growing?, overfished, no-recovery?

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What is a Model? In generic terms: A simplified

abstraction of a more complex system. Conceptual model: set of assumptions

represented in natural language that describe a system.

Mathematical model: set of assumptions represented mathematically that describe a system.

Note: the assumptions underlying a model can be considered as alternative hypotheses (e.g. is growth asymptotic?)

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Mathematical Models We use mathematical models because:

Mathematics is more precise than speech. Mathematical models are replicable (same results

given same equations and data). Mathematical models provide a formal framework to

use data to select among alternative assumptions. Conservation decisions usually need to be based on

quantitative considerations as the decisions are usually quantitative (fraction of habitat closed, catch limit).

Population dynamics hypotheses can best be stated as (mathematical) relationships among individuals and (sub)populations.

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Some types of models - I Structure of models:

Age-based, size-based, stage-based, spatially-structured.

Deterministic / stochastic. Continuous / discrete.

All the models in this course consider temporal dynamics – most predictions in ecology relate to the consequences of (management) actions (e.g. extinction risk).

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Statistical Models “Statistical models” represent the

system by fitting empirical relationships to data, e.g.:

Statistical models provide a good basis for interpolation but often behave badly when used for extrapolation (prediction) as they have no biological basis.

1 2y ax bx

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Some types of models - II Continuous models / time-steps:

Discrete models / time-steps:

Stochastic models allow for noise in the population dynamics equations / deterministic models do not:

( )dNdt f N

( )t t t tN N f N t

( )t t t t tN N f N t

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Stochastic vs deterministic

0.002.004.006.008.0010.0012.0014.0016.00

0 20 40 60

Year

Po

pu

lati

on

Siz

e

Deterministic

Stoch-1

Stoch-2

Stoch-2

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Continuous vs. Discrete models Continuous models :

Consider the rate of change of some quantity (e.g. population size) with time.

Are often mathematically more tractable than discrete models.

However: In general, biological populations do not exhibit

continuous dynamics (e.g. discrete breeding seasons).

Discrete models are implemented more straightforwardly on a PC.

Most of the models in this course are discrete.

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Designing models – some initial rules

Rule 1: The level of complexity of a model depends on the questions being asked (e.g. individual births / deaths are important for extinction risk estimation but not for determining optimal harvest levels).

Rule 2 : Complex models require large amounts of data, simple models make strong assumptions. “Everything should be as simple as possible but not simpler” – Einstein! Don’t substitute unrealistic model structure for inestimable parameters!

Rule 3 : Apply several alternative models – be wary if key model predictions are sensitive to changing poorly-known assumptions.

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Nomenclature-I State variables are quantities that vary over

space, time, etc, and which we are interested in predicting (e.g. total population size, number of recruits, presence of a species in a community).

Forcing functions are variables that are external to the model that perturb the state variables in some way (e.g. temperature, fishery catches, rainfall). We do not attempt to predict the future for forcing functions. A key part of the modeling process is to identify the relationships among the forcing functions and the state variables (e.g. how does temperature impact growth rate?)

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Nomenclature II Mathematical models are the mathematical

relationships among the state variables and the forcing functions. They predict the future state of the system based on its current state and the future values for the forcing functions. The mathematical relationships are:

logical statements (tautologies): e.g. law of conservation of energy, numbers next year = numbers this year + births – deaths

based on postulated functional relationships between state variables and forcing functions.

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Nomenclature - III Mathematical relationships among state

variables usually include parameters (constants). Examples: growth rate, rate of natural

mortality. The values for the parameters do not change

over time (or they would be state variables). The values for the parameters need to be

specified (guessed, obtained from the literature, or estimated from data).

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Nomenclature-IV Hypothetical growth model:

( Rain )

(1 / )Height

Height

State variable Forcing function

ParametersMathematical relationships

(rules of change / assumptions)

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The Modeling Cycle1. Identify the questions that are to be addressed.2. Select a set of hypotheses on which a model

could be built.3. Select the values for the parameters (fit the

model to the data).4. Do the model predictions make sense / are they

consistent with auxiliary information?5. Modify the model based on the results of step 4.6. Repeat steps 2-5 using alternative hypotheses.

Start simple and increase complexity as needed.

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Readings Burgman: Chapters 1-3. Haddon: Chapter 1.