Capture-recapture Models for Open Populations Abundance, Recruitment and Growth Rate Modeling 6.15 UF-2015.

Slides:



Advertisements
Similar presentations
The Simple Linear Regression Model Specification and Estimation Hill et al Chs 3 and 4.
Advertisements

Population Ecology & Demography; Leslie Matrices and Population Projection Methods Introduction to linking demography, population growth and extinction.
MARK RECAPTURE Lab 10 Fall Why?  We have 4 goals as managers of wildlife  Increase a population  Decrease a population  Maintain a population.
Estimating Abundance Weight Sub-sample
Lecture 8 review Options for estimating population size –Direct census (visual, acoustic, etc.) –Density expansion (time, area) –Change in index methods.
The current status of fisheries stock assessment Mark Maunder Inter-American Tropical Tuna Commission (IATTC) Center for the Advancement of Population.
Maximum likelihood estimates What are they and why do we care? Relationship to AIC and other model selection criteria.
Vocabulary Review Ch 19 Populations. A group of organisms of the same species that live in a specific geographical area and interbreed Population.
Population Ecology Chapter 27. Population Ecology Certain ecological principles govern the growth and sustainability of all populations Human populations.
Generalized Regression Model Based on Greene’s Note 15 (Chapter 8)
The Tools of Demography and Population Dynamics
CSE 221: Probabilistic Analysis of Computer Systems Topics covered: Statistical inference (Sec. )
OPEN CAPTURE-RECAPTURE
CLOSED CAPTURE-RECAPTURE
Computer vision: models, learning and inference Chapter 19 Temporal models.
1 POPULATION PROJECTIONS Session 2 - Background & first steps Ben Jarabi Population Studies & Research Institute University of Nairobi.
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc. Chap 8-1 Confidence Interval Estimation.
Resource Selection Functions and Patch Occupancy Models: Similarities and Differences Lyman L. McDonald Senior Biometrician Western EcoSystems Technology,
Closed Vs. Open Population Models Mark L. Taper Department of Ecology Montana State University.
Mixture models for estimating population size with closed models Shirley Pledger Victoria University of Wellington New Zealand IWMC December 2003.
Modeling Cure Rates Using the Survival Distribution of the General Population Wei Hou 1, Keith Muller 1, Michael Milano 2, Paul Okunieff 1, Myron Chang.
In-depth Analysis of Census Data on Migration Country Course on Analysis and Dissemination of Population and Housing Census Data with Gender Concern
Integral projection models
Statistical Inference for the Mean Objectives: (Chapter 9, DeCoursey) -To understand the terms: Null Hypothesis, Rejection Region, and Type I and II errors.
Population Parameters – Chapter 9. Population – a group of organisms of the same species occupying a particular space at a particular time. Demes – groups.
CS Statistical Machine learning Lecture 24
Biodiversity and Measuring Abundance Lab Manual Chapters 3, 7, and 13.
Population ecology Gauguin. 15 populations (various patch sizes) Time since fire: 0 to >30 years 9 years ( ) >80 individuals per population each.
BRIEF INTRODUCTION TO ROBUST DESIGN CAPTURE-RECAPTURE.
- We have samples for each of two conditions. We provide an answer for “Are the two sample means significantly different from each other, or could both.
Parameter Redundancy in Mark-Recapture and Ring-Recovery Models with Missing Data Diana Cole University of Kent.
Population Ecology and Ecosystems Concepts and Applications: Chapters 40 & 43 Basic Concepts: Chapters 27 & 30 Concepts and Applications: Chapters 40 &
Populations. What is a population? -a group of actively interacting and interbreeding individuals in space and time.
Matrix Models for Population Management & Conservation March 2014 Lecture 10 Uncertainty, Process Variance, and Retrospective Perturbation Analysis.
Estimation of Animal Abundance and Density Miscellaneous Observation- Based Estimation Methods 5.2.
Multistate models UF Outline  Description of the model  Data structure and types of analyses  Multistate with 2 and 3 states  Assumptions 
Estimation of Vital Rates: Use of Index Statistics? Relevance of Detection Probability.
Capture-recapture Models for Open Populations “Single-age Models” 6.13 UF-2015.
Chapter 8 Estimating Population Size: Capture-Recapture Model Examples: Estimating number of blue whales Estimating number of fish in a lake Estimating.
Pollock’s Robust Design: Model Extensions. Estimation of Temporary Emigration Temporary Emigration: = individual emigrated from study area, but only temporarily.
3.1 Statistical Distributions. Random Variable Observation = Variable Outcome = Random Variable Examples: – Weight/Size of animals – Animal surveys: detection.
Pollock’s Robust Design: Extensions II. Quick overview 1.Separation of Recruitment Components in a single patch context (Source-Sink) 2.Separation of.
Spatially Explicit Capture-recapture Models for Density Estimation 5.11 UF-2015.
K-Sample Closed Capture-recapture Models UF 2015.
Population Dynamics Ms. Byers and Ms. Jacobs. Why Estimate Population Size? To compare populations in different areas To assess the health of wildlife.
Capture-recapture Models for Open Populations Multiple Ages.
Review. Common probability distributions Discrete: binomial, Poisson, negative binomial, multinomial Continuous: normal, lognormal, beta, gamma, (negative.
Closed Capture-Recapture Models 2 Sample Model Outline: Model description/ data structure Encounter history Estimators Assumptions and study design.
 Occupancy Model Extensions. Number of Patches or Sample Units Unknown, Single Season So far have assumed the number of sampling units in the population.
Population Ecology and Conservation Population Ecology and Conservation A Conceptual Framework 2.1 UF-2015.
Université d’Ottawa / University of Ottawa 2003 Bio 8102A Applied Multivariate Biostatistics L4.1 Lecture 4: Multivariate distance measures l The concept.
Probability distributions and likelihood
Demographic PVAs.
From: Tipping the Balance of Benefits and Harms to Favor Screening Mammography Starting at Age 40 YearsA Comparative Modeling Study of Risk Ann Intern.
Propagating Uncertainty In POMDP Value Iteration with Gaussian Process
Estimating Population Size
Hidden Markov Models Part 2: Algorithms
Confidence Intervals Chapter 10 Section 1.
OVERVIEW OF LINEAR MODELS
Mark Recapture.
Multistate models Lecture 10.
Estimating mean abundance from repeated presence-absence surveys
OVERVIEW OF LINEAR MODELS
Wildlife Population Analysis
Chapter 4 SURVIVAL AND LIFE TABLES
Wildlife Population Analysis
Time symmetrical (reverse-time) models
Population Ecology.
Population Growth & Measurement
Probabilistic Surrogate Models
Presentation transcript:

