FISH 458 / QSCI 458 (2015) Applying ecological models to manage and conserve natural resources Instructor: Trevor A. Branch Room FSH 322B,

Class web site TA: Melissa Muradian, room FSH 214

This is a methods course The key purpose is to teach you how to implement models useful for management using three disciplines: Modeling: how to describe hypotheses Statistics: how to compare models to data Simulation and programming: how to implement models –Excel: fitting models to data, manipulating data –R: automate tasks, speed up computing, generalize

Example biological problems Risk of extinction—too few Optimal harvesting—how many Design of reserves—where

Class logistics Classes: 10:30-11:20am MWF Computer labs: 1:00-2:50pm Tuesdays Homework due: 9:00pm Tuesdays Readings Midterms: 8 May and 5 June Lab exam: 2 June Instructor/TA office hours: after lectures, labs

Student responsibility Labs and lectures: 5 hours/week Two mid-term exams: 2 hour prep./week Readings: 1 hour/week Homework: 4–8 hours/week One lab exam No final exam

Grading Mid term I 15% Mid term II 15% Lab exam 20% Assignments50% –Four one-week assignments each 5% of the total grade –Three two-week assignments each 10% of the total grade

University policy on plagiarism and misconduct “Plagiarism, cheating, and other misconduct are serious violations of the student conduct code. We expect that you will know and follow the UW's policies on cheating and plagiarism. Any suspected cases of academic misconduct will be handled according to UW regulations. More information, including definitions and examples, can be found in the Faculty Resource for Grading and the Student Conduct Code (WAC 478‐120).”

Recommended books Hilborn R & Mangel M (1997) The ecological detective: confronting models with data, Princeton University Press, Princeton, New Jersey, 315 pp. ($60) –For understanding model fitting to data, AIC, likelihoods, Bayesian methods Matloff, N (2011) The Art of R Programming ($25) –Draft version available for free online –Somewhat advanced; especially relevant are chapters 1-4, 8-9, and 11

How to learn in this course PowerPoint presentations outline the key material that I want you to learn Excel sheets allow you to experiment with models presented in the lectures R code allows you to reuse and modify models, and embed them in your own programs Occasional handouts provide detailed derivations and proofs (for interest)

Questions about the course?

Lecture plan this week What is a model? General modelling concepts and definitions Models with no age structure: exponential, logistic, Pella-Tomlinson, Fox Age-structured models Recruitment models Yield-per-recruit models Estimating maximum sustainable yield (MSY)

What is a model? A simplified abstraction of a more complex object A model airplane has some of the characteristics Boeing now tests new planes using computer models instead of physical models of airplanes and wings Source: rodynamic-analysis-and-design Source: Ca/CAD-CAM.html#b

Architectural models Source: architecture-cad-software html Source: architectural-details-architectural-detail-drawings.html

Experimentalist models Animal models: Drosophila, zebrafish, mice Field ecologists interested in studying a phenomenon should look for an appropriate model E.O. Wilson said if he was beginning again he would work on micro-organisms Bob Paine: long-term studies of intertidal communities on Tatoosh Island Source: rg/ conversations/anemone-like Bob Paine Source: en.wikipedia.org/wiki/E._O._Wilson E. O. Wilson Kimmel et al. (1995) Developmental Dynamics 203:

Saye RI & Sethian JA (2013) Multiscale modeling of membrane rearrangement, drainage, and rupture in evolving foams. Science 340: Movie of simulation: Computer models

Typical uses of models To explore consequences of alternative hypotheses: How likely is extinction? How much can I harvest? To clarify ideas about relationships within a system (food web models) To ask how well hypotheses are supported by data (which model is best?) To help coordinate research teams (which data to collect?) To design management programs (which rules work best?)

General modeling concepts

Types of mathematical models Statistical models Dynamic models –Stochastic or deterministic –Continuous or discrete –Lumped models –Stage based –Size structured –Age structured –Individual based

Statistical models Predicted values depend upon some observed values and some parameters (constants) Multiple linear regression: Model prediction Parameters to estimate Observed values

Dynamic models Observed variables depend upon past conditions of the system, constants, and any perturbations Exponential growth: Population at start Increase rate Numbers in next time step Numbers at time t

Components of dynamic models State variables Parameters Forcing functions Rules of change State variables in the future depend upon the current state, the parameters (constants), any external perturbations (the forcing functions), and the rules of change

State variables The complete description of the current state of the system—those elements that change over time—complete enough that you can “rebuild” the system with this amount of information Examples: number of animals in the population, age structure of a population, presence or absence of species in a community matrix, etc.

Parameters Do not change over time and are the constants that describe the rates or limits Intrinsic rate of growth, carrying capacity, survival rate, fecundity rate, movement rate, etc.

Forcing functions Natural or anthropogenic factors that affect the state variables Climate impacts on survival or reproduction Harvesting These are “external” to the model—we don’t need to describe the dynamics of these factors

Rules of change The equations that describe how the state variables change over time in relation to the current values of the state, the parameters, the forcing functions. Rules of change (equations) Parameters (e.g. rate of increase) State variables next time step Forcing functions (e.g. catch) State variables (e.g. numbers)

Logistic growth (deterministic, dynamic, lumped model) Numbers next year are numbers this year plus net production minus removals Catch in time t Intrinsic (maximum) rate of increase Population size time t+1 Carrying capacity Surplus production

Logistic growth 1. What are the state variable(s)? 2. What are the parameter(s)? 3. What are the forcing function(s)? 4. What are the rules of change?

Components of rules of change Logical relationships –Statements that are true by definition –numbers next year = numbers this year + births – deaths + immigration – emigration –Also known as tautologies Functional relationships –Specify the relationship between a rate and a state variable or something related to a state variable (survival as a function of density, recruitment as a function of spawning biomass)

For logistic growth model A logical relationship –number alive next year is number alive this year plus net production minus catch The functional relationship –net production =

Deterministic or stochastic models Do we allow for random events or not Deterministic model A stochastic version where w t is a random variable from a normal distribution with mean 0 and standard deviation s 1 Logistic.xlsx – Deterministic discrete 1 Logistic.xlsx – Stochastic discrete

Continuous or discrete models Continuous models use differential equations Discrete models use “difference” equations

Continuous logistic model Source: Mangel M (2006) The theoretical ecologist's toolbox, Cambridge University Press, Cambridge This equation is quite different to the discrete model! 1 Logistic.xlsx – Deterministic continuous

1 Logistic.xlsx – Discrete oscillations

How to decide between discrete and continuous models Are the processes discrete or continuous? In individual-based models discrete processes are almost always appropriate For most computer software discrete models are easier Differential equations provide analytic solutions for simple problems Tradition

Common conservation and management models Biomass-dynamics models (logistic, Schaefer, Fox, Pella-Tomlinson) Generation-to-generation models (Ricker, Beverton-Holt) Delay-difference models (Deriso-Schnute) Size- and stage-structured models Age-structured models

Extensions to all Stochastic or deterministic Adding environmental impacts Extending to multiple species