Application of a Maximum Sustainable Yield Model
to White Sturgeon (Acipenser transmontanus)
Erin M. Collins
Advanced Ecology
Fall 2012
INTRODUCTION
ABSTRACT
White sturgeon populations have been in
decline for more than a century. The decline is
due to the take of mature spawning fish and not
attributed to general over fishing. White
sturgeon do not reach sexual maturity until they
are approximately 15-25 years old and can live
upwards of 100 years. Although their numbers
are in decline, there is still an active fishery for
white sturgeon. In order to protect the spawning
population and provide a fishery for anglers, a
restricted fishery has been enacted. Take is
restricted to fish between 46-66 inches and one
angler may keep only three fish per year, this is
monitored by a report card system.
Maximum sustainable yield is a
management tool created in the 1930’s as a way
to combat worldwide declines in global fisheries.
This tool seeks to determine the maximum
exploitation level a population can handle
without crashing. The idea is that is a population
is held at a level where it is growing at its
maximum, that there will be a surplus of
individuals available for harvest.
OBJECTIVE
The purpose of this project was to apply a
maximum sustainable yield model to an artificial
white sturgeon population.
METHODS
The model chosen for this project was a
combination of logistics growth and the
Graham-Schaefer sustainable yield equation.
Equations for maximum sustainable yield and
equilibrium were taken from the literature.
Reasonable values for the parameters were
adapted from the literature as well as
knowledge of the life-history of white sturgeon.
Actual values could not be found in the
literature.
A simple maximum sustainable yield model was
applied to an artificial white sturgeon population. The
model was an adaptation of the logistics growth model
and the Graham-Schaefer surplus production model.
The application was unsuccessful. The population
crashed with the addition of the harvest. This was most
likely a result of user error and artificial data used in
the model.
RESULTS
I could not get the model to work with the parameters
that I selected. I used the calculated maximum sustainable
yield value of 1,563 tons but the population crashed. Then I
tried to use the yield equation instead, value is 138, but this
also crashed the population. When population equilibrium at
maximum sustainable yield was calculated I got a negative
number.
Model Equations
Logistics growth
dN/dt= rN* (1-N/K)
Graham-Schaefer
Y = qEK- (q2KE2/ r)
Population growth
with yield
dXt/dt =rXt *1-(Nt/ K)qEtX
Model Parameters
Nt
X0
q
r
Et
K
25,000
628 tons
0.11
0.20
2 trips
3,125
tons
DISCUSSION
Table 1. (Left) Equations used to calculate maximum
sustainable yield model.
Maximum
sustainable yield
Steady State
MSY= rK/4
Table 2: (Above) Values used in calculation of maximum
X= K-qEK/r
sustainable yield and yield calculations.
Definitions of parameters
N= population size
X= population biomass
Y= yield
r= intrinsic rate of increase
K= carrying capacity
Figure 1: Graph shows how the sturgeon population biomass
behaves under logistics growth alone. The population
increases until its carrying capacity when population growth
E= fishing effort
slows down.
q= catch ability quotient
Figure 3: The study subject white sturgeon Acipenser
transmontanus.
Figure 2: Graph shows the effect of harvest on the
populations biomass. Harvesting at both maximum
sustainable yield and calculated harvest levels caused a
crash in biomass.
I could not successfully model the sturgeon
population using the maximum sustainable yield
equations that I found. When deciding on a model I
had many to choose from, which leads me to
believe that there is not one single model, and that
not every model will work for each type of species
out there. When modeling sturgeon, the model will
need to include parameters for slot limits and life
stage. Data on their population growth rates and
their catch ability will also need to be readily
available for use in the models, they currently are
not published anywhere. I believe that because I did
not have access to any data and therefore had to
make up the model parameters, that I ultimately
caused my population to crash no matter the values
that I used.