Capture-recapture Models for Open Populations Abundance, Recruitment and Growth Rate Modeling 6.15 UF-2015

Population Growth Model

Estimated from capture-recapture data = “finite rate of population increase” Closely related to population changes Difference with the obtained from projection matrices –It does not rely on asymptotics (e.g., temporal constancy of vital rates, stable age distribution) –It incorporates movement as well as birth and death

3 approaches Jolly-Seber Superpopulation Reverse-time

Jolly-Seber Model

Concept of the JS model Same kind of modeling as CJS model, but extended to abundance (N) Idea: apply the p estimated based on marked animals to unmarked animals => allows modeling Pr(animal never caught)

Data u m m 0 m u m 0 0 m u m m 0 0 Etc…

Conceptual model

Estimation of Abundance Apply the p estimated based on marked animals to unmarked animals as well Abundance is estimated as: (marked + unmarked caught) / (estimated capture probability)

Estimation of Abundance, N i, and Recruitment From i to i+1, B i n i = number of animals caught/detected at sample period i p estimated from marked animals # of survivors

2 important assumptions In addition to ‘classic’ CJS assumptions, we assume: Same survival for marked and unmarked animals Same detection for marked and unmarked animals

Superpopulation Model (called POPAN in MARK)

Superpopulation Approach B0B0 N 1 = B 0 N 1 –S 1 N 2 = S 1 + B 1 N3N3 N4N4 B1B1 N 2 –S 2 B2B2 N 3 –S 3 B3B3 k=1k=2k=3 K=4

Special Application: Estimation of Birds Passing Through a Migration Stopover Site

Superpopulation and JS models Data: marked animals and unmarked animals detected Key Assumption: Marked and unmarked animals have similar capture probabilities

...a backward process with recruitment and no mortality is statistically equivalent to a forward process with mortality and no recruitment Pollock et al. (1974) Reverse-time Model

Reverse time modeling  i = seniority parameter = probability that an animal in the sampled population at period i was already in the sampled population at i-1

Reverse time modeling

Reverse-time Modeling: Potential Uses

Pradel’s Full Likelihood 2 ways to write expected number of animals alive in 2 successive sample periods:

Pradel’s Full Likelihood Simultaneous forward- and reverse-time modeling (called temporal-symmetry model)

Pradel’s Full Likelihood: 3 Parameterizations  i = seniority parameter i = population growth rate f i = recruitment rate (recruits at i+1 per animal at i) = B i / N i

Relationships Reminder:  i = seniority parameter = probability that an animal in the sampled population at period i was already in the sampled population at i-1 = contribution to pop growth due to survival

Pradel’s Full Likelihood: Potential Uses Direct estimation of and its temporal variance This should correspond more closely than projection matrix ’s to observed population changes because: –It does not rely on asymptotics (e.g., temporal constancy of vital rates, stable age distribution) –It incorporates movement as well as birth and death Can model as a function of covariates and specific vital rates (proper way to do “key factor analysis”)

Remember: Jolly-Seber annual population size (one value/year) Superpopulation N* is # animal ever in population (summed over years…) Reverse-time (gives you estimate of λ or recruitment directly)