Applications of Markov chains in demography and population
- Slides: 67
Applications of Markov chains in demography and population ecology Hal Caswell Biology Department Woods Hole Oceanographic Institution Copyright 2006 Hal Caswell
Markov chains in demography • • particle = individual organism states = stages in the life cycle chains absorbing questions relate to absorbtion – where – timing – perturbation analysis June 2006 Hal Caswell -- Markov Anniversary Meeting 2
• Patterns and rates of transition reflect hypotheses about biological processes – growth – development – maturation – reproduction – mortality June 2006 Hal Caswell -- Markov Anniversary Meeting 3
Discrete demography • • • life cycle stages projection interval transitions reproduction June 2006 Hal Caswell -- Markov Anniversary Meeting 4
Age-classified life cycle June 2006 Hal Caswell -- Markov Anniversary Meeting 5
Size-classified life cycles Teasel (Dipsacus sylvestris) 1. 2. 3. 4. 5. 6. June 2006 Hal Caswell -- Markov Anniversary Meeting Dormant seeds 1 Dormant seeds 2 Small rosettes Medium rosettes Large rosettes Flowering plants 6
Stage-classified life cycles Wandering albatross (Diomedea exulans) June 2006 Hal Caswell -- Markov Anniversary Meeting extracted from Croxall et al. 71990
North Atlantic right whale calf June 2006 immature Hal Caswell -- Markov Anniversary Meeting mom post-mom 8
June 2006 Hal Caswell -- Markov Anniversary Meeting 9
June 2006 Hal Caswell -- Markov Anniversary Meeting 10
Analysis within the life cycle • partition entries into transitions and reproduction • recognize that death is present as an absorbing state • life cycle describes dynamics on transient states of an absorbing Markov chain June 2006 Hal Caswell -- Markov Anniversary Meeting 11
June 2006 Hal Caswell -- Markov Anniversary Meeting 12
reproduction rates (s x s) transition probabilities (s x s) mortality probabilities (1 x s) absorbtion probabilities (a x s) June 2006 Hal Caswell -- Markov Anniversary Meeting 13
1=calf 2=immature 3=mature 4=mom 5=post-mom 6=dead June 2006 Hal Caswell -- Markov Anniversary Meeting 14
Importance? • population dynamics • conservation (growth and persistence, invasion and recolonization) • evolution (success of life cycles, aging, environmental response) June 2006 Hal Caswell -- Markov Anniversary Meeting 15
June 2006 Hal Caswell -- Markov Anniversary Meeting 16
June 2006 Hal Caswell -- Markov Magnus and Neudecker 1988, Nel 1980 Anniversary Meeting 17
hours of fun for everybody! June 2006 Hal Caswell -- Markov Anniversary Meeting 18
The North Atlantic right whale (Eubalaena glacialis) June 2006 Hal Caswell -- Markov Anniversary Meeting 19
Endangered, by any standard N < 300 individuals feeding Minimal recovery since 1935 Ship strikes calving June 2006 Hal Caswell -- Markov Anniversary Meeting Entanglement with fishing gear 20
Mortality and serious injury due to entanglement and ship strikes 2030: died October 1999 entanglement June 2006 1014 “Staccato” died April 1999 ship strike Hal Caswell -- Markov Anniversary Meeting 21
1=calf 2=immature 3=mature 4=mom 5=post-mom 6=dead June 2006 Hal Caswell -- Markov Anniversary Meeting 22
Parameter estimation • photographic ID catalog • multistage markrecapture analysis • maximum likelihood estimates June 2006 Hal Caswell -- Markov Anniversary Meeting 23
Results • data 1980 -1998 • series of statistical models • evidence for declining trend in survival of moms, and of birth rate • population growth rate declined to negative levels Fujiwara and Caswell 2001 Caswell and Fujiwara 2004 June 2006 Hal Caswell -- Markov Anniversary Meeting 24
Time-invariant model June 2006 Hal Caswell -- Markov Anniversary Meeting 25
June 2006 Hal Caswell -- Markov Anniversary Meeting 26
E(number of reproductive events) June 2006 Hal Caswell -- Markov Anniversary Meeting 27
Right whale calf 18 16 Expected occupancy (yrs) 14 12 10 8 6 4 2 0 June 2006 calf imm mature Hal Caswell -- Markov Anniversary Meeting mom post-mom 28
June 2006 Hal Caswell -- Markov Anniversary Meeting 29
June 2006 Hal Caswell -- Markov Anniversary Meeting 30
June 2006 Hal Caswell -- Markov Anniversary Meeting 31
Right whale calf CV of stage occupancy time 1. 5 1 0. 5 0 June 2006 calf imm mature Hal Caswell -- Markov Anniversary Meeting mom post-mom 32
June 2006 Hal Caswell -- Markov Anniversary Meeting 33
June 2006 Hal Caswell -- Markov Anniversary Meeting 34
June 2006 Hal Caswell -- Markov Anniversary Meeting 35
June 2006 Hal Caswell -- Markov Anniversary Meeting 36
June 2006 Hal Caswell -- Markov Anniversary Meeting 37
June 2006 Hal Caswell -- Markov Anniversary Meeting 38
June 2006 Hal Caswell -- Markov Anniversary Meeting 39
Right whale 40 35 Life expectancy (yrs) 30 25 20 15 10 5 0 June 2006 calf imm mature Hal Caswell -- Markov Anniversary Meeting mom post-mom 40
