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Paper by Owen Bullard and Pamela Young, December 1990 ofr a class in optimization, Virginia Tech
INTRODUCTION
History of the Turkey The wild turkey (Meleaqris gallopavo) is a game bird found throughout the united states. It is one of the finest upland game birds and has immense economic, recreational, and esthetic value (Virginia commission of Game and Inland Fisheries, 1942). This bird is quite important to hunters and nonhunters. When the country was first founded, the wild turkey was being considered as the national bird instead of the bald eagle (Hewitt, 1967). This bird was quite valuable to early settlers as a food source (Hewitt, 1967).Without the turkey a lot of the first settlers at Jamestown may have starved (Virginia commission of Game and Inland Fisheries, 1942). As the country became more settled, the turkey was exploited by settlers and Indians, and the accompanying loss of habitat due to settlement caused the turkey population to decline to a dangerously low number. The turkey was extirpated in some states (Hewitt, 1967). The turkey is at present making a comeback due to better habitat conditions and transplanting of birds (Hewitt, 1967). A result of this resurgence is that the turkey has again become an important game species. Mosby (1973) stated that the importance of the turkey as a sporting species has increased greatly since 1943.It is worthwhile for game managers and private land owners to consider the worth of the turkey as a game bird and the money that some hunters are willing to pay for quality turkey hunting habitat. One aspect of turkey habitat manipulation, turkey food plots,will be examined here.
Why study Turkey Food Plots
Turkey food plots, and food plots in general, are used by many state agencies as a means of supplementing food needed at critical times of the year.Food plantings were found to be a principal management tool in Virginia for turkeys (Mosby, 1940). Deer, rodents, and other animals compete with turkeys for mast (Schorger, 1966) so food plantings help supplement natural foods. The Virginia Commission of Game and Inland Fisheries (1942) showed that food plantings make up deficiencies in natural food supplies and provide a more even distribution of food over their range. Larson (1966) stated that these plots are essential for edge effect and supplemental food. It was found among managers that agricultural treatment of openings and supplemental food plantings are essential for forest game species (Larson, 1966). Korschgen(1967) stated that food patch planting helps insure against food scarcity.He further stated that food plot plantings proved to be favorite feeding grounds of turkeys in Virginia. Since food plots are demonstrated to be widely needed and widely used, study of their composition, size, and distribution is needed to ensure proper management. The composition of food plots will be examined here.
Problems with Existinq Compositions of Food Plots
Food plots are designed with a variety of seed mixes.These seed mixes are recommended by preference data and are extremely variable between different managers.Major problems exist with these seed mixes, however. One problem is that the cost of buying seed is often very high (Smart, Rayburn, and Sanders, 1972) especially for investing in a game bird . Another major problem with these seed mixes is that they are typically designed using food preference data. This method of selection does not take into account nutritional requirements or cost of seed (Smart, Rayburn, and Sanders, 1972). Food plots must use palatable foods but nutrition of foods chosen is extremely important. Analysis has not been done relative to palatability, nutrition, and cost of seed mixes (Smart, Rayburn, and Sanders 1972). Since food patches are quite expensive to maintain, costs can be lowered by using a cost minimization procedure, relative to nutrients needed and obtained, and palatability analysis.
Objectives
The problem to be solved then is what is the best seed mix that turkeys will eat, satisfies their nutritional requirements, and minimizes the cost of seed. The objectives then are as follows:
The overall objective here is to examine the seed mix itself and nutrient content of this mix Other costs are incurred when planting food plots but they will not be considered in. this analysis.
Why Use Linear Programming
With increased biochemical analysis of nutrients contained in seeds, increased operations research, and computer capabilities, linear programming provides a better way than in the past for managers to minimize costs and maximize benefits (Smart, Rayburn, and Sanders 1972). With more seeds and seed mixtures available and the corresponding desire to obtain stipulated percentages of nutrients, the mathematical process of linear programming provides an efficient way to obtain optimum mixes (Crampton and Harris, 1969). Linear programming further provides a way to incorporate cost into the mix. As stated by Crampton and Harris (1969), "What is the least-cost formula that meets the stipulated nutrient makeup?"Linear programming is the best way to solve this problem. Using linear programming will obtain the above objectives in an efficient manner.
