APD Lecture 2 - The BIDE Model

Introduction to modeling and the Birth-Immigration-Death-Emigration (BIDE) model.

Transcript

1. The BIDE model q q q q q q q q q q q q q q q q q q q q 5 10 15 20 0 50 100 150 200 Year q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q Population size (N) Births (B) Immigrants (I) Deaths (D) Emigrants (E)
2. Today’s topics 1 Definitions 2 Modeling 101 3 BIDE 4 Assignment Definitions Modeling 101 BIDE Assignment 2 / 10
3. Definitions Population dynamics The study of spatial and temporal variation in population size and structure Definitions Modeling 101 BIDE Assignment 3 / 10
4. Definitions Population dynamics The study of spatial and temporal variation in population size and structure Population Individuals of the same species occuring in the same geographic region Definitions Modeling 101 BIDE Assignment 3 / 10
5. Definitions Population dynamics The study of spatial and temporal variation in population size and structure Population Individuals of the same species occuring in the same geographic region Population size and structure Size: Abundance Structure: Distribution of individuals among age groups, sexes, habitat patches, etc. . . Definitions Modeling 101 BIDE Assignment 3 / 10
6. Models and science A model is an abstraction of reality that describes the relationship between two or more variables. Definitions Modeling 101 BIDE Assignment 4 / 10
7. Models and science A model is an abstraction of reality that describes the relationship between two or more variables. Models help us. . . • Describe complex natural systems in a manageable way Definitions Modeling 101 BIDE Assignment 4 / 10
8. Models and science A model is an abstraction of reality that describes the relationship between two or more variables. Models help us. . . • Describe complex natural systems in a manageable way • Formalize and evaluate hypotheses Definitions Modeling 101 BIDE Assignment 4 / 10
9. Models and science A model is an abstraction of reality that describes the relationship between two or more variables. Models help us. . . • Describe complex natural systems in a manageable way • Formalize and evaluate hypotheses • Predict future outcomes Definitions Modeling 101 BIDE Assignment 4 / 10
10. Models and science A model is an abstraction of reality that describes the relationship between two or more variables. Models help us. . . • Describe complex natural systems in a manageable way • Formalize and evaluate hypotheses • Predict future outcomes • . . . all while accounting from uncertainty Definitions Modeling 101 BIDE Assignment 4 / 10
11. Models and science But don’t models require assumptions? Definitions Modeling 101 BIDE Assignment 5 / 10
12. Models and science But don’t models require assumptions? Yes. Definitions Modeling 101 BIDE Assignment 5 / 10
13. Models and science But don’t models require assumptions? Yes. We have to simplify, so we have to make assumptions. Definitions Modeling 101 BIDE Assignment 5 / 10
14. Models and science But don’t models require assumptions? Yes. We have to simplify, so we have to make assumptions. We do this all the time, for example when deciding how long it will take you to get to class. Definitions Modeling 101 BIDE Assignment 5 / 10
15. Models and science But don’t models require assumptions? Yes. We have to simplify, so we have to make assumptions. We do this all the time, for example when deciding how long it will take you to get to class. “All models are wrong, but some are useful.” G.E.P. Box (1987) Definitions Modeling 101 BIDE Assignment 5 / 10
16. Model validation Putting the model to the test • How well does it predict? Definitions Modeling 101 BIDE Assignment 6 / 10
17. Model validation Putting the model to the test • How well does it predict? • Will your results hold up in court? Definitions Modeling 101 BIDE Assignment 6 / 10
18. Model validation Putting the model to the test • How well does it predict? • Will your results hold up in court? • Can your results be replicated/reproduced? Definitions Modeling 101 BIDE Assignment 6 / 10
19. Types of models • Conceptual • Physical • Graphical • Mathematical • Statistical Definitions Modeling 101 BIDE Assignment 7 / 10
20. Types of models • Conceptual • Physical • Graphical • Mathematical • Statistical Definitions Modeling 101 BIDE Assignment 7 / 10
21. The BIDE model Nt+1 = Nt + Bt + It − Dt − Et Nt : population size (state variable) at time t Bt : births It : immigrants Dt : deaths Et : emigrants Definitions Modeling 101 BIDE Assignment 8 / 10
22. The BIDE model Nt+1 = Nt + Bt + It − Dt − Et As written, this model implies the following: • B, I, D, and E are not rates, they are the number of events at time t. • The model is deterministic, not stochastic • Time is discrete, not continuous Definitions Modeling 101 BIDE Assignment 9 / 10
23. The BIDE model Nt+1 = Nt + Bt + It − Dt − Et As written, this model implies the following: • B, I, D, and E are not rates, they are the number of events at time t. • The model is deterministic, not stochastic • Time is discrete, not continuous In reality, things are more complicated, and interest lies in understanding the factors influencing each process. Definitions Modeling 101 BIDE Assignment 9 / 10
24. The BIDE model Nt+1 = Nt + Bt + It − Dt − Et As written, this model implies the following: • B, I, D, and E are not rates, they are the number of events at time t. • The model is deterministic, not stochastic • Time is discrete, not continuous In reality, things are more complicated, and interest lies in understanding the factors influencing each process. Group exercise: Break into teams of 4-5 and create list of factors influenceing B, I, D, and E. Definitions Modeling 101 BIDE Assignment 9 / 10
25. Assignment Read the first 3 pages of Chapter 3 in Conroy and Carroll Expect a quiz on Wednesday Definitions Modeling 101 BIDE Assignment 10 / 10