{"id":277,"date":"2017-04-18T03:41:43","date_gmt":"2017-04-18T03:41:43","guid":{"rendered":"http:\/\/sites.warnercnr.colostate.edu\/gwhite\/?page_id=277"},"modified":"2017-04-18T03:42:25","modified_gmt":"2017-04-18T03:42:25","slug":"occupancy-estimation-two-species","status":"publish","type":"page","link":"https:\/\/sites.warnercnr.colostate.edu\/gwhite\/occupancy-estimation-two-species\/","title":{"rendered":"Occupancy Estimation Two Species"},"content":{"rendered":"

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

\n

Occupancy Estimation Two Species<\/b><\/span><\/p>\n

Parameterization<\/b><\/span><\/p>\n

Two versions of the 2-species <\/span>occupancy models<\/a><\/span> are included in Program MARK.\u00a0 The first is the original parametrization developed in the <\/span>MacKenzie et al. (2006)<\/a><\/span> book.\u00a0 This parametrization is difficult to use because of a multinomial constraint on the r parameters.\u00a0 Further, this parametrization does not work well with covariates.\u00a0 It is identified in MARK as 113. 2SpecOccup: Two species Occupancy Estimation\u00a0\u00a0<\/span><\/p>\n

The parametrization for the <\/span>MacKenzie et al. (2006)<\/a><\/span> 2-species model is:<\/span><\/p>\n

psi<\/span>AB<\/span>\u00a0 Probability of both species being present<\/span>
\npsi<\/span>A<\/span>\u00a0 Probability of occupancy for species A, regardless of occupancy status of species B<\/span>
\npsi<\/span>B<\/span>\u00a0 Probability of occupancy for species B, regardless of occupancy status of species A<\/span>
\np<\/i><\/span>A\u00a0<\/span> Probability of detection for species A, given species B is absent<\/span>
\np<\/i><\/span>B\u00a0<\/span> Probability of detection for species B, given species A is absent<\/span>
\nr<\/i><\/span>AB<\/span>\u00a0 Probability of detecting both species, given both species are present<\/span>
\nr<\/i><\/span>Ab<\/span>\u00a0 Probability of detecting species A, but not B, given both species are present<\/span>
\nr<\/i><\/span>aB\u00a0<\/span> Probability of detecting species B, but not A, given both species are present<\/span>
\nr<\/i><\/span>ab\u00a0<\/span> Probability of detecting neither, given both species are present.\u00a0 This parameter is obtained by subtraction: 1 – r<\/i><\/span>AB – <\/span>r<\/i><\/span>Ab – <\/span>r<\/i><\/span>aB<\/span>, so is not in the <\/span>PIMs<\/a><\/span>.<\/span><\/p>\n

Because r<\/i><\/span>ab<\/span> is obtained by subtraction, the <\/span>multinomial logit<\/a><\/span>\u00a0<\/span> (MLogit <\/span>link function<\/a><\/span>) is often required to obtain a numerical solution.\u00a0\u00a0\u00a0\u00a0<\/span><\/p>\n

The second parametrization is termed the conditional occupancy model and is stable when covariates are included.\u00a0 Also, this parameterization assumes that Species A is the dominant species, and Species B the subordinate species.\u00a0 The data type is identified in MARK as 137. 2SpecConOccup: Two species Conditional Occupancy Estimation.\u00a0 The parametrization for this 2-species conditional occupancy model (<\/span>Richmond et al. 2010<\/a><\/span>) follows.<\/span><\/p>\n

psi<\/span>A<\/span>\u00a0 Probability of occupancy for species A<\/span>
\npsi<\/span>BA<\/span>\u00a0 Probability of occupancy for species B, given species A is present<\/span>
\npsi<\/span>Ba<\/span>\u00a0 Probability of occupancy for species B, given species A is absent<\/span>
\np<\/i><\/span>A\u00a0<\/span> Probability of detection for species A, given species B is absent<\/span>
\np<\/i><\/span>B\u00a0<\/span> Probability of detection for species B, given species A is absent<\/span>
\nr<\/i><\/span>A<\/span>\u00a0 Probability of detection for species A, given both species are present<\/span>
\nr<\/i><\/span>BA<\/span>\u00a0 Probability of detection for species B, given both species are present and species A is detected<\/span>
\nr<\/i><\/span>Ba\u00a0<\/span> Probability of detection for species B, given both species are present and species A is not detected<\/span><\/p>\n

Some of the parameters of the McKenzie et al. parametrization can be defined in terms of the conditional :<\/span><\/p>\n

\u00a0 psi<\/span>B<\/span> = psi<\/span>A<\/span>*psi<\/span>BA<\/span> + (1 – psi<\/span>A<\/span>) psi<\/span>Ba<\/span><\/p>\n

\u00a0 psi<\/span>AB<\/span> = psi<\/span>A*<\/span>psi<\/span>BA<\/span><\/p>\n

\u00a0 psi<\/span>B<\/span> and psi<\/span>AB<\/span> are included as a <\/span>derived parameter<\/a><\/span> for this data type.<\/span><\/p>\n

