| Title: | Two Event Mark-Recapture Experiment |
|---|---|
| Description: | Tools are provided for estimating, testing, and simulating abundance in a two-event (Petersen) mark-recapture experiment. Functions are given to calculate the Petersen, Chapman, and Bailey estimators and associated variances. However, the principal utility is a set of functions to simulate random draws from these estimators, and use these to conduct hypothesis tests and power calculations. Additionally, a set of functions are provided for generating confidence intervals via bootstrapping. Functions are also provided to test abundance estimator consistency under complete or partial stratification, and to calculate stratified or partially stratified estimators. Functions are also provided to calculate recommended sample sizes. Referenced methods can be found in Arnason et al. (1996) <ISSN:0706-6457>, Bailey (1951) <DOI:10.2307/2332575>, Bailey (1952) <DOI:10.2307/1913>, Chapman (1951) NAID:20001644490, Cohen (1988) ISBN:0-12-179060-6, Darroch (1961) <DOI:10.2307/2332748>, and Robson and Regier (1964) <ISSN:1548-8659>. |
| Authors: | Matt Tyers [aut, cre] |
| Maintainer: | Matt Tyers <[email protected]> |
| License: | GPL-2 |
| Version: | 0.4.4 |
| Built: | 2024-11-04 04:19:24 UTC |
| Source: | https://github.com/mbtyers/recapr |
Tools are provided for estimating, testing, and simulating abundance in a two-event (Petersen) mark-recapture experiment. Functions are given to calculate the Petersen, Chapman, and Bailey estimators and associated variances. However, the principal utility is a set of functions to simulate random draws from these estimators, and use these to conduct hypothesis tests and power calculations. Additionally, a set of functions are provided for generating confidence intervals via bootstrapping. Functions are also provided to test abundance estimator consistency under complete or partial stratification, and to calculate stratified or Darroch estimators. Functions are also provided to calculate recommended sample sizes.
| Package: | recapr |
| Type: | Package |
| Version: | 0.4.2 |
| Date: | 2021-09-02 |
| License: | GPL-2 |
Matt Tyers
Maintainer: Matt Tyers <[email protected]>
Calculates approximate confidence intervals(s) for the Bailey estimator, using bootstrapping, the Normal approximation, or both.
The bootstrap interval is created by resampling the data in the second sampling event, with replacement; that is, drawing bootstrap values of m2 from a binomial distribution with probability parameter m2/n2. This technique has been shown to better approximate the distribution of the abundance estimator. Resulting CI endpoints both have larger values than those calculated from a normal distribution, but this better captures the positive skew of the estimator. Coverage has been investigated by means of simulation under numerous scenarios and has consistently outperformed the normal interval. The user is welcomed to investigate the coverage under relevant scenarios.
ciBailey(n1, n2, m2, conf = 0.95, method = "both", bootreps = 10000)ciBailey(n1, n2, m2, conf = 0.95, method = "both", bootreps = 10000)
n1 |
Number of individuals captured and marked in the first sample |
n2 |
Number of individuals captured in the second sample |
m2 |
Number of marked individuals recaptured in the second sample |
conf |
The confidence level of the desired intervals. Defaults to 0.95. |
method |
Which method of confidence interval to return. Allowed values
are |
bootreps |
Number of bootstrap replicates to use. Defaults to 10000. |
A list with the abundance estimate and confidence interval bounds for the normal-distribution and/or bootstrap confidence intervals.
Any Petersen-type estimator (such as this) depends on a set of assumptions:
The population is closed; that is, that there are no births, deaths, immigration, or emigration between sampling events
All individuals have the same probability of capture in one of the two events, or complete mixing occurs between events
Marking in the first event does not affect probability of recapture in the second event
Individuals do not lose marks between events
All marks will be reported in the second event
Matt Tyers
NBailey, vBailey, seBailey, rBailey, pBailey, powBailey
ciBailey(n1=100, n2=100, m2=20)ciBailey(n1=100, n2=100, m2=20)
Calculates approximate confidence intervals(s) for the Chapman estimator, using bootstrapping, the Normal approximation, or both.
The bootstrap interval is created by resampling the data in the second sampling event, with replacement; that is, drawing bootstrap values of m2 from a binomial distribution with probability parameter m2/n2. This technique has been shown to better approximate the distribution of the abundance estimator. Resulting CI endpoints both have larger values than those calculated from a normal distribution, but this better captures the positive skew of the estimator. Coverage has been investigated by means of simulation under numerous scenarios and has consistently outperformed the normal interval. The user is welcomed to investigate the coverage under relevant scenarios.
ciChapman(n1, n2, m2, conf = 0.95, method = "both", bootreps = 10000)ciChapman(n1, n2, m2, conf = 0.95, method = "both", bootreps = 10000)
n1 |
Number of individuals captured and marked in the first sample |
n2 |
Number of individuals captured in the second sample |
m2 |
Number of marked individuals recaptured in the second sample |
conf |
The confidence level of the desired intervals. Defaults to 0.95. |
method |
Which method of confidence interval to return. Allowed values
are |
bootreps |
Number of bootstrap replicates to use. Defaults to 10000. |
A list with the abundance estimate and confidence interval bounds for the normal-distribution and/or bootstrap confidence intervals.
Any Petersen-type estimator (such as this) depends on a set of assumptions:
The population is closed; that is, that there are no births, deaths, immigration, or emigration between sampling events
All individuals have the same probability of capture in one of the two events, or complete mixing occurs between events
Marking in the first event does not affect probability of recapture in the second event
Individuals do not lose marks between events
All marks will be reported in the second event
Matt Tyers
NChapman, vChapman, seChapman, rChapman, pChapman, powChapman
ciChapman(n1=100, n2=100, m2=20)ciChapman(n1=100, n2=100, m2=20)
Calculates approximate confidence intervals(s) for the Petersen estimator, using bootstrapping, the Normal approximation, or both.
The bootstrap interval is created by resampling the data in the second sampling event, with replacement; that is, drawing bootstrap values of m2 from a binomial distribution with probability parameter m2/n2. This technique has been shown to better approximate the distribution of the abundance estimator. Resulting CI endpoints both have larger values than those calculated from a normal distribution, but this better captures the positive skew of the estimator. Coverage has been investigated by means of simulation under numerous scenarios and has consistently outperformed the normal interval. The user is welcomed to investigate the coverage under relevant scenarios.
ciPetersen( n1, n2, m2, conf = 0.95, method = "both", bootreps = 10000, useChapvar = FALSE )ciPetersen( n1, n2, m2, conf = 0.95, method = "both", bootreps = 10000, useChapvar = FALSE )
n1 |
Number of individuals captured and marked in the first sample |
n2 |
Number of individuals captured in the second sample |
m2 |
Number of marked individuals recaptured in the second sample |
conf |
The confidence level of the desired intervals. Defaults to 0.95. |
method |
Which method of confidence interval to return. Allowed values
are |
bootreps |
Number of bootstrap replicates to use. Defaults to 10000. |
useChapvar |
Whether to use the Chapman estimator variance instead of
the Petersen estimator variance for the normal-distribution interval.
Defaults to |
A list with the abundance estimate and confidence interval bounds for the normal-distribution and/or bootstrap confidence intervals.
Any Petersen-type estimator (such as this) depends on a set of assumptions:
The population is closed; that is, that there are no births, deaths, immigration, or emigration between sampling events
All individuals have the same probability of capture in one of the two events, or complete mixing occurs between events
Marking in the first event does not affect probability of recapture in the second event
Individuals do not lose marks between events
All marks will be reported in the second event
Matt Tyers
NPetersen, vPetersen, sePetersen, rPetersen, pPetersen, powPetersen
ciPetersen(n1=100, n2=100, m2=20)ciPetersen(n1=100, n2=100, m2=20)
Calculates approximate confidence intervals(s) for the Stratified estimator, using bootstrapping, the Normal approximation, or both.
