View
229
Download
2
Tags:
Embed Size (px)
Citation preview
458
Fish 458 - Spring 2005Fisheries Stock Assessments
(Models for Conservation)
458
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
458
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.
458
Class Evaluation Submission of homework
assignments. Homework assignments (70%). Mid-term examination (30%).
458
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.
458
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.
458
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)!
458
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?
458
458
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?)
458
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.
458
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).
458
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
458
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
458
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
458
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.
458
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.
458
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?)
458
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.
458
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).
458
Nomenclature-IV Hypothetical growth model:
( Rain )
(1 / )Height
Height
State variable Forcing function
ParametersMathematical relationships
(rules of change / assumptions)
458
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.
458
Readings Burgman: Chapters 1-3. Haddon: Chapter 1.