458 Fish Spring 2005 Fisheries Stock Assessments (Models for Conservation)

458 Basic Information Instructor: Dr Andre Punt (FISH 206A; Office hours: Class web-site 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 ( :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 Risk Assessment in Conservation Biology, Chapman & Hall. Haddon, M Modelling and Quantitative Methods in Fisheries. CRC. Hilborn, R., Mangel, M The Ecological Detective. Princeton. Hilborn, R., Walters, C.J Quantitative Fisheries Stock Assessment. Chapman and Hall. Quinn, T.J., Deriso, R.B 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

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.

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:

458 Stochastic vs deterministic

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: State variable Forcing function Parameters Mathematical relationships (rules of change / assumptions)

458 The Modeling Cycle 1. 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 Repeat steps 2-5 using alternative hypotheses. Start simple and increase complexity as needed.

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