The bootstrap interval is created by resampling the data in the second sampling event, with replacement for each stratum; that is, drawing bootstrap values of m2 from a binomial distribution with probability parameter m2/n2.
cistrat( n1, n2, m2, conf = 0.95, method = "both", bootreps = 10000, estimator = "Chapman", useChapvar = FALSE )cistrat( n1, n2, m2, conf = 0.95, method = "both", bootreps = 10000, estimator = "Chapman", useChapvar = FALSE )
n1 |
Number of individuals captured and marked in the first sample |
n2 |
Number of individuals captured in the second sample |
m2 |
Number of marked individuals recaptured in the second sample |
conf |
The confidence level of the desired intervals. Defaults to 0.95. |
method |
Which method of confidence interval to return. Allowed values
are |
bootreps |
Number of bootstrap replicates to use. Defaults to 10000. |
estimator |
The type of estimator to use. Allowed values are
|
useChapvar |
Whether to use the Chapman estimator variance instead of
the Petersen estimator variance for the normal-distribution interval, if
|
A list with the abundance estimate and confidence interval bounds for the normal-distribution and/or bootstrap confidence intervals.
Both the bootstrap and the normal approximation intervals make the naive assumption of independence between strata, which may not be the case. The user therefore cautioned, and is encouraged to investigate the coverage under relevant scenarios.
Matt Tyers
\linkstrattest, Nstrat, rstrat, vstrat, sestrat, NChapman, NPetersen, NBailey
cistrat(n1=c(100,200), n2=c(100,500), m2=c(10,10))cistrat(n1=c(100,200), n2=c(100,500), m2=c(10,10))
Conducts three chi-squared tests for the consistency of the Petersen-type abundance estimator. These tests explore evidence against the second traditional assumption of the Petersen mark-recapture experiment: that equal capture probabilities exist in either the first or second sampling event, or that complete mixing occurs between events.
Typically, if any of these test p-values is greater than the significance level, use of a Petersen-type estimator is considered justified. If all three tests give p-values below the significance level and no movement occurs between strata (and strata are the same between events), a stratified estimator may be used. If all three tests give p-values below the significance level and some movement between strata occurs, a partially stratified (Darroch-type) estimator must be used, such as NDarroch.
This function assumes stratification in both sampling events, and in different ways (by time, area, etc.) If stratification was the same in both events such that individuals could not move from one strata to another (such as by size or gender), use of strattest is recommended.
consistencytest( n1, n2, m2strata1 = NULL, m2strata2 = NULL, stratamat = NULL, ... )consistencytest( n1, n2, m2strata1 = NULL, m2strata2 = NULL, stratamat = NULL, ... )
n1 |
A vector of the total sample sizes in the first event, by
strata. For example, setting |
n2 |
A vector of the total sample sizes in the second event, by strata. |
m2strata1 |
A vector of the first-event stratum membership of each
recaptured individual. Only values |
m2strata2 |
A vector of the second-event stratum membership of each
recaptured individual. Only values |
stratamat |
A matrix specifying the number of recaptures in each
combination of event 1 and event 2 strata, with rows corresponding to event
1 strata and columns corresponding to event 2 strata. May be used instead
of |
... |
Additional arguments for chisq.test |
A list of class "recapr_consistencytest" with the following components:
test1_tab The contingency table used for the first test
test1_Xsqd The chi-squared test statistic in the first test
test1_df The associated degrees of freedom in the first test
test1_pval The p-value returned from the first test
test2_tab The contingency table used for the second test
test2_Xsqd The chi-squared test statistic in the second test
test2_df The associated degrees of freedom in the second test
test2_pval The p-value returned from the second test
test3_tab The contingency table used for the third test
test3_Xsqd The chi-squared test statistic in the third test
test3_df The associated degrees of freedom in the third test
test3_pval The p-value returned from the third test
Naming conventions for the second and third tests are taken from SPAS (see reference)
Any Petersen-type estimator (such as this) depends on a set of assumptions:
The population is closed; that is, that there are no births, deaths, immigration, or emigration between sampling events
All individuals have the same probability of capture in one of the two events, or complete mixing occurs between events
Marking in the first event does not affect probability of recapture in the second event
Individuals do not lose marks between events
All marks will be reported in the second event
Matt Tyers
Stratified Population Analysis System (Arnason, A.N., C.W. Kirby, C.J. Schwarz and J.R. Irvine. 1996. Computer Analysis of Data from Stratified Mark-Recovery Experiments for Estimation of Salmon Escapements and Other Populations, Canadian Technical Report of Fisheries and Aquatic Sciences 2106).
consistencytest(n1=c(15,12,6), n2=c(12,9,10,8), m2strata1=c(1,1,1,1,1,2,2,2,3,3), m2strata2=c(1,1,3,3,4,1,2,4,1,3), simulate.p.value=TRUE) mat <- matrix(c(30,15,1,0,22,15), nrow=2, ncol=3, byrow=TRUE) consistencytest(n1=c(284,199), n2=c(347,3616,1489), stratamat=mat)consistencytest(n1=c(15,12,6), n2=c(12,9,10,8), m2strata1=c(1,1,1,1,1,2,2,2,3,3), m2strata2=c(1,1,3,3,4,1,2,4,1,3), simulate.p.value=TRUE) mat <- matrix(c(30,15,1,0,22,15), nrow=2, ncol=3, byrow=TRUE) consistencytest(n1=c(284,199), n2=c(347,3616,1489), stratamat=mat)
Calculates minimum sample size for one sampling event in a Petersen mark-recapture experiment, given the sample size in the other event and an best guess at true abundance.
n2RR( N, n1, conf = c(0.99, 0.95, 0.9, 0.85, 0.8, 0.75), acc = c(0.5, 0.25, 0.2, 0.15, 0.1, 0.05, 0.01) )n2RR( N, n1, conf = c(0.99, 0.95, 0.9, 0.85, 0.8, 0.75), acc = c(0.5, 0.25, 0.2, 0.15, 0.1, 0.05, 0.01) )
N |
The best guess at true abundance |
n1 |
The size of the first (or second) sampling event |
conf |
A vector of the desired levels of confidence to investigate.
Allowed values are any of |
acc |
A vector of the desired levels of relative accuracy to
investigate. Allowed values are any of
|
A list of minimum sample sizes. Each list element corresponds to a unique level of confidence, and is defined as a data frame with each row corresponding to a unique value of relative accuracy. Two minimum sample sizes are given: one calculated from the sample size provided for the other event, and the other calculated under n1=n2, the most efficient scenario.
Any Petersen-type estimator (such as this) depends on a set of assumptions:
The population is closed; that is, that there are no births, deaths, immigration, or emigration between sampling events
All individuals have the same probability of capture in one of the two events, or complete mixing occurs between events
Marking in the first event does not affect probability of recapture in the second event
Individuals do not lose marks between events
All marks will be reported in the second event
It is possible that the sample size - accuracy relationship will be better illustrated using plotn2sim.
Matt Tyers
Robson, D. S., and H. A. Regier. 1964. Sample size in Petersen mark-recapture experiments. Transactions of the American FisheriesSociety 93:215-226.
n2RR(N=1000, n1=100)n2RR(N=1000, n1=100)
Calculates the value of the Bailey estimator for abundance in a mark-recapture experiment, with given values of sample sizes and number of recaptures. The Bailey estimator assumes a binomial probability model in the second sampling event (i.e. sampling with replacement), rather than the hypergeometric model assumed by the Petersen and Chapman estimators.
NBailey(n1, n2, m2)NBailey(n1, n2, m2)
n1 |
Number of individuals captured and marked in the first sample. This may be a single number or vector of values. |
n2 |
Number of individuals captured in the second sample. This may be a single number or vector of values. |
m2 |
Number of marked individuals recaptured in the second sample. This may be a single number or vector of values. |
The value of the Bailey estimator, calculated as n1*(n2+1)/(m2+1)
Any Petersen-type estimator (such as this) depends on a set of assumptions:
The population is closed; that is, that there are no births, deaths, immigration, or emigration between sampling events
All individuals have the same probability of capture in one of the two events, or complete mixing occurs between events
Marking in the first event does not affect probability of recapture in the second event
Individuals do not lose marks between events
All marks will be reported in the second event
Matt Tyers
Bailey, N.T.J. (1951). On estimating the size of mobile populations from capture-recapture data. Biometrika 38, 293-306.
Bailey, N.T.J. (1952). Improvements in the interpretation of recapture data. J. Animal Ecol. 21, 120-7.
NPetersen, NChapman, vBailey, seBailey, rBailey, pBailey, powBailey, ciBailey
NBailey(n1=100, n2=100, m2=20)NBailey(n1=100, n2=100, m2=20)
Calculates the value of the Chapman estimator for abundance in a mark-recapture experiment, with given values of sample sizes and number of recaptures. The Chapman estimator (Chapman modification of the Petersen estimator) typically outperforms the Petersen estimator, even though the Peterson estimator is the MLE.
