Oyster Production in Barataria-Terrebonne National Estuary

GIS in Water Resources

Travis Warziniack

December 7, 2000

Table of Contents

• Introduction
• Natural Production Functions: Economic Theory
• Study Area
• Data Collection
• Graphical Analysis
• Comparison to GIS Data
• Implications and Future Work
• References

Under current estimates, by the year 2040, Louisiana will have lost 868,000 acres of coastal wetlands.  Some of this loss will result in the displacement of entire towns now located in Southern Louisiana.

Any sort of restoration plan will inevitably affect the lives of thousands of people living in the southern parishes.  The fishing industry alone supports at least 50,000 jobs in Louisiana, bringing in an estimated $1 billion per year.

Many of the restoration plans involve increasing the freshwater-saltwater ratio in order to preserve native plants and wildlife.  While the fishing industry should see positive net gains, some will probably suffer.  Introducing freshwater will result in a forced relocation of oyster beds, which survive in a relatively narrow salinity range. 

The purpose of my project is to examine the link between wetland salinity and the productivity of oyster producing zones off the coast of Louisiana.  What does changing salinity levels mean for fishermen who are leasing the present beds?  This will largely be done by comparing time series trends among several gauging stations within the Barataria-Terrebonne National Estuary.

A developing theme in environmental economics is the state of nature as an input into natural production processes.  Natural production processes include farming, fishing, and in this case, oyster harvesting.  

 The theory describes species population size as a function of a variable called maximum potential biomass.  This is the size a species population would reach given no outside influences.  In practice, maximum potential biomass is unobservable but largely assumed to depend on the quality of habitat.

Oyster production zones in coastal Louisiana are leased out by government agencies according to geographic location. As the Louisiana coastline moves in, the saltwater freshwater barrier moves in as well.  This has huge impacts on oyster leases near that barrier and is the justification for using salinity level as a proxy for maximum potential biomass. 

We derive a production function for oyster harvests (where output is measured in the number of oysters) with two inputs, fishing effort and another that is some function of salinity level.  Derivatives of this production function with respect to either of the inputs give the marginal product of that input; these marginal products can be used as a measure of the value added to oyster harvesting by an additional unit of the input. 

 The economic model can be directly derived from biological theory on the growth of natural populations.  Schaeffer (1954) derived a relationship that can describe each species population as a function of the habitat available.  Without any human intervention, the natural population would grow in a logistic manner.  Let  B*  be the maximum possible population size given a fixed habitat, B(t) be the population size at time t, and a and b be growth parameters.  The logistic function is:

(1)        

Differentiating this function with respect to time provides

(2)        

Lynne (1981) describes aB(t) as the "increase potential" of a population and  as the "resistance to growth."  Notice that

for every B(t) < B*.

The above model holds fixed the state of nature, or the maximum potential biomass.  If B(t) is observable, then knowing B* and a  implies that one could, with some degree of certainty, predict the changes in population size over time.  In practice, B* is rarely known; this issue is addressed later. 

Dividing both sides by B(t) gives an expression for the growth rate of the species population.

(3)        

People are introduced into the model as a predators; they produce a flow variable called "catch," C(t) that will depend on their choice of effort level H(t).  It is assumed that effort exhibits diminishing marginal returns.  That is, catch can be increased by raising the effort level, but only up to a point.  Beyond this point, called the maximum sustainable yield (MSY), C(t) becomes a decreasing function of H(t).   If natural carrying capacity is held constant, then the population must decrease as the catch increases. 

 Let us now define a function  F[H(t)] to describe the rate of loss, or subtraction from the rate of growth, of the biomass due to effort, H(t).  That is, F[H(t)] is the catch as the fraction of the stock 

(4)        

Accounting for the presence of man, the new growth rate becomes

(5)        

For simplicity we assume F[H(t)] to be  a linear function of H(t), so  where k is a constant.  Plugging this into equation (4) and setting the growth rate to zero gives the condition for steady-state oyster population with a positive catch:

(6)        

Plugging  into equation (4) and solving for B(t) yields .  Substituting this into equation (6) for B(t) and solving for C(t) provides

(7)        

The Problem

Unfortunately, the above is dependent on B*, an unobservable variable, so we look for a reasonable instrument for B*.    It is assumed that larger fish populations can live in better and larger habitats, or conversely, that reducing the size or degrading the habitat reduces the maximum potential population.  Previous research efforts have used a function of wetland acreage as a proxy of B*, namely .  This implicitly assumes that wetland acres are homogenous, when in fact, the actual productivity of any one acre of wetland is quite unique.

