{"id":237,"date":"2017-04-18T03:16:59","date_gmt":"2017-04-18T03:16:59","guid":{"rendered":"http:\/\/sites.warnercnr.colostate.edu\/gwhite\/?page_id=237"},"modified":"2017-04-18T03:16:59","modified_gmt":"2017-04-18T03:16:59","slug":"popan-model","status":"publish","type":"page","link":"https:\/\/sites.warnercnr.colostate.edu\/gwhite\/popan-model\/","title":{"rendered":"POPAN Model"},"content":{"rendered":"

Contents<\/a> – Index<\/a><\/span><\/p>\n

\n

POPAN Model<\/b><\/span><\/p>\n

Program POPAN-5 provides a parameterization of the Jolly-Seber model (Schwarz and Arnason 1996) that is particularly robust.\u00a0 The POPAN data type in MARK emulates this model.\u00a0\u00a0\u00a0 Schwarz and Arnason (1996) parameterized the Jolly-Seber model in terms of a super population (N<\/i>), and the probability of entry (pent in MARK, beta in the paper).\u00a0 The POPAN data type implements this model in Program MARK.<\/span><\/p>\n

Four PIMs<\/a> are created for each group<\/a>: phi (apparent survival), p<\/i> (capture probability given the animal is alive and on the study area, i.e., available for capture), pent (probability of entry into the population for this occasion), and N<\/i> (super-population size).\u00a0 For t<\/i> occasions, there are t<\/i> – 1 phi estimates, t<\/i> p estimates, t<\/i> – 1 pent estimates, and 1 N<\/i> estimate.\u00a0 The t<\/i> – 1 pent estimates correspond to the probability of entry for occasions 2, 3, …, t<\/i>.\u00a0 The probability of being in the population on the first occasion is equal to pent(0) = 1 – sum(pent(i)).\u00a0 The MLogit link function<\/a> provides a constraint that makes the sum of the pent parameters <= 1, with the probability of occurring in the population on the first occasion as 1 – sum(pent(t)).\u00a0 An example<\/a> of how to constrain parametes within a MLogit link is also provided.\u00a0 Convergence of this model is problematic unless the MLogit link function is used with the pent parameters.<\/span><\/p>\n

The number of animals in the population on occasion 1 is N<\/i>(1) = pent(0) times N<\/i>.\u00a0 The number of new animals (births, B<\/i>) entering the population prior to occasions i<\/i> = 2, 3, …, t<\/i> is B<\/i>(i<\/i>) = pent(i <\/i>– 1) times N<\/i>.\u00a0 The population size on occasion i<\/i> = 2, 3, …, t<\/i> is N<\/i>(i<\/i>) = (N<\/i>(i<\/i> – 1) – losses on capture) times phi(i<\/i> – 1) + B<\/i>(i<\/i>).\u00a0 Estimates of the B<\/i>(i<\/i>) and N<\/i>(i<\/i>) are provided as derived parameters from models with the POPAN data type.\u00a0 In addition, the N(i)<\/i> dereived parameters can also be used with model averaging<\/a> and variance components<\/a> analyses.<\/span><\/p>\n

One limitation of the POPAN data type is with the use of individual covariates.\u00a0 Because the super-populations size (N<\/i>) estimates the number of animals never captured, this parameter includes animals for which the individual covariate is not known.\u00a0 Thus, modeling N<\/i> as a function of individual covariates is inappropriate.\u00a0 Further, the B(i)<\/i> and N(i)<\/i> parameters are functions of N<\/i>, as well at the pent(i<\/i>) and phi(i<\/i>).\u00a0\u00a0 Thus, if the pent(i<\/i>) or phi(i<\/i>) are modeled as functions of individual covariates, the derived parameters will also be functions of these individual covariates, creating a illogical estimate.\u00a0 The best strategy for use of individual covariates with the POPAN data type is to use the mean values of the individual covariates for providing the estimates of the real and derived parameters.<\/span><\/p>\n

Link and Barker (2003) reparameterized the Schwarz and Arnason (1996) parameterization in the Link-Barker<\/a> data type, with the pent parameter replaced by the recruitment (f<\/i>) parameter.\u00a0 Burnham’s Jolly-Seber model is also a competing model available in MARK.\u00a0 None of these 3 models have the same likelihood, so AIC<\/a> values are not comparable among these models.\u00a0 Note, however, that the Link-Barker<\/a> data type and the Pradel recruitment<\/a> data types do have the same likelihood, so AIC<\/a> values are comparable among the Link-Barker and Pradel data types.\u00a0<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

Contents – Index POPAN Model Program POPAN-5 provides a parameterization of the Jolly-Seber model (Schwarz and Arnason 1996) that is particularly robust.\u00a0 The POPAN data type in MARK emulates this model.\u00a0\u00a0\u00a0 Schwarz and Arnason (1996) parameterized the Jolly-Seber model in …<\/p>\n

POPAN Model<\/span> Read More »<\/a><\/p>\n","protected":false},"author":117,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-237","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sites.warnercnr.colostate.edu\/gwhite\/wp-json\/wp\/v2\/pages\/237","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.warnercnr.colostate.edu\/gwhite\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sites.warnercnr.colostate.edu\/gwhite\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sites.warnercnr.colostate.edu\/gwhite\/wp-json\/wp\/v2\/users\/117"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.warnercnr.colostate.edu\/gwhite\/wp-json\/wp\/v2\/comments?post=237"}],"version-history":[{"count":1,"href":"https:\/\/sites.warnercnr.colostate.edu\/gwhite\/wp-json\/wp\/v2\/pages\/237\/revisions"}],"predecessor-version":[{"id":238,"href":"https:\/\/sites.warnercnr.colostate.edu\/gwhite\/wp-json\/wp\/v2\/pages\/237\/revisions\/238"}],"wp:attachment":[{"href":"https:\/\/sites.warnercnr.colostate.edu\/gwhite\/wp-json\/wp\/v2\/media?parent=237"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}