NChapman(n1, n2, m2)NChapman(n1, n2, m2)
n1 |
Number of individuals captured and marked in the first sample. This may be a single number or vector of values. |
n2 |
Number of individuals captured in the second sample. This may be a single number or vector of values. |
m2 |
Number of marked individuals recaptured in the second sample. This may be a single number or vector of values. |
The value of the Chapman estimator, calculated as (n1+1)*(n2+1)/(m2+1) - 1
Any Petersen-type estimator (such as this) depends on a set of assumptions:
The population is closed; that is, that there are no births, deaths, immigration, or emigration between sampling events
All individuals have the same probability of capture in one of the two events, or complete mixing occurs between events
Marking in the first event does not affect probability of recapture in the second event
Individuals do not lose marks between events
All marks will be reported in the second event
Matt Tyers
Chapman, D.G. (1951). Some properties of the hypergeometric distribution with applications to zoological censuses. Univ. Calif. Public. Stat. 1, 131-60.
NPetersen, NBailey, vChapman, seChapman, rChapman, pChapman, powChapman, ciChapman
NChapman(n1=100, n2=100, m2=20)NChapman(n1=100, n2=100, m2=20)
Computes abundance estimates and associated variance in the event of spatial or temporal stratification, or in any stratification in which individuals can move between strata. Marking (event 1) and recapture (event 2) strata do not need to be the same.
Inputs are vectors of total event 1 and 2 sample sizes, and either vectors of event 1 and 2 strata corresponding to each recaptured individual, or a matrix of total number of recaptures for each combination of event 1 and event 2 strata.
Implementation is currently using Darroch's method, and will only accept non-singular input matrices.
NDarroch( n1counts, n2counts, m2strata1 = NULL, m2strata2 = NULL, stratamat = NULL )NDarroch( n1counts, n2counts, m2strata1 = NULL, m2strata2 = NULL, stratamat = NULL )
n1counts |
A vector of the total sample sizes in the first event, by
strata. For example, setting |
n2counts |
A vector of the total sample sizes in the second event, by strata. |
m2strata1 |
A vector of the first-event stratum membership of each
recaptured individual. Only values |
m2strata2 |
A vector of the second-event stratum membership of each
recaptured individual. Only values |
stratamat |
A matrix specifying the number of recaptures in each
combination of event 1 and event 2 strata, with rows corresponding to event
1 strata and columns corresponding to event 2 strata. May be used instead
of |
A numeric list, giving the strata matrix if originally given in vector form, abundance estimates and standard errors by event 1 and event 2 strata, and the total abundance estimate and standard error.
Matt Tyers
Darroch, J.N. (1961). The two-sample capture-recapture census when tagging and sampling are stratified. Biometrika 48, 241-60.
mat <- matrix(c(59,30,1,45,280,38,0,42,25), nrow=3, ncol=3, byrow=TRUE) NDarroch(n1counts=c(484,1468,399), n2counts=c(847,6616,2489), stratamat=mat)mat <- matrix(c(59,30,1,45,280,38,0,42,25), nrow=3, ncol=3, byrow=TRUE) NDarroch(n1counts=c(484,1468,399), n2counts=c(847,6616,2489), stratamat=mat)
Calculates the value of the Petersen estimator for abundance in a mark-recapture experiment, with given values of sample sizes and number of recaptures. The Petersen estimator is the MLE, but is typically outperformed by the Chapman estimator.
NPetersen(n1, n2, m2)NPetersen(n1, n2, m2)
n1 |
Number of individuals captured and marked in the first sample. This may be a single number or vector of values. |
n2 |
Number of individuals captured in the second sample. This may be a single number or vector of values. |
m2 |
Number of marked individuals recaptured in the second sample. This may be a single number or vector of values. |
The value of the Petersen estimator, calculated as n1*n2/m2
Any Petersen-type estimator (such as this) depends on a set of assumptions:
The population is closed; that is, that there are no births, deaths, immigration, or emigration between sampling events
All individuals have the same probability of capture in one of the two events, or complete mixing occurs between events
Marking in the first event does not affect probability of recapture in the second event
Individuals do not lose marks between events
All marks will be reported in the second event
Matt Tyers
NChapman, NBailey, vPetersen, sePetersen, rPetersen, pPetersen, powPetersen, ciPetersen
NPetersen(n1=100, n2=100, m2=20)NPetersen(n1=100, n2=100, m2=20)
Calculates the value of the stratified estimator for abundance in a mark-recapture experiment, from vectors of sample sizes and number of recaptures, with each element corresponding to each sampling stratum.
Nstrat(n1, n2, m2, estimator = "Chapman")Nstrat(n1, n2, m2, estimator = "Chapman")
n1 |
Vector of individuals captured and marked in the first sample, from each stratum |
n2 |
Vector of individuals captured and marked in the second sample, from each stratum |
m2 |
Vector of marked individuals recaptured in the second sample, from each stratum |
estimator |
The type of estimator to use. Allowed values are
|
The value of the stratified estimator
It is possible that even the stratified estimate may be biased if capture probabilities differ greatly between strata. However, the bias in the stratified estimator will be much less than an estimator calculated without stratification.
Matt Tyers
strattest, rstrat, vstrat, sestrat, cistrat, NChapman, NPetersen, NBailey
Nstrat(n1=c(100,200), n2=c(100,500), m2=c(10,10))Nstrat(n1=c(100,200), n2=c(100,500), m2=c(10,10))
Approximates a p-value for a hypothesis test of the Bailey estimator by means of many simulated draws from the null distribution, conditioned on sample sizes.
pBailey( estN = NULL, nullN, n1, n2, m2 = NULL, nsim = 1e+05, alternative = "less" )pBailey( estN = NULL, nullN, n1, n2, m2 = NULL, nsim = 1e+05, alternative = "less" )
estN |
The estimated abundance. Either this or the number of recaptures
( |
nullN |
The abundance given by the null hypothesis |
n1 |
Number of individuals captured and marked in the first sample |
n2 |
Number of individuals captured in the second sample |
m2 |
Number of recaptures. Either this or the estimated abundance
( |
nsim |
Number of simulated values to draw. Defaults to 100000. |
alternative |
Direction of the alternative hypothesis. Allowed values
are |
An approximate p-value for the specified hypothesis test. If
m2 is specified rather than estN, output will be returned as
a list with two elements: the estimated abundance and p-value.
Any Petersen-type estimator (such as this) depends on a set of assumptions:
The population is closed; that is, that there are no births, deaths, immigration, or emigration between sampling events
All individuals have the same probability of capture in one of the two events, or complete mixing occurs between events
Marking in the first event does not affect probability of recapture in the second event
Individuals do not lose marks between events
All marks will be reported in the second event
Matt Tyers
NBailey, vBailey, seBailey, rBailey, powBailey, ciBailey
output <- pBailey(nullN=500, n1=100, n2=100, m2=28) output plotdiscdensity(rBailey(length=100000, N=500, n1=100, n2=100)) abline(v=output$estN, lwd=2, col=2) abline(v=500, lwd=2, lty=2) output <- pBailey(nullN=500, n1=100, n2=100, m2=28, alternative="2-sided") output plotdiscdensity(rBailey(length=100000, N=500, n1=100, n2=100)) twosided <- 500 + c(-1,1)*abs(500-output$estN) abline(v=twosided, lwd=2, col=2) abline(v=500, lwd=2, lty=2)output <- pBailey(nullN=500, n1=100, n2=100, m2=28) output plotdiscdensity(rBailey(length=100000, N=500, n1=100, n2=100)) abline(v=output$estN, lwd=2, col=2) abline(v=500, lwd=2, lty=2) output <- pBailey(nullN=500, n1=100, n2=100, m2=28, alternative="2-sided") output plotdiscdensity(rBailey(length=100000, N=500, n1=100, n2=100)) twosided <- 500 + c(-1,1)*abs(500-output$estN) abline(v=twosided, lwd=2, col=2) abline(v=500, lwd=2, lty=2)
Approximates a p-value for a hypothesis test of the Chapman estimator by means of many simulated draws from the null distribution, conditioned on sample sizes.
pChapman( estN = NULL, nullN, n1, n2, m2 = NULL, nsim = 1e+05, alternative = "less" )pChapman( estN = NULL, nullN, n1, n2, m2 = NULL, nsim = 1e+05, alternative = "less" )
estN |
The estimated abundance. Either this or the number of recaptures
( |
nullN |
The abundance given by the null hypothesis |
n1 |
Number of individuals captured and marked in the first sample |
n2 |
Number of individuals captured in the second sample |
m2 |
Number of recaptures. Either this or the estimated abundance
( |
nsim |
Number of simulated values to draw. Defaults to 100000. |
alternative |
Direction of the alternative hypothesis. Allowed values
are |
An approximate p-value for the specified hypothesis test. If
m2 is specified rather than estN, output will be returned as
a list with two elements: the estimated abundance and p-value.
