Characteristics of Fish Populations

Transcription

1 Characteristics of Fish Populations Unexploited Populations Recruitment Mortality (natural) Growth Exploited Populations Recruitment and Yield Fishing and Natural Mortality Compensatory Growth

2 Recruitment and Yield Recruitment is defined as the addition of new members to the aggregate under consideration Generally in fishing the life history stage they are vulnerable to gear

3 Typical Stocks Harvested Pre recruitment Post recruitment

4 Relationships between Recruits and Parents and Sources of Mortality Adult stock numbers can be related to recruits. Two sources of mortality Density dependent - Density Independent Size and growth characteristics influence production of young

5 Stock Recruitment Developed using assumption that density dependent mortality is operating.

6 Factors that regulate numbers Predation (disease episodes) Competition Habitat Parent stock abundance

7 Density Independent Factors Temperatures Floods Drought

8 No. Recruits or Progeny Replacement Line No. Parents or Spawners

9 Two Famous Models Developed in 1950s Both density dependent driven Ricker & Beverton-Holt

10 Ricker type relationship No. Recruits Replacement Line No. Parents

11 Beaverton Holt Stock Recruit Curves and Models No. Recruits Replacement Line No. Parents

12 General Characteristics of Models Pass thru origin Should not decline to abscissa (X) at larger stock Rate of recruitment (R/P or R/S) should decrease continuously with increase in parental stock (P or S) Recruitment must exceed parental stock over some part of the range, otherwise stock cannot persist.

13 1.2 Recruits 0.9 Curves and Yields A B A - B = surplus production Replacement Line 0 C Parents 1.0

14 Theoretical relationship between adult stock and progeny returning as adults Reproduction curve can be expressed as a ratio R/RE = P/PE e [Pe-P/Pm] When R is the filial generation P is parent generation PE is equilibrium stock (replacement); Re is filial generation reproduced by PE and Pm is stock that produces maximum recruitment

15 By placing R and S (or P) in the same units (eggs or spawning adults) The denominators are equal and thus the equation is reduced to : R = P e [(Pe-P)/Pm] ---- R/S = e [(Pe-P)/Pm] The two parameters Pe and Pm Equilibrium and Maximum determine particular curve from a family

16 Ricker Curve R = αp exp -βp R = Recruits P = Parent stock or R = P e a(1-p/pr) α = dimensionless parameter Rm βe β = parameter with dimensions 1/Pm Rm = maximum recruits Pm = Parental stock that provides max recruits

17 Simplest form R = αp exp -βp R/P = a exp -βp For hints on ln transformation steps see cheat sheet. Solve for slope at equilibrium by plotting ln R/P against P, fit with Least Squares Regression or other regressions to determine generalized parameters

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19 Beverton-Holt Beverton, RJH and SJ Holt On the dynamics of exploited fish populations. Fisheries Investment Series 2 Volume 19, UK Ministry of Agriculture and Fisheries R = 1/{α + β / P} R = Recruits P = Parent stock α = dimensionless parameter (considered ~ max rate repro) β = parameter with dimensions (compensatory mortality as function of stock size)

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21 Solutions 1/R = α + β/p P/R = β + α P With either linear solution you estimate 1/R and therefore must correct for this

22 Ricker assumed that densitydependence was based on mobile, aggregating predators Beverton-Holt assumed that predators were always present

23 Problems with Both Predation can occur in constant rate. If spawning stock becomes very small. They may not be able to produce enough recruits to recover to previous levels Do not account for numbers of spawners becoming so low that compensatory mechanisms can no longer occur Inability to find mates (or low fertilization success) with low broodstock numbers problems with ecosystem functions etc.

24 Simple Case for Exploitation Slope of descending leg determines the type of population cycles that would occur. If population is in descending leg then a slope of 1 will result in undampened oscillations of equal magnitude about the equilibrium point. Slopes between 0 and 1 will cause oscillations about the equilibrium point.

25 Slopes between 1 and inf will cause oscillations up to the apex of the dome, and then the series of oscillations would be repeated

26 Multiple age spawning stocks Smaller deflections from equilibrium Populations with reproduction curves having descending legs and slopes between 1 and 1 all eventually become stable

27 Yield or exploitation for desired equilibrium Yield is that portion of a fish population removed by humans Units are generally weight per unit time or unit area Production is the total elaboration of new biomass at the trophic level under consideration generally within some spatial and temporal unit

28 E = 1 0C/AC = 1 BC/AC 1.2 A = surplus equilibrium Recruits Arbitary units 0.9 B Replacement Line 0 C Parents Exploitation = 1 (0.9/1.2) = 0.25 or 25% of the stock

29 Exploitation E = 1 OC/AC = 1 BC/AC If B is 0.9 units of stock; A is 1.2 units, then the calculation would be E = 1 (0.9/1.2) or 0.25 or 25% of the stock

30 Surplus Production The objective of models is to determine the optimum level of effort, that is the effort that produces the maximum yield that can be sustained without affecting me long-term productivity of the stock, the so-called maximum sustainable yield (MSY). The theory behind the surplus production models has been reviewed by many authors, for example, Ricker (1975), Caddy (1980), Gulland (1983) and Pauly (1984).

31 Maximum Sustainable yield The highest theoretical equilibrium yield that can be continuously taken (on average) from a stock under existing (average) environmental conditions without affecting significantly the reproduction process.

32 Surplus Production Models Catch A 0 Effort

33 For instance, the accuracy of MSY estimates depends upon such measures as rates of growth, mortality, and reproduction that are difficult to determine and that change over time. As a result, scientists generally produce a range of estimates for MSY, based on different assumptions.

34 Peter Larkin, 1977 An epitaph for the Concept of Maximum Sustained Yield TAFS 106:1-11 MSY 1930s Here lies the concept MSY It advocated yields too high And didn t spell out how to slice the pie. We bury it with the best of wishes Especially on behalf of fishes We don t know yet what will take its place. Be we hope it s as good for the human race. R.I.P