Dept., “Patterns of first passage probabilities in population monitoring data”, This was an informal almost philosophical talk where I tried to ennunciate some of my ideas about the meaning of parsimony in population modeling

  Patternsoffirst-passageprobabilitiesinpopulationmonitoringdata  Confronting the theory with data(Holmes & Fagan 2002) •141 chinookand 41 steelhead 30-70 year time seriesfrom ESUsin WA, OR, and CA 01020304050607080    1   9   5   2   1   9   5   5   1   9   5   8   1   9   6   1   1   9   6  4   1   9   6   7   1   9   7   0   1   9   7   3   1   9   7   6   1   9   7   9   1   9   8   2   1   9   8   5   1   9   8   8   1   9   9   1   1   9   9  4   1   9   9   7   r  e   d   d  s  p  e  r  m   i   l  e parameterization evaluation  1),(~ ),0(~ )log()log( )log()log( 2,2,,111 ,1 =+=++= ++++ bf NormalNyNbN anptpptnpttt pttt σ  β ε σ ε ε ε µ  No density-dependencei.i.d. errors -> no auto-correlationsHolmes (2001) Corrupted Diffusion Approximation (CDA)really a ‘Corrupted Random Walk Model’   Theory makes a prediction about the distribution of mu_hat*random walk*N_t+1/N_t variance is related in a particular way to mu_hatvariance 1 5 9 13 171 5 9 13 17 1 5 9 13 17 1 5 9 13 17 True µ and σ µ  ˆ µ  ˆof pdf