Any Petersen-type estimator (such as this) depends on a set of assumptions:
The population is closed; that is, that there are no births, deaths, immigration, or emigration between sampling events
All individuals have the same probability of capture in one of the two events, or complete mixing occurs between events
Marking in the first event does not affect probability of recapture in the second event
Individuals do not lose marks between events
All marks will be reported in the second event
Matt Tyers
NChapman, vChapman, seChapman, rChapman, powChapman, ciChapman
output <- pChapman(nullN=500, n1=100, n2=100, m2=28) output plotdiscdensity(rChapman(length=100000, N=500, n1=100, n2=100)) abline(v=output$estN, lwd=2, col=2) abline(v=500, lwd=2, lty=2) output <- pChapman(nullN=500, n1=100, n2=100, m2=28, alternative="2-sided") output plotdiscdensity(rChapman(length=100000, N=500, n1=100, n2=100)) twosided <- 500 + c(-1,1)*abs(500-output$estN) abline(v=twosided, lwd=2, col=2) abline(v=500, lwd=2, lty=2)output <- pChapman(nullN=500, n1=100, n2=100, m2=28) output plotdiscdensity(rChapman(length=100000, N=500, n1=100, n2=100)) abline(v=output$estN, lwd=2, col=2) abline(v=500, lwd=2, lty=2) output <- pChapman(nullN=500, n1=100, n2=100, m2=28, alternative="2-sided") output plotdiscdensity(rChapman(length=100000, N=500, n1=100, n2=100)) twosided <- 500 + c(-1,1)*abs(500-output$estN) abline(v=twosided, lwd=2, col=2) abline(v=500, lwd=2, lty=2)
Plots the empirical density of a vector of discrete values, approximating the probability mass function (pmf). This can be considered a more appropriate alternative to plot(density(x)) in the case of a vector with a discrete (non-continuous) support, such as that calculated by an abundance estimator.
plotdiscdensity(x, xlab = "value", ylab = "density", ...)plotdiscdensity(x, xlab = "value", ylab = "density", ...)
x |
The vector of values to plot |
xlab |
The X-axis label for plotting |
ylab |
The Y-axis label for plotting |
... |
Additional plotting arguments |
Matt Tyers
draws <- rChapman(length=100000, N=500, n1=100, n2=100) plotdiscdensity(draws) #plots the density of a vector of discrete valuesdraws <- rChapman(length=100000, N=500, n1=100, n2=100) plotdiscdensity(draws) #plots the density of a vector of discrete values
Produces a plot of the simulated relative accuracy of a mark-recapture abundance estimator for various sample sizes in both events. This may be a useful exploration, but it is possible that plotn2sim may be more informative.
plotn1n2simmatrix( N, conf = 0.95, nrange = NULL, nstep = NULL, estimator = "Chapman", nsim = 10000, ... )plotn1n2simmatrix( N, conf = 0.95, nrange = NULL, nstep = NULL, estimator = "Chapman", nsim = 10000, ... )
N |
The best guess at true abundance |
conf |
The desired level of confidence to investigate. Defaults to 0.95. |
nrange |
A two-element vector describing the range of sample sizes to
investigate. If the default ( |
nstep |
The step size between sample sizes to investigate. If the
default ( |
estimator |
The abundance estimator to use. Allowed values are
|
nsim |
The number of replicates. Defaults to 10000. |
... |
Additional plotting parameters |
Any Petersen-type estimator (such as this) depends on a set of assumptions:
The population is closed; that is, that there are no births, deaths, immigration, or emigration between sampling events
All individuals have the same probability of capture in one of the two events, or complete mixing occurs between events
Marking in the first event does not affect probability of recapture in the second event
Individuals do not lose marks between events
All marks will be reported in the second event
Matt Tyers
plotn1n2simmatrix(N=10000, nsim=2000)plotn1n2simmatrix(N=10000, nsim=2000)
Produces a plot of the simulated relative accuracy of a mark-recapture abundance estimator for various sample sizes. This may be a better representation of the sample size - accuracy relationship than that provided by n2RR.
plotn2sim( N, n1, conf = c(0.99, 0.95, 0.85, 0.8, 0.75), n2range = NULL, n2step = NULL, estimator = "Chapman", nsim = 10000, accrange = 1, ... )plotn2sim( N, n1, conf = c(0.99, 0.95, 0.85, 0.8, 0.75), n2range = NULL, n2step = NULL, estimator = "Chapman", nsim = 10000, accrange = 1, ... )
N |
The best guess at true abundance |
n1 |
The size of the first (or second) sampling event |
conf |
A vector of the desired levels of confidence to investigate.
Allowed values are any of |
n2range |
A two-element vector describing the range of sample sizes to
investigate. If the default ( |
n2step |
The step size between sample sizes to investigate. If the
default ( |
estimator |
The abundance estimator to use. Allowed values are
|
nsim |
The number of replicates. Defaults to 10000. |
accrange |
The maximum level of relative accuracy for plotting. Defaults to 1. |
... |
Additional plotting parameters |
Any Petersen-type estimator (such as this) depends on a set of assumptions:
The population is closed; that is, that there are no births, deaths, immigration, or emigration between sampling events
All individuals have the same probability of capture in one of the two events, or complete mixing occurs between events
Marking in the first event does not affect probability of recapture in the second event
Individuals do not lose marks between events
All marks will be reported in the second event
Matt Tyers
plotn2sim(N=1000, n1=100)plotn2sim(N=1000, n1=100)
Approximates the power of a hypothesis test of the Bailey estimator by means of many simulated draws from a specified alternative distribution, conditioned on sample sizes.
powBailey( nullN, trueN, n1, n2, alpha = 0.05, nsim = 10000, alternative = "less" )powBailey( nullN, trueN, n1, n2, alpha = 0.05, nsim = 10000, alternative = "less" )
nullN |
The abundance given by the null hypothesis |
trueN |
The assumed abundance for the power calculation |
n1 |
Number of individuals captured and marked in the first sample |
n2 |
Number of individuals captured in the second sample |
alpha |
The alpha level for the test |
nsim |
Number of simulated values to draw. Defaults to 10000. |
alternative |
Direction of the alternative hypothesis. Allowed values
are |
The approximate power of the specified hypothesis test, for the specified alternative value.
Any Petersen-type estimator (such as this) depends on a set of assumptions:
The population is closed; that is, that there are no births, deaths, immigration, or emigration between sampling events
All individuals have the same probability of capture in one of the two events, or complete mixing occurs between events
Marking in the first event does not affect probability of recapture in the second event
Individuals do not lose marks between events
All marks will be reported in the second event
Matt Tyers
NBailey, vBailey, seBailey, rBailey, pBailey, ciBailey
powBailey(nullN=500, trueN=400, n1=100, n2=100, nsim=1000) Ntotry <- seq(from=250, to=450, by=25) pows <- sapply(Ntotry, function(x) powBailey(nullN=500, trueN=x, n1=100, n2=100, nsim=1000)) plot(Ntotry, pows)powBailey(nullN=500, trueN=400, n1=100, n2=100, nsim=1000) Ntotry <- seq(from=250, to=450, by=25) pows <- sapply(Ntotry, function(x) powBailey(nullN=500, trueN=x, n1=100, n2=100, nsim=1000)) plot(Ntotry, pows)
Approximates the power of a hypothesis test of the Chapman estimator by means of many simulated draws from a specified alternative distribution, conditioned on sample sizes.
powChapman( nullN, trueN, n1, n2, alpha = 0.05, nsim = 10000, alternative = "less" )powChapman( nullN, trueN, n1, n2, alpha = 0.05, nsim = 10000, alternative = "less" )
nullN |
The abundance given by the null hypothesis |
trueN |
The assumed abundance for the power calculation |
n1 |
Number of individuals captured and marked in the first sample |
n2 |
Number of individuals captured in the second sample |
alpha |
The alpha level for the test |
nsim |
Number of simulated values to draw. Defaults to 10000. |
alternative |
Direction of the alternative hypothesis. Allowed values
are |
The approximate power of the specified hypothesis test, for the specified alternative value.
