1. FISH 458 / QSCI 458 (2013) Modeling and estimation in conservation and resource management Instructor: Trevor A. Branch tbranch@uw.edu http://fish.washington.edu/people/branch/

2. Class web site https://catalyst.uw.edu/workspace/tbranch/28677/ (Or google “Trevor Branch” and click on “Courses”)

3. Aim Use of models in examining alternative management policies Modeling resource dynamics: how to describe hypotheses in mathematics Relating models to data: calculating the support the data provide for competing hypotheses Evaluating alternative management actions: what happens if?

4. This is a methods course The key purpose is to teach you how to implement models useful for management Three primary 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

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

6. Class logistics Classes: 9:30-10:20am MWF Computer labs: 1:30-3:20pm Tuesdays Homework due: 11:45pm Wednesdays Readings Weekly quiz on Friday (for self-evaluation) Midterms: 8 May and 7 June Lab exam: 4 June Instructor office hours: after lectures, labs

7. Student responsibility Labs and lectures: 5 hours/week Two mid-term exams: 1 hour prep./week Readings: 1 hour/week Friday quiz: 1 hour prep./week Homework: 4 hours/week One lab exam No final exam, no term paper

8. Grading Mid term I 15% Mid term II 15% Lab exam 20% Homework 50%

9. 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).”

10. Recommended textbooks Hilborn R, Mangel M (1997) The ecological detective: confronting models with data, Princeton University Press, Princeton, New Jersey, 315 pp. Hilborn R, Walters CJ (1992) Quantitative fisheries stock assessment: choice, dynamics and uncertainty, Chapman & Hall, New York, 570 pp.

11. Go through class list

12. Modeling concepts

13. 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:http://aero.konelek.com/aerodynamics/ae rodynamic-analysis-and-design Source: http://www.scienceclarified.com/Bi- Ca/CAD-CAM.html#b

14. Architecture models Source: http://www.archiexpo.com/prod/arc-technology/2d- architecture-cad-software-1701-91443.html Source: http://www.prlog.org/10478600-high-quality- architectural-details-architectural-detail-drawings.html

15. 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: http://histories.naturalhistorynetwork.o rg/ conversations/anemone-like Bob Paine Source: en.wikipedia.org/wiki/E._O._Wilson E. O. Wilson Kimmel et al. (1995) Developmental Dynamics 203:253-310.

16. Traveling salesman problem What is the shortest route that visits each city exactly once and returns to the original city? Source: http://en.wikipedia.org/wiki/File:Bruteforce.gif

17. Slime mold model Source: Jones J & Adamatsky A (2013) Computation of the traveling salesman problem by a shrinking blob. http://arxiv.org/pdf/1303.4969v1.pdf

18. Uses of mathematical models in conservation Study of population dynamics (how populations change over time), which we describe quantitatively Population dynamics hypotheses: what are the relationships between individuals or populations, and associated rates of change Mathematics is the natural language to express these relationships

19. 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?)

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

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

22. 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

23. 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

24. 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, …

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

26. 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

27. 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)

28. Logistic growth (deterministic, dynamic, grouped 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 Net production

29. Real time quiz Take a piece of paper. From this logistic growth model: 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?

30. Answer The state variable is the population size, N The parameters are the intrinsic rate of increase r, and the carrying capacity K The forcing function is the catch, C There is one rule of change: the logistic equation

31. 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)

32. 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 =

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

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

35. 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

36. 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

37. The modeling toolbox for conservation of single populations 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

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

39. Upcoming Tuesday lab: age-structured model of elephants in Kruger National Park, could contraceptives remove the need for a cull? –Paper Whyte et al. posted under “labs” for background information Wed/Fri/Mon lectures: non-age models and introduction to age-structured models Homework handed out Wed, due Wed April 10