The short labels for the 9 derived parameters for the conditional data type are: 1) “PsiA”, 2) “PsiBA”, 3) “PsiBa”, 4) “PsiB”, 4) “PsiAB”, 6) “SIF”, 7) “A only”, 8) “B only”, and 9) “Unoccupied”.<\/span> The following diagram from Larissa Bailey helps explain the 9 derived parameters of the Richmond conditional parameterization.<\/span><\/p>\n

<\/span><\/p>\n

So, derived parameters #1-3 are seen in the above figure: #1 psi(A) is the unconditional probability that species A is present at the site, but #2 psi(BA) = probability that B is present given A is present and #3 psi(Ba) = probability that B is present given A is not present are conditional on the presence or absence of A, respectively.\u00a0 The remaining 6 derived parameters within each season are derived from these three.<\/span><\/p>\n

Moving from left to right at the bottom of the figure:<\/span>
\n#9 Unoccupied, is the first product on the left, derived from (1 – psi(A)) (1 – psi(Ba)), is the probability that neither A or B are present at the site.<\/span>
\n#8 Species B Only, is the second product on the left, derived from (1 – psi(A)) psi(Ba), is the probability that the site is occupied by B only.<\/span>
\n#7 Species A Only, is the third product on the left, derived from psi(A) (1 – psi(BA)), is the probability that the site is occupied by A only.\u00a0<\/span>
\n#5 Both Species Occupancy, is the final\/fourth product from the left, derived from psi(A) psi(BA), is the probability of both species being present at the site.<\/span>
\n#4 Species B Occupancy, is the sum of Species B Only and Both Species Occupancy, derived from (1 – psi(A)) psi(Ba) +\u00a0 psi(A) psi(BA), is the probability the site is occupied by species B.<\/span>
\n#6 is the SIF (Species Interaction Factor), defined below for the Richmond model, as SIF = (psi<\/span>A <\/span>psi<\/span>BA<\/span>) \/ (psi<\/span>A<\/span>(psi<\/span>A*<\/span>psi<\/span>BA<\/span> + (1 – psi<\/span>A<\/span>)psi<\/span>Ba<\/span>).<\/span><\/p>\n

The following graphic from Brittainy Mosher provides a visual definition of the derived parameters.<\/span><\/p>\n

<\/span><\/p>\n

Species Interaction Factor<\/b><\/span><\/p>\n

Both parameterizations provide estimates of the species interaction factor, SIF.\u00a0 The estimate of SIF for each <\/span>attribute group<\/a><\/span> is provided as a <\/span>derived parameter<\/a><\/span>.\u00a0 For the McKenzie et al. (2006) model,\u00a0<\/span><\/p>\n

\u00a0 SIF = psi<\/span>AB<\/span>\/<\/span>(psi<\/span>A<\/span>*psi<\/span>B<\/span>) .<\/span><\/p>\n

For the conditional occupancy model, SIF = (psi<\/span>A <\/span>psi<\/span>BA<\/span>) \/ (psi<\/span>A<\/span>(psi<\/span>A*<\/span>psi<\/span>BA<\/span> + (1 – psi<\/span>A<\/span>)psi<\/span>Ba<\/span>).<\/span><\/p>\n

Encounter Histories<\/b><\/span><\/p>\n

The <\/span>encounter histories<\/a><\/span> for the 2-species occupancy model are provided as a pair for each occasion.\u00a0 The first member of the pair is the status of species A: 1 = detected; 0 = not detected; and . (dot) = not searched.\u00a0 The same codes are used for the second member of the pair for species B.<\/span><\/p>\n

As an example, the encounter history 11001001.11. means that both A and B were detected at time 1, neither were detected at time 2, only A was detected at time 3, and only B was detected at time 4.\u00a0 Species A was not searched for at time 5, but B was detected.\u00a0 Species A was detected at time 6, but B was not searched for.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

Contents – Index Occupancy Estimation Two Species Parameterization Two versions of the 2-species occupancy models are included in Program MARK.\u00a0 The first is the original parametrization developed in the MacKenzie et al. (2006) book.\u00a0 This parametrization is difficult to use …<\/p>\n

Occupancy Estimation Two Species<\/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-277","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sites.warnercnr.colostate.edu\/gwhite\/wp-json\/wp\/v2\/pages\/277","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=277"}],"version-history":[{"count":2,"href":"https:\/\/sites.warnercnr.colostate.edu\/gwhite\/wp-json\/wp\/v2\/pages\/277\/revisions"}],"predecessor-version":[{"id":279,"href":"https:\/\/sites.warnercnr.colostate.edu\/gwhite\/wp-json\/wp\/v2\/pages\/277\/revisions\/279"}],"wp:attachment":[{"href":"https:\/\/sites.warnercnr.colostate.edu\/gwhite\/wp-json\/wp\/v2\/media?parent=277"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}