Any Petersen-type estimator (such as this) depends on a set of assumptions:
The population is closed; that is, that there are no births, deaths, immigration, or emigration between sampling events
All individuals have the same probability of capture in one of the two events, or complete mixing occurs between events
Marking in the first event does not affect probability of recapture in the second event
Individuals do not lose marks between events
All marks will be reported in the second event
Matt Tyers
NChapman, vChapman, seChapman, rChapman, pChapman, ciChapman
powChapman(nullN=500, trueN=400, n1=100, n2=100, nsim=1000) Ntotry <- seq(from=250, to=450, by=25) pows <- sapply(Ntotry, function(x) powChapman(nullN=500, trueN=x, n1=100, n2=100, nsim=1000)) plot(Ntotry, pows)powChapman(nullN=500, trueN=400, n1=100, n2=100, nsim=1000) Ntotry <- seq(from=250, to=450, by=25) pows <- sapply(Ntotry, function(x) powChapman(nullN=500, trueN=x, n1=100, n2=100, nsim=1000)) plot(Ntotry, pows)
Conducts power calculations of the chi-squared tests for the consistency of the Petersen-type abundance estimator, in a partial stratification setting, such as by time or geographic area. In the case of partial stratification, individuals may move from one stratum to another between the first and second sampling events, and strata do not need to be the same between events.
powconsistencytest(n1, n2, pmat, alpha = 0.05, sim = TRUE, nsim = 10000)powconsistencytest(n1, n2, pmat, alpha = 0.05, sim = TRUE, nsim = 10000)
n1 |
Vector of anticipated n1 counts (sample size in the first event), each element corresponding to one stratum. |
n2 |
Vector of anticipated n2 counts (sample size in the second event), each element corresponding to one stratum. |
pmat |
Matrix of assumed movement probabilities between strata, with rows corresponding to first-event strata and columns corresponding to second-event strata, and an additional column corresponding to the probability of NOT being recaptured in the second event. Values will be standardized by row, that is, by first-event strata. See note on usage below. |
alpha |
Significance level for testing. Defaults to |
sim |
Whether to conduct power calculation by simulation as well as
Cohen's method. Defaults to |
nsim |
Number of simulations if |
An object of class "recapr_consistencypow" with the following
components:
pwr1_c Power of the first test,
according to Cohen's method
pwr1_sim Power of the first
test, from simulation
ntest1 The sample size used for the
first test
p0test1 The null-hypothesis probabilities for
the first test
p1test1 The alt-hypothesis probabilities for
the first test
pwr2_c Power of the second test, according
to Cohen's method
pwr2_sim Power of the second test, from
simulation
ntest2 The sample size used for the second test
p0test2 The null-hypothesis probabilities for the second
test
p1test2 The alt-hypothesis probabilities for the
second test
pwr3_c Power of the third test, according to
Cohen's method
pwr3_sim Power of the third test, from
simulation
ntest3 The sample size used for the third test
p0test3 The null-hypothesis probabilities for the third
test
p1test3 The alt-hypothesis probabilities for the third
test
alpha The significance level used
The movement probability matrix specified in pmat is considered
conditional on each row, that is, first-event strata, with columns
corresponding to second-event strata and the final column specifying the
probability of not being recaptured in the second event. Values do not
need to sum to one for each row, but will be standardized by the function
to sum to one.
A pmat with a first row equal to (0.05, 0.1, 0.15, 0.7) would
imply a 5 percent chance that individuals captured in the first-event
strata 1 will be recaptured in second-event strata 1, and a 70 percent
chance that individuals captured in the first-event strata 1 will not be
recaptured in event 2.
Because of the row-wise scaling, specifying a row equal to (0.05,
0.1, 0.15, 0.7) would be equivalent to that row having values (1, 2, 3, 14).
Matt Tyers
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale,NJ: Lawrence Erlbaum.
Code adapted from the 'pwr' package: Stephane Champely (2015). pwr: Basic Functions for Power Analysis. R package version 1.1-3. https://CRAN.R-project.org/package=pwr
mat <- matrix(c(4,3,2,1,10,3,4,3,2,10,2,3,4,3,10,1,2,3,4,10), nrow=4, ncol=5, byrow=TRUE) powconsistencytest(n1=c(50,50,50,50), n2=c(50,50,50,50), pmat=mat) mat <- matrix(c(4,3,2,1,10,4,3,2,1,10,4,3,2,1,10,4,3,2,1,10), nrow=4, ncol=5, byrow=TRUE) powconsistencytest(n1=c(50,50,50,50), n2=c(50,50,50,50), pmat=mat) mat <- matrix(c(1,1,1,1,10,2,2,2,2,10,3,3,3,3,10,4,4,4,4,10), nrow=4, ncol=5, byrow=TRUE) powconsistencytest(n1=c(50,50,50,50), n2=c(50,50,50,50), pmat=mat) mat <- matrix(c(1,1,1,1,10,1,1,1,1,10,1,1,1,1,10,1,1,1,1,10), nrow=4, ncol=5, byrow=TRUE) powconsistencytest(n1=c(50,50,50,50), n2=c(20,30,40,50), pmat=mat) mat <- matrix(c(1,1,1,1,5,1,1,1,1,8,1,1,1,1,10,1,1,1,1,15), nrow=4, ncol=5, byrow=TRUE) powconsistencytest(n1=c(50,50,50,50), n2=c(50,50,50,50), pmat=mat)mat <- matrix(c(4,3,2,1,10,3,4,3,2,10,2,3,4,3,10,1,2,3,4,10), nrow=4, ncol=5, byrow=TRUE) powconsistencytest(n1=c(50,50,50,50), n2=c(50,50,50,50), pmat=mat) mat <- matrix(c(4,3,2,1,10,4,3,2,1,10,4,3,2,1,10,4,3,2,1,10), nrow=4, ncol=5, byrow=TRUE) powconsistencytest(n1=c(50,50,50,50), n2=c(50,50,50,50), pmat=mat) mat <- matrix(c(1,1,1,1,10,2,2,2,2,10,3,3,3,3,10,4,4,4,4,10), nrow=4, ncol=5, byrow=TRUE) powconsistencytest(n1=c(50,50,50,50), n2=c(50,50,50,50), pmat=mat) mat <- matrix(c(1,1,1,1,10,1,1,1,1,10,1,1,1,1,10,1,1,1,1,10), nrow=4, ncol=5, byrow=TRUE) powconsistencytest(n1=c(50,50,50,50), n2=c(20,30,40,50), pmat=mat) mat <- matrix(c(1,1,1,1,5,1,1,1,1,8,1,1,1,1,10,1,1,1,1,15), nrow=4, ncol=5, byrow=TRUE) powconsistencytest(n1=c(50,50,50,50), n2=c(50,50,50,50), pmat=mat)
Approximates the power of a hypothesis test of the Petersen estimator by means of many simulated draws from a specified alternative distribution, conditioned on sample sizes.
powPetersen( nullN, trueN, n1, n2, alpha = 0.05, nsim = 10000, alternative = "less" )powPetersen( nullN, trueN, n1, n2, alpha = 0.05, nsim = 10000, alternative = "less" )
nullN |
The abundance given by the null hypothesis |
trueN |
The assumed abundance for the power calculation |
n1 |
Number of individuals captured and marked in the first sample |
n2 |
Number of individuals captured in the second sample |
alpha |
The alpha level for the test |
nsim |
Number of simulated values to draw. Defaults to 10000. |
alternative |
Direction of the alternative hypothesis. Allowed values
are |
The approximate power of the specified hypothesis test, for the specified alternative value.
