Bionomic dynamics

1
Bionomic dynamics

• Basic concern is with unregulated dynamics of
  fishing effort (fish-fisher interaction as
  predator-prey system)
• Four key dynamic relationships to consider
• Stock response to harvest rate
• Catchability variation with stock size/distn.
• Short-term effort response to expected cpue
• Long-term effort response (fleet size dynamics)

2
Stock response to harvest

• Often sufficient to model with simple surplus
  production model of the form Bt1Btg(Bt)-Ct
• Surplus production function g(B) is typically
  domeshaped with variable initial slope (r ) and
  carrying capacity (K)
• Should consider slow dynamics of change in r
  and K with habitat/environment
• Key prediction problem is Ct

3
Catchability variation

• Can predict Ct as either CtqtEtBt (short
  prediction time steps) Ct(1-e-qtEt)Bt (longer
  time steps)
• Key problem is predicting qt (changes with
  technology and stock size) remember qta/A,
  aarea swept/effort, Astock area
• Non-random search and range contraction dynamics
  cause A to change a lot with B

Hyperstable
qt
Hyperdepleting
Bt
4
Short term effort response

• Whether or not individuals fish depends on
  expected price x cpue (relative to cost)
• Variation among individuals results in a
  cumulative increase in proportion of vessels
  fishing as stock size increases
• Usually model the cumulative proportion of
  vessels fishing as a function of expected cpue by
  using a logit choice model

5
Impact of short-term effort responses on
catch-effort relationships
6
Logit (logistic) choice models(switching models)
7
Can also think about the short-term effort
response as a sum of individual efforts, each
turning on at a different overall average cpue
Effort
Average cpue
8
Long term fleet size response

• Model this as a population dynamics with
  recruitment (investment) and mortality
  (depreciation) Ntnumber of vessels
• Nt1(1-d)Ntk(profit)tINEWt
• Depreciation rates d are typically around
  0.05/yr
• (profit)tprice x catch (cost/effort) x effort
• Proportion of profit reinvested (k) is likely to
  be around 0.5
• New investment INEW from outside the fishery
  can be highly unpredictable

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Predicted dynamics of linked stock-fleet models

• Key determinant of predicted pattern is how q
  varies with stock size (and rarely, increases in
  price as stock declines)
• Constant q and price lead to simple dynamics that
  approach stable equilibrium point
• Hyperstable q (increasing at low stock size) can
  cause unstable dynamics with effort cycles,
  multiple equilibria in stock abundance

10
Bionomic equilibrium Gulf of Mexico shrimp
fishery
In shrimp fisheries, it is common for seasonal
effort to start out high, then drop off to near
zero as abundance declines to an unprofitable
level each year. The Remaining spawning stock
produces next years catch
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Bionomic equilibrium tuna longline fisheries