Emperor Goose Modeling Update

Erik Osnas

2024-01-01

Outline

  • Revision process
  • Define objectives
  • Develop alternatives
  • Analyze alternatives
    • model and predictions

Revision process

  • first plan went into effect 2017
  • harvest data 2017 to 2019
  • population survey data 2017 - now (ex. 2020)

Is the current plan consistent with these data and our objectives?

Current strategy and history

Objectives

(partial list)

  • harvest (\(\uparrow\))
  • frequency of change between season types (\(\downarrow\))
  • frequency of closure (\(\downarrow\))
  • population viability (future population size) (\(\uparrow\))

Develop alternatives

  • closure level (“red”)
  • Conservation measures (“yellow”)
    • egg harvest closure
    • season length restriction
    • bag limits
    • permit numbers

Analyize alternatives

Population model

  • updates
    • subsistence harvest data
    • permit harvest data
    • survey data - added observer effects
  • predict performance on objectives

The Theta-logistic model

State process

\[N_{t+1} = N_t + N_t r \left[1 - \left(\frac{N_t}{K}\right)^\theta \right] - \frac{H_t(N_t)}{(1 - c)}\]

Observation process: data

\[Y_{obs,t} \sim Normal(q N_t, \sigma_{Yobs,t})\] \[H_{obs,t} \sim Normal(H_t, \sigma_{Hobs,t})\]

Survey Data and Model

Harvest

Alternatives to evaluate

  • open/closed (“green/red”)
    • close to current strategy (ex. egg closure)
  • open/conservation/closed (“green/yellow/red”)
    • yellow is midway between red and green

Prediction

Alternatives to evaluate

  1. Where to put the closure threshold?

Results: Open/Closed

Expected population size in 100 years

Results: Open/Closed

Expected harvest per year over 100 years

Results: Open/Closed

Frequency of open hunting over 100 years

Results: Open/Closed

Frequency of extinction over 100 years

Alternatives to evaluate

  1. Where to put the closure and green thresholds?

Results: Open/Conservation/Closed

Expected harvest per year over 100 years

Results: Open/Conservation/Closed

Expected harvest per year over 100 years

. . .

Results: Open/Conservation/Closed

Expected harvest per year over 100 years

Results: Open/Conservation/Closed

Expected population size in 100 years

Results: Open/Conservation/Closed

Frequency of open hunting over 100 years

Results: Open/Conservation/Closed

Frequency of a changed hunting season over 100 years

Results: Open/Conservation/Closed

Frequency of extinction over 100 years

Example alternatives to compare

Name Closure Green Mean Har. Pr(Hunt) Mean Pop. Pr(Change) Pr(Ext.)
1 17500 17500 5398.17 0.74 154640.2 0.07 0.15
2 19500 19500 5350.24 0.71 159912.0 0.10 0.12
3 23000 23000 5139.57 0.62 167303.8 0.15 0.09
4 23000 28000 5171.90 0.62 169235.5 0.15 0.08
5 18500 30500 5438.30 0.74 160228.8 0.08 0.12
6 20500 30500 5305.57 0.69 163425.3 0.11 0.11
7 0 41250 4610.75 0.91 166892.8 0.04 0.19
8 16000 41250 5108.25 0.81 160485.2 0.18 0.14
9 50000 50000 3575.87 0.04 193624.7 0.02 0.06

Alternatives to compare

Expected harvest per year over 100 years

Alternatives to compare

Frequency of open hunting over 100 years

Alternatives to compare

Frequency of extinction over 100 years

Alternatives to compare

Frequency of a changed hunting season over 100 years

Kill rate (2023) posterior from model

\[k = K/N\]

Potential Take Level posterior

\[PTL_t = F \left ( \frac {r_{max} \theta}{(\theta + 1)} \right ) N_t \]

Sustainable Harvest Index

2023 population size posterior

Population process SD posterior

Theta posterior

r_max posterior

Hunter functional response