Any Petersen-type estimator (such as this) depends on a set of assumptions:
The population is closed; that is, that there are no births, deaths, immigration, or emigration between sampling events
All individuals have the same probability of capture in one of the two events, or complete mixing occurs between events
Marking in the first event does not affect probability of recapture in the second event
Individuals do not lose marks between events
All marks will be reported in the second event
Matt Tyers
NPetersen, vPetersen, sePetersen, rPetersen, pPetersen, ciPetersen
powPetersen(nullN=500, trueN=400, n1=100, n2=100, nsim=1000) Ntotry <- seq(from=250, to=450, by=25) pows <- sapply(Ntotry, function(x) powPetersen(nullN=500, trueN=x, n1=100, n2=100, nsim=1000)) plot(Ntotry, pows)powPetersen(nullN=500, trueN=400, n1=100, n2=100, nsim=1000) Ntotry <- seq(from=250, to=450, by=25) pows <- sapply(Ntotry, function(x) powPetersen(nullN=500, trueN=x, n1=100, n2=100, nsim=1000)) plot(Ntotry, pows)
Conducts power calculations of the chi-squared tests for the consistency of the Petersen-type abundance estimator, in a complete stratification setting.
powstrattest(N, n1, n2, alpha = 0.05, sim = TRUE, nsim = 1e+05)powstrattest(N, n1, n2, alpha = 0.05, sim = TRUE, nsim = 1e+05)
N |
Vector of total abundance, with each element corresponding to one stratum. |
n1 |
Vector of anticipated n1 counts (sample size in the first event), each element corresponding to one stratum. |
n2 |
Vector of anticipated n2 counts (sample size in the second event), each element corresponding to one stratum. |
alpha |
Significance level for testing. Defaults to |
sim |
Whether to conduct power calculation by simulation as well as
Cohen's method. Defaults to |
nsim |
Number of simulations if |
A list of three elements, each with class "recapr_stratpow"
with the following components:
prob A vector of
capture probabilities corresponding to the alternative hypothesis
investigated
prob_null A vector of capture probabilities
corresponding to the null hypothesis (all probabilities equal)
n The sample size used for the test
alpha The significance level used for testing
power The test power, calculated by Cohen's method
power_sim The test power, calculated via simulation
Matt Tyers
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale,NJ: Lawrence Erlbaum.
Code adapted from the 'pwr' package: Stephane Champely (2015). pwr: Basic Functions for Power Analysis. R package version 1.1-3. https://CRAN.R-project.org/package=pwr
powstrattest(N=c(10000,20000), n1=c(1000,2000), n2=c(200,200))powstrattest(N=c(10000,20000), n1=c(1000,2000), n2=c(200,200))
Approximates a p-value for a hypothesis test of the Petersen estimator by means of many simulated draws from the null distribution, conditioned on sample sizes.
pPetersen( estN = NULL, nullN, n1, n2, m2 = NULL, nsim = 1e+05, alternative = "less" )pPetersen( estN = NULL, nullN, n1, n2, m2 = NULL, nsim = 1e+05, alternative = "less" )
estN |
The estimated abundance. Either this or the number of recaptures
( |
nullN |
The abundance given by the null hypothesis |
n1 |
Number of individuals captured and marked in the first sample |
n2 |
Number of individuals captured in the second sample |
m2 |
Number of recaptures. Either this or the estimated abundance
( |
nsim |
Number of simulated values to draw. Defaults to 100000. |
alternative |
Direction of the alternative hypothesis. Allowed values
are |
An approximate p-value for the specified hypothesis test. If
m2 is specified rather than estN, output will be returned as
a list with two elements: the estimated abundance and p-value.
Any Petersen-type estimator (such as this) depends on a set of assumptions:
The population is closed; that is, that there are no births, deaths, immigration, or emigration between sampling events
All individuals have the same probability of capture in one of the two events, or complete mixing occurs between events
Marking in the first event does not affect probability of recapture in the second event
Individuals do not lose marks between events
All marks will be reported in the second event
Matt Tyers
NPetersen, vPetersen, sePetersen, rPetersen, powPetersen, ciPetersen
output <- pPetersen(nullN=500, n1=100, n2=100, m2=28) output plotdiscdensity(rPetersen(length=100000, N=500, n1=100, n2=100)) abline(v=output$estN, lwd=2, col=2) abline(v=500, lwd=2, lty=2) output <- pPetersen(nullN=500, n1=100, n2=100, m2=28, alternative="2-sided") output plotdiscdensity(rPetersen(length=100000, N=500, n1=100, n2=100)) twosided <- 500 + c(-1,1)*abs(500-output$estN) abline(v=twosided, lwd=2, col=2) abline(v=500, lwd=2, lty=2)output <- pPetersen(nullN=500, n1=100, n2=100, m2=28) output plotdiscdensity(rPetersen(length=100000, N=500, n1=100, n2=100)) abline(v=output$estN, lwd=2, col=2) abline(v=500, lwd=2, lty=2) output <- pPetersen(nullN=500, n1=100, n2=100, m2=28, alternative="2-sided") output plotdiscdensity(rPetersen(length=100000, N=500, n1=100, n2=100)) twosided <- 500 + c(-1,1)*abs(500-output$estN) abline(v=twosided, lwd=2, col=2) abline(v=500, lwd=2, lty=2)
Print method for consistency test power
## S3 method for class 'recapr_consistencypow' print(x, ...)## S3 method for class 'recapr_consistencypow' print(x, ...)
x |
Output from |
... |
additional print arguments |
Matt Tyers
Print method for consistency test
## S3 method for class 'recapr_consistencytest' print(x, ...)## S3 method for class 'recapr_consistencytest' print(x, ...)
x |
Output from |
... |
additional print arguments |
Matt Tyers
Print method for stratification test power
## S3 method for class 'recapr_stratpow' print(x, ...)## S3 method for class 'recapr_stratpow' print(x, ...)
x |
Output from |
... |
additional print arguments |
Matt Tyers
Print method for stratification test
## S3 method for class 'recapr_strattest' print(x, ...)## S3 method for class 'recapr_strattest' print(x, ...)
x |
Output from |
... |
additional print arguments |
Matt Tyers
Returns a vector of random draws from the Bailey estimator in a mark-recapture experiment, given values of the true abundance and the sample size in both events. The function first simulates a vector of recaptures (m2) from a binomial distribution, and then uses these to compute a vector of draws from the estimator.
If capture probabilities (p1 and/or p2) are specified instead of sample size(s), the sample size(s) will first be drawn from a binomial distribution, then the number of recaptures. If both sample size and capture probability are specified for a given sampling event, only the sample size will be used.
rBailey(length, N, n1 = NULL, n2 = NULL, p1 = NULL, p2 = NULL)rBailey(length, N, n1 = NULL, n2 = NULL, p1 = NULL, p2 = NULL)
length |
The length of the random vector to return. |
N |
The value of the true abundance. This may be a single number or
vector of values equal to |
n1 |
Number of individuals captured and marked in the first sample. This
may be a single number or vector of values equal to |
n2 |
Number of individuals captured in the second sample. This may be a
single number or vector of values equal to |
p1 |
Alternately, probability of capture in the first sample. This
may be a single number or vector of values equal to |
p2 |
Alternately, probability of capture in the second sample. This may be a
single number or vector of values equal to |
A vector of random draws from the Bailey estimator
Any Petersen-type estimator (such as this) depends on a set of assumptions:
The population is closed; that is, that there are no births, deaths, immigration, or emigration between sampling events
All individuals have the same probability of capture in one of the two events, or complete mixing occurs between events
Marking in the first event does not affect probability of recapture in the second event
Individuals do not lose marks between events
All marks will be reported in the second event
Matt Tyers
NBailey, vBailey, seBailey, pBailey, powBailey, ciBailey
draws <- rBailey(length=100000, N=500, n1=100, n2=100) plotdiscdensity(draws) #plots the density of a vector of discrete valuesdraws <- rBailey(length=100000, N=500, n1=100, n2=100) plotdiscdensity(draws) #plots the density of a vector of discrete values
Returns a vector of random draws from the Chapman estimator in a mark-recapture experiment, given values of the true abundance and the sample size in both events. The function first simulates a vector of recaptures (m2) from a hypergeometric distribution, and then uses these to compute a vector of draws from the estimator.
