Brant brood site-fidelity model (multistate m-array version)

Nest Success

• Parameter estimates do not indicate an effect of nest success on transitions away from colony sites (Tut, Kashtut), either with or without an interaction with distance

• Some scatterplots of those data/estimates:

Nest success over time:

Probability of fidelity to colony sites (Tut, Kashtut) as a function of nest success:

(Probabilities are posterior means)

Probability of transitions away from colony as a function of nest success:

(Probabilities are posterior means)

Stone Distance

• Negative effect of distance on transition probabilities (which is obvious from \(\psi\) estimates with or without this term included in the model)
• ~ 80% decrease in the odds of transitioning to a site in year t for every 1 stone increase in distance from the site used in year t-1

Parameter Estimates (\(\psi\), \(\phi\), and \(p\))

• Because of the apparent lack of influence of nest success (for which data are avilable from 1986-2016), I dropped that term and included data from 1986-2019, as used previously

\(\psi\):

\(\phi\):

\(p\):

Model Notes (mostly the same as previous summaries)

Specification Notes:

• \(p\) estimated for each site-year combination
• \(\phi\) smoothed with an autoregressive (lag 1) term
• Distance between sites (in stones) as a covariate with a year-specific intercept on the \(\psi\) parameters

State Transition Matrix:

• \(\psi\) = transition probability, \(\phi\) = survival probability
  
• subscripts depict sites (T=Tutakoke, K=Kashtut, B=Bend Slough, H=Hock Slough, E=Emperor)
  
• rows: time = t, columns: time = t+1
  
• last row and column represent “dead” state

\(\left[\begin{array}{ccc} (1-\Sigma\psi_{T})\phi_T & \psi_{TK}\phi_T & \psi_{TB}\phi_T & \psi_{TH}\phi_T & \psi_{TE}\phi_T & 1-\phi_T\\ \psi_{KT}\phi_K & (1-\Sigma\psi_{K})\phi_K & \psi_{KB}\phi_K & \psi_{KH}\phi_K & \psi_{KE}\phi_K & 1-\phi_K\\ \psi_{BT}\phi_B & \psi_{BK}\phi_B & (1-\Sigma\psi_{B})\phi_B & \psi_{BH}\phi_B & \psi_{BE} \phi_B & 1-\phi_B\\ \psi_{HT}\phi_H & \psi_{HK}\phi_H & \psi_{HB}\phi_H & (1-\Sigma\psi_{H})\phi_H & \psi_{HE}\phi_H & 1-\phi_H\\ \psi_{ET}\phi_E & \psi_{EK}\phi_E & \psi_{EB}\phi_E & \psi_{EB}\phi_E & (1-\Sigma\psi_{E})\phi_E & 1-\phi_E\\ 0 & 0 & 0 & 0 & 0 & 1\\ \end{array}\right]\)

Site Delineations

(same as previous; aggregated labels from master file in parentheses):

• Tutakoke (Tutakoke, Camp)
  
• Kashtut (Kashtut)
  
• Bend Slough (Bend Slough, Lensink Pt, Lensink)
  
• Hock Slough (Hock Slough, Village Slough)
  
• Emperor (Emperor)