Right whale 1. 4 CV of life expectancy 1. 2 1 0. 8 0. 6 0. 4 0. 2 0 June 2006 calf imm mature Hal Caswell -- Markov Stage Anniversary Meeting mom post-mom 41
June 2006 Hal Caswell -- Markov Anniversary Meeting 42
June 2006 Hal Caswell -- Markov Anniversary Meeting 43
June 2006 Hal Caswell -- Markov Anniversary Meeting 44
June 2006 Hal Caswell -- Markov Anniversary Meeting 45
June 2006 Hal Caswell -- Markov Anniversary Meeting 46
June 2006 Hal Caswell -- Markov Anniversary Meeting 47
June 2006 Hal Caswell -- Markov Anniversary Meeting 48
June 2006 Hal Caswell -- Markov Anniversary Meeting 49
June 2006 Hal Caswell -- Markov Anniversary Meeting 50
The birth interval • • • interval between births determines birth rate varies over time responds to environment especially important in species producing few offspring • a special case of the “timing problem” • calculation uses machinery for absorbtion times, but conditional times June 2006 Hal Caswell -- Markov 51 Anniversary Meeting
Modified life cycle graph reproduce before dying died before breeding June 2006 Hal Caswell -- Markov Anniversary Meeting 52
June 2006 Hal Caswell -- Markov Anniversary Meeting 53
June 2006 Hal Caswell -- Markov Anniversary Meeting 54
Right whale 12 Mean time to reproduction (yrs) 10 8 6 4 2 0 June 2006 calf imm mature Hal Caswell -- Markov Starting. Meeting stage Anniversary mom post-mom 55
Time variation • the vital rates of the right whale changed between 1980 and 1998 June 2006 Hal Caswell -- Markov Anniversary Meeting 56
0. 96 time trend best model 0. 94 Calf survival 0. 92 0. 9 0. 88 0. 86 0. 84 0. 82 1980 June 2006 1984 1988 Hal Caswell -- Markov Year Anniversary Meeting 1992 1996 57
1 time trend best model 0. 95 Mother survival 0. 9 0. 85 0. 8 0. 75 0. 7 0. 65 0. 6 1980 June 2006 1984 1988 Hal Caswell Year -- Markov Anniversary Meeting 1992 1996 58
0. 5 time trend best model 0. 45 Birth probability 0. 4 0. 35 0. 3 0. 25 0. 2 0. 15 0. 1 1980 June 2006 1984 1988 Hal Caswell Year -- Markov Anniversary Meeting 1992 1996 59
June 2006 Hal Caswell -- Markov Anniversary Meeting 60
70 period Life expectancy 60 50 40 30 20 10 1980 June 2006 1982 1984 1986 1988 1990 Hal Caswell -- Markov Year Anniversary Meeting 1992 1994 1996 1998 61
June 2006 Hal Caswell -- Markov Anniversary Meeting 62
June 2006 Hal Caswell -- Markov Anniversary Meeting 63
June 2006 Hal Caswell -- Markov Anniversary Meeting 64
June 2006 Hal Caswell -- Markov Anniversary Meeting 65
70 period cohort Life expectancy 60 50 40 30 20 10 1980 June 2006 1982 1984 1986 1988 1990 Hal Caswell -- Markov Year Anniversary Meeting 1992 1994 1996 1998 66
Summary • stage-classified demography from Markov chains – – – – expected stage occupancy times variance in stage occupancy times expected longevity variance in longevity net reproductive rate generation time birth and other intervals period and cohort effects in variable envionments • perturbation analyses • connection to data • things don’t look good for the right whale June 2006 Hal Caswell -- Markov Anniversary Meeting 67
Population demography definition
Transition matrix example
Static demography
Cso business demography
Elements of demography
Demography ap human geography
Sources of demographic data
Components of demography
Demography antonym
Section 1 population dynamics answer key
Population ecology section 1 population dynamics answer key
Population ecology section 1 population dynamics
Chapter 4 population ecology answer key
Hidden markov map matching through noise and sparseness
Scm retail management
Food chain of producers and consumers
Energy flow trophic levels
Section 4 food chains and food webs
Food chains, food webs and ecological pyramids
Lab food chains and energy in ecosystems
Food webs and energy pyramids worksheet answers
Food web in forest ecosystem
Difference between food chain and food web
Lifting tackles list
Seated on high the undefeated one
Markov chain absorbing state
Gauss markov assumptions
Integrated knowledge sets within an organization
Veton kepuska
Aperiodic markov chain
Hidden markov model rock paper scissors
Mdp example
Gauss markov assumptions
Gauss markov theorem
Discrete bayes filter
Embedded markov chain
Markov chain nlp
Aperiodic markov chain
Hidden markov model tutorial
Birth and death process examples
Markov random field
Local markov assumption
Markov decision process merupakan tuple dari
Markov model
Markov decision
Puterman markov decision processes
Aperiodic markov chain
Markov analysis
Aperiodic markov chain
What is markov analysis
Concept of probability
Ratio test rules
Markov localization
Markov localization
Hidden markov chain
Bmics
Interpolated markov model
What is markov analysis in hrm
Hidden markov chain
Gauss markov varsayımları
Aperiodic markov chain
Gauss markov assumptions
Aperiodic markov chain
Chebyshev inequality
Markov decision
Markov inequality proof
Markov decision
Kiểm định sự phù hợp của mô hình