If capture probabilities (p1 and/or p2) are specified instead of sample size(s), the sample size(s) will first be drawn from a binomial distribution, then the number of recaptures. If both sample size and capture probability are specified for a given sampling event, only the sample size will be used.
rChapman(length, N, n1 = NULL, n2 = NULL, p1 = NULL, p2 = NULL)rChapman(length, N, n1 = NULL, n2 = NULL, p1 = NULL, p2 = NULL)
length |
The length of the random vector to return. |
N |
The value of the true abundance. This may be a single number or
vector of values equal to |
n1 |
Number of individuals captured and marked in the first sample. This
may be a single number or vector of values equal to |
n2 |
Number of individuals captured in the second sample. This may be a
single number or vector of values equal to |
p1 |
Alternately, probability of capture in the first sample. This
may be a single number or vector of values equal to |
p2 |
Alternately, probability of capture in the second sample. This may be a
single number or vector of values equal to |
A vector of random draws from the Chapman estimator
Any Petersen-type estimator (such as this) depends on a set of assumptions:
The population is closed; that is, that there are no births, deaths, immigration, or emigration between sampling events
All individuals have the same probability of capture in one of the two events, or complete mixing occurs between events
Marking in the first event does not affect probability of recapture in the second event
Individuals do not lose marks between events
All marks will be reported in the second event
Matt Tyers
NChapman, vChapman, seChapman, pChapman, powChapman, ciChapman
draws <- rChapman(length=100000, N=500, n1=100, n2=100) plotdiscdensity(draws) #plots the density of a vector of discrete valuesdraws <- rChapman(length=100000, N=500, n1=100, n2=100) plotdiscdensity(draws) #plots the density of a vector of discrete values
Returns a vector of random draws from the Petersen estimator in a mark-recapture experiment, given values of the true abundance and the sample size in both events. The function first simulates a vector of recaptures (m2) from a hypergeometric distribution, and then uses these to compute a vector of draws from the estimator.
If capture probabilities (p1 and/or p2) are specified instead of sample size(s), the sample size(s) will first be drawn from a binomial distribution, then the number of recaptures. If both sample size and capture probability are specified for a given sampling event, only the sample size will be used.
rPetersen(length, N, n1 = NULL, n2 = NULL, p1 = NULL, p2 = NULL)rPetersen(length, N, n1 = NULL, n2 = NULL, p1 = NULL, p2 = NULL)
length |
The length of the random vector to return. |
N |
The value of the true abundance. This may be a single number or
vector of values equal to |
n1 |
Number of individuals captured and marked in the first sample. This
may be a single number or vector of values equal to |
n2 |
Number of individuals captured in the second sample. This may be a
single number or vector of values equal to |
p1 |
Alternately, probability of capture in the first sample. This
may be a single number or vector of values equal to |
p2 |
Alternately, probability of capture in the second sample. This may be a
single number or vector of values equal to |
A vector of random draws from the Petersen estimator
Any Petersen-type estimator (such as this) depends on a set of assumptions:
The population is closed; that is, that there are no births, deaths, immigration, or emigration between sampling events
All individuals have the same probability of capture in one of the two events, or complete mixing occurs between events
Marking in the first event does not affect probability of recapture in the second event
Individuals do not lose marks between events
All marks will be reported in the second event
Matt Tyers
NPetersen, vPetersen, sePetersen, pPetersen, powPetersen, ciPetersen
draws <- rPetersen(length=100000, N=500, n1=100, n2=100) plotdiscdensity(draws) #plots the density of a vector of discrete valuesdraws <- rPetersen(length=100000, N=500, n1=100, n2=100) plotdiscdensity(draws) #plots the density of a vector of discrete values
Returns a vector of random draws from the stratified estimator in a mark-recapture experiment, given values of the true abundance and the sample size in both events. The function first simulates a vector of recaptures (m2) for each stratum, and then uses these to compute a vector of draws from the estimator.
It may prove useful to investigate the behavior of the stratified estimator under relevant scenarios.
If capture probabilities (p1 and/or p2) are specified instead of sample size(s), the sample size(s) will first be drawn from a binomial distribution, then the number of recaptures. If both sample size and capture probability are specified for a given sampling event, only the sample size will be used.
rstrat( length, N, n1 = NULL, n2 = NULL, p1 = NULL, p2 = NULL, estimator = "Chapman" )rstrat( length, N, n1 = NULL, n2 = NULL, p1 = NULL, p2 = NULL, estimator = "Chapman" )
length |
The length of the random vector to return. |
N |
A vector of values of the true abundance for each stratum. |
n1 |
A vector of the number of individuals captured and marked in the first sample, for each stratum. |
n2 |
A vector of the number of individuals captured in the second sample, for each stratum. |
p1 |
Alternately, a vector of probabilities of capture for the first event, for each stratum. |
p2 |
Alternately, a vector of probabilities of capture for the second event, for each stratum. |
estimator |
The type of estimator to use. Allowed values are
|
A vector of random draws from the stratified estimator
Matt Tyers
strattest, Nstrat, vstrat, cistrat,NChapman, NPetersen, NBailey
draws <- rstrat(length=100000, N=c(5000,10000), n1=c(500,200), n2=c(500,200)) plotdiscdensity(draws) #plots the density of a vector of discrete values mean(draws)draws <- rstrat(length=100000, N=c(5000,10000), n1=c(500,200), n2=c(500,200)) plotdiscdensity(draws) #plots the density of a vector of discrete values mean(draws)
Calculates the standard error of the Bailey estimator in a mark-recapture experiment, with given values of sample sizes and number of recaptures.
seBailey(n1, n2, m2)seBailey(n1, n2, m2)
n1 |
Number of individuals captured and marked in the first sample. This may be a single number or vector of values. |
n2 |
Number of individuals captured in the second sample. This may be a single number or vector of values. |
m2 |
Number of marked individuals recaptured in the second sample. This may be a single number or vector of values. |
The estimate variance of the Bailey estimator, calculated as sqrt((n1^2)*(n2+1)*(n2-m2)/(m2+1)/(m2+1)/(m2+2))
Any Petersen-type estimator (such as this) depends on a set of assumptions:
The population is closed; that is, that there are no births, deaths, immigration, or emigration between sampling events
All individuals have the same probability of capture in one of the two events, or complete mixing occurs between events
Marking in the first event does not affect probability of recapture in the second event
Individuals do not lose marks between events
All marks will be reported in the second event
Matt Tyers
NBailey, vBailey, rBailey, pBailey, powBailey, ciBailey
seBailey(n1=100, n2=100, m2=20)seBailey(n1=100, n2=100, m2=20)
Calculates the standard error of the Chapman estimator in a mark-recapture experiment, with given values of sample sizes and number of recaptures.
seChapman(n1, n2, m2)seChapman(n1, n2, m2)
n1 |
Number of individuals captured and marked in the first sample. This may be a single number or vector of values. |
n2 |
Number of individuals captured in the second sample. This may be a single number or vector of values. |
m2 |
Number of marked individuals recaptured in the second sample. This may be a single number or vector of values. |
The estimate variance of the Chapman estimator, calculated as sqrt((n1+1)*(n2+1)*(n1-m2)*(n2-m2)/((m2+2)*(m2+1)^2))
Any Petersen-type estimator (such as this) depends on a set of assumptions:
The population is closed; that is, that there are no births, deaths, immigration, or emigration between sampling events
All individuals have the same probability of capture in one of the two events, or complete mixing occurs between events
Marking in the first event does not affect probability of recapture in the second event
Individuals do not lose marks between events
All marks will be reported in the second event
Matt Tyers
NChapman, vChapman, rChapman, pChapman, powChapman, ciChapman
seChapman(n1=100, n2=100, m2=20)seChapman(n1=100, n2=100, m2=20)
Calculates the standard error of the Petersen estimator in a mark-recapture experiment, with given values of sample sizes and number of recaptures.
sePetersen(n1, n2, m2)sePetersen(n1, n2, m2)
n1 |
Number of individuals captured and marked in the first sample. This may be a single number or vector of values. |
n2 |
Number of individuals captured in the second sample. This may be a single number or vector of values. |
m2 |
Number of marked individuals recaptured in the second sample. This may be a single number or vector of values. |
The estimate variance of the Petersen estimator, calculated as sqrt((n1^2)*n2*(n2-m2)/(m2^3))
Any Petersen-type estimator (such as this) depends on a set of assumptions:
The population is closed; that is, that there are no births, deaths, immigration, or emigration between sampling events
All individuals have the same probability of capture in one of the two events, or complete mixing occurs between events
Marking in the first event does not affect probability of recapture in the second event
Individuals do not lose marks between events
All marks will be reported in the second event
Matt Tyers
NPetersen, vPetersen, rPetersen, pPetersen, powPetersen, ciPetersen
sePetersen(n1=100, n2=100, m2=20)sePetersen(n1=100, n2=100, m2=20)
Calculates the standard error of the stratified estimator for abundance in a mark-recapture experiment, from vectors of sample sizes and number of recaptures, with each element corresponding to each sampling stratum.
sestrat(n1, n2, m2, estimator = "Chapman")sestrat(n1, n2, m2, estimator = "Chapman")
n1 |
Vector of individuals captured and marked in the first sample, from each stratum |
n2 |
Vector of individuals captured and marked in the second sample, from each stratum |
m2 |
Vector of marked individuals recaptured in the second sample, from each stratum |
estimator |
The type of estimator to use. Allowed values are
|
The standard error of the stratified estimator
It is possible that even the stratified estimate of abundance may be biased if capture probabilities differ greatly between strata. However, the bias in the stratified estimator will be much less than an estimator calculated without stratification.