This research looks at salinity levels and their effects on oyster production in hopes of developing a better proxy for maximum potential biomass.  Salinity, by nature, is a local phenomenon, and thus should serve well for an approximation for B*.  We assume a priori no functional form for this proxy, only that

where S(t) is the salinity level in time t.

Plugging this into equation (6) gives the following theoretical model with observable variables:

(8)        

To a very large extent, the above equation is meaningless unless a relationship can be drawn between salinity level and catch in time t.  GIS will be used in the remainder of this project to examine this relationship.

This study is limited to the Barataria-Terrebonne National Estuary (BTNE), a region of wetlands in South Louisiana bounded by the Mississippi River on the east and the Atchafalaya River on the west.  Spanning a large portion of the Louisiana coast, the BTNE is a large player in the state economy. 

In 1994 alone, estuary-related industries accounted for almost $3.5 billion in revenues.  This figure includes $204 million in commercial fishing, $308 million in agriculture, $11 million in aquaculture, and $7 million in commercial hunting and trapping (The Executive Summary, 1996).

            Fig. 1: Enlarged view of Barataria-Terrebonne National Estuary

Data Collection  

Historic bottom salinity values were taken for the years 1989-1992 for 22 gauging stations throughout the BTNE.  These values are part of a publication by the Barataria-Terrebonne National Estuary Program (BTNEP) entitled The Oyster Resource Zones Within Louisiana's Barataria and Terrebonne Estuaries.  Due to time constraints, data from selected gauging stations were entered into an Excel spreadsheet and graphed to provide a visual representation; these graphs are included in the Results section of this paper. 

GIS:

          GIS data for the entire state of Louisiana can be downloaded from the Louisiana Atlas website.  The Atlas website is maintained by the CADGIS Research Laboratory at LSU in Baton Rouge, Louisiana, a lab supported by the LSU College of Design and the Department of Geography and Anthropology.  The site began with work related to the Louisiana Coastal GIS Network, and has developed over the last three years to become a comprehensive source for Louisiana GIS data.

          Data obtained from the Atlas site includes shapefiles of the outline of Louisiana, the Louisiana coastal zone, cities, reach files of the Louisiana rivers and major bodies of water, 25k Quads, salinity zones across South Louisiana. 

Atlas: Statewide GIS data for Louisiana

Graphical Analysis

Several gauging stations were chosen as a representative sample of the BTNE.  The following stations were selected based on their relative dispersion throughout the estuary as well as the completeness of monitoring data:

Table I: Salinity Monitoring Stations in Barataria-Terrebonne National Estuary

Hackberry Lake has had salinity levels considered conducive to oyster production, and indeed, traditionally oysters harvests in the lake have been plentiful.  Therefore, the remaining gauging stations salinity levels have been graphed against those of Hackberry Lake.  By clicking on the station names in the chart, one can visually compare the historic salinity levels.

The graphs show that Upper Lake Mechant (Station 61) and Wonder Lake (Station 70) have low historic salinity levels.  Bayou Grand Caillou (Station 65) has salinity levels within the ranges defined by Hackberry Lake.  Terrebonne Bay (Station 72), Lower Lake Felicity (Station 73), and Timbalier Bay (Station 75) all have salinities that may be too high to support oyster production.  High peaks in salinity levels open oysters to disease and predators.   

Fig 2: Shapefile Representation of Salinity Levels in BTNE

The historic levels can be compared with maps of salinity levels produced by the State of Louisiana.  Projecting the gauging stations onto the map in Figure 2 shows the location of the stations with respect to salinity zones throughout the estuary.  Those stations considered to have salinity levels conducive to oyster production lie within the Saline Zone.  Those sites with salinity levels considered low lie within the Intermediate to Brackish Zones, and those with high salinity peaks lie beyond the Saline Zone in fairly open water.

The above results were compared to responses given during a study by the BTNEP by oystermen with leases in the area.  The responses were consistent with the predictions, i.e., high producing leases tend to like within the Saline Zone.

Figure 3: 24k Quads of BTNE

Figure 3 shows a map of BTNE overlaid with a 24k grid.  Quad 43, for example, contains 79 oyster leases ranging in size from 3 to 939 acres.  Some of these leases last until the year 2015.  At the current rate of coastal erosion and saltwater intrusion, salinity conditions will not persist for any one acre through the duration of the lease.  These changes can have large monetary consequences if the productivity of the lease changes dramatically.

The exact location of the oyster leases throughout South Louisiana can be obtained from the Louisiana Department of Wildlife and Fisheries via their web page.  The location of each lease has not been added to this model.  This would require large amounts of work for marginal gains in information.

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