This function makes the naive assumption of independence between strata. Caution is therefore recommended.
Matt Tyers
strattest, Nstrat, rstrat, vstrat, cistrat, NChapman, NPetersen, NBailey
sestrat(n1=c(100,200), n2=c(100,500), m2=c(10,10))sestrat(n1=c(100,200), n2=c(100,500), m2=c(10,10))
Conducts two chi-squared tests for the consistency of the Petersen-type abundance estimator. These tests provide explore evidence against equal capture probabilities in either the first or second sampling event. Also conducts a third chi-squared test of unequal capture probabilities between sampling events for each stratum, in the case of small sample sizes (fewer than 100 in either sampling event and fewer than 30 recaptures), which may be used to suggest unequal capture probabilities in either the first or second event.
Typically, if either of the first two test p-values is greater than the significance level, use of a Petersen-type estimator is considered justified.
If tests give evidence of unequal capture probabilities between strata, a stratified estimator should be used, such as Nstrat.
This function assumes stratification in both sampling events, such that individuals cannot move from one strata to another (such as by size or gender). If movement between strata may occur (such as in the case of stratification by time or area), use of consistencytest is recommended.
strattest(n1, n2, m2, ...)strattest(n1, n2, m2, ...)
n1 |
Vector of n1 counts (sample size in the first event), each element corresponding to one stratum. |
n2 |
Vector of n2 counts (sample size in the second event), each element corresponding to one stratum. |
m2 |
Vector of m2 counts (number of recaptures in the second event), each element corresponding to one stratum. |
... |
Additional arguments for chisq.test |
A list of class "recapr_strattest" with the following
components:
event1_table The contingency table
used for the first test
event1_Xsqd The chi-squared test
statistic in the first test
event1_df The associated
degrees of freedom in the first test
event1_pval The
p-value returned from the first test
event2_table The
contingency table used for the second test
event2_Xsqd The
chi-squared test statistic in the second test
event2_df The
associated degrees of freedom in the second test
event2_pval
The p-value returned from the second test
event1v2_table
The contingency table used for the third test
event1v2_Xsqd
The chi-squared test statistic in the third test
event1v2_df The associated degrees of freedom in the third
test
event1v2_pval The p-value returned from the second
third
Any Petersen-type estimator (such as this) depends on a set of assumptions:
The population is closed; that is, that there are no births, deaths, immigration, or emigration between sampling events
All individuals have the same probability of capture in one of the two events, or complete mixing occurs between events
Marking in the first event does not affect probability of recapture in the second event
Individuals do not lose marks between events
All marks will be reported in the second event
Matt Tyers
powstrattest, Nstrat, consistencytest
strattest(n1=c(100,100), n2=c(50,200), m2=c(20,15))strattest(n1=c(100,100), n2=c(50,200), m2=c(20,15))
Calculates the estimated variance of the Bailey estimator in a mark-recapture experiment, with given values of sample sizes and number of recaptures.
vBailey(n1, n2, m2)vBailey(n1, n2, m2)
n1 |
Number of individuals captured and marked in the first sample. This may be a single number or vector of values. |
n2 |
Number of individuals captured in the second sample. This may be a single number or vector of values. |
m2 |
Number of marked individuals recaptured in the second sample. This may be a single number or vector of values. |
The estimate variance of the Bailey estimator, calculated as (n1^2)*(n2+1)*(n2-m2)/(m2+1)/(m2+1)/(m2+2)
Any Petersen-type estimator (such as this) depends on a set of assumptions:
The population is closed; that is, that there are no births, deaths, immigration, or emigration between sampling events
All individuals have the same probability of capture in one of the two events, or complete mixing occurs between events
Marking in the first event does not affect probability of recapture in the second event
Individuals do not lose marks between events
All marks will be reported in the second event
Matt Tyers
NBailey, seBailey, rBailey, pBailey, powBailey, ciBailey
vBailey(n1=100, n2=100, m2=20)vBailey(n1=100, n2=100, m2=20)
Calculates the estimated variance of the Chapman estimator in a mark-recapture experiment, with given values of sample sizes and number of recaptures.
vChapman(n1, n2, m2)vChapman(n1, n2, m2)
n1 |
Number of individuals captured and marked in the first sample. This may be a single number or vector of values. |
n2 |
Number of individuals captured in the second sample. This may be a single number or vector of values. |
m2 |
Number of marked individuals recaptured in the second sample. This may be a single number or vector of values. |
The estimate variance of the Chapman estimator, calculated as (n1+1)*(n2+1)*(n1-m2)*(n2-m2)/((m2+2)*(m2+1)^2)
Any Petersen-type estimator (such as this) depends on a set of assumptions:
The population is closed; that is, that there are no births, deaths, immigration, or emigration between sampling events
All individuals have the same probability of capture in one of the two events, or complete mixing occurs between events
Marking in the first event does not affect probability of recapture in the second event
Individuals do not lose marks between events
All marks will be reported in the second event
Matt Tyers
NChapman, seChapman, rChapman, pChapman, powChapman, ciChapman
vChapman(n1=100, n2=100, m2=20)vChapman(n1=100, n2=100, m2=20)
Calculates the estimated variance of the Petersen estimator in a mark-recapture experiment, with given values of sample sizes and number of recaptures.
vPetersen(n1, n2, m2)vPetersen(n1, n2, m2)
n1 |
Number of individuals captured and marked in the first sample. This may be a single number or vector of values. |
n2 |
Number of individuals captured in the second sample. This may be a single number or vector of values. |
m2 |
Number of marked individuals recaptured in the second sample. This may be a single number or vector of values. |
The estimate variance of the Petersen estimator, calculated as (n1^2)*n2*(n2-m2)/(m2^3)
Any Petersen-type estimator (such as this) depends on a set of assumptions:
The population is closed; that is, that there are no births, deaths, immigration, or emigration between sampling events
All individuals have the same probability of capture in one of the two events, or complete mixing occurs between events
Marking in the first event does not affect probability of recapture in the second event
Individuals do not lose marks between events
All marks will be reported in the second event
Matt Tyers
NPetersen, sePetersen, rPetersen, pPetersen, powPetersen, ciPetersen
vPetersen(n1=100, n2=100, m2=20)vPetersen(n1=100, n2=100, m2=20)
Calculates the estimated variance of the stratified estimator for abundance in a mark-recapture experiment, from vectors of sample sizes and number of recaptures, with each element corresponding to each sampling stratum.
vstrat(n1, n2, m2, estimator = "Chapman")vstrat(n1, n2, m2, estimator = "Chapman")
n1 |
Vector of individuals captured and marked in the first sample, from each stratum |
n2 |
Vector of individuals captured and marked in the second sample, from each stratum |
m2 |
Vector of marked individuals recaptured in the second sample, from each stratum |
estimator |
The type of estimator to use. Allowed values are
|
The estimated variance of the stratified estimator
It is possible that even the stratified estimate of abundance may be biased if capture probabilities differ greatly between strata. However, the bias in the stratified estimator will be much less than an estimator calculated without stratification.
This function makes the naive assumption of independence between strata. Caution is therefore recommended.
Matt Tyers
strattest, Nstrat, rstrat, sestrat, cistrat, NChapman, NPetersen, NBailey
vstrat(n1=c(100,200), n2=c(100,500), m2=c(10,10))vstrat(n1=c(100,200), n2=c(100,500), m2=c(10,10))