METHODS
A literature search was done to obtain the data needed for this project. Data gathered were about crops to be planted in the food plot, cost of the crops to be planted, nutritional content of seeds, nutritional requirements of turkeys, size of the plot, and proportion of each crop allowable in the turkeys' diet. These data was developed into the objective function and constraints for the model.
Objective Function
The objective function was obtained by first finding the crops to put into the food plot. Crops to be planted are corn (Zea mays), oats (Avena sativa), wheat (Triticum spp), barley (Hordeum vulqare), milo (Sorghum vulgare), cowpeas (Vigna spp) , clover (Trifolium spp), and chufa (Cyperus esculentus). Korschgen (1973) and Marsden and Martin (1949) recommend corn as a valuable turkey food. Marsden and Martin (1949) stated that corn provides needed nutrients when mixed with other feeds and helps with fattening. Stoddard (1935), Korschgen (1973), and Marsden and Martin (1949) stated that oats are a valuable food which helps with growth, feathering, and prevention of gizzard erosion. Wheat is recommended by Marsden and Martin (1949), Virginia Commission of Game and Inland Fisheries (1942), and Stoddard (1935). Wheat helps with fattening of turkeys. Barley is an excellent food recommended by Marsden and Martin (1949). Milo is a suggested food by Stoddard (1935), Marsden and Martin (1949), and Korschgen (1973). Cowpeas are recommended by all the authors previosly mentioned, as is chufa. Chufa is an extremely good source of fat and protein and is widely used by managers as turkeys prefer it. Ladino clover, although not mentioned by any of the above authors, is being increasingly used by managers and is a good source of protein and other nutrients. Marsden and Martin (1949) showed that nutritional requirements are met by mixes of these feeds. They further explained that combining these feeds allow turkeys to obtain the vitamins and minerals they need along with the nutritional constraints stated below.
| Table 1. Prices of seed. (1990) | |||
| Price/pound | lb/acre | Price$/acre | |
| corn | 1.50 | 30 | 45.00 |
| Oats | 0.30 | 60 | 18.00 |
| Barley | 0.30 | 60 | 18.00 |
| Wheat | 0.30 | 60 | 18.00 |
| Milo | 0.85 | 40 | 34.00 |
| Chufa | 1.00 | 25 | 25.00 |
| Clover | 2.75 | 5 | 13.75 |
| Cowpeas | 1.00 | 25 | 25.00 |
The objective function is: Based on this information the
Min Z = 45.00 corn + 18.00 oats + 18.00 barley + 18.00 wheat + 34.00 milo + 25.00 chufa + 13.75 clover + 25.00 cowpeas
with the general form
Min Z = C X
where X is in units of acres, and C is in units of dollars per acre.
Constraints
After obtaining the objective function, constraints were then found for the model. Nutritional requirements of turkeys were the first constraints to be looked at. Values for nutrition needed by turkeys were found in Hewitt (1967). The values needed were as follows and are on a percentage of diet basis: Protein Fat Carbohydrates Crude Fiber Calcium Phosphorous
| Protein | 13 % |
| Fat | 2 |
| Carbohydrates (NFE) | 64 |
| Crude Fiber | 8 |
| Calcium | 1 |
| Phosphorus | 0.3 |
Water makes up the rest of the percentages in the diet along with other vitamins and minerals.Based on these values then, the additive effects of crops or the percentages of those nutrients in each crop when added must be greater than or equal to the above. Table 2 is a summary of percentages of nutrients in each crop. These values were obtained from Marsden and Martin (1949) and King and McClure (1944).
The next constraint is the land constraint. Although this is quite variable between managers, the size of a plot must be larger than a half acre in size(Virginia commission of Game and Inland Fisheries 1942). For purposes of this model it was found that in order to satisfy nutritional constraints the plot must be greater than or equal to two acres in size. This value can be changed to fit management needs as long as it never falls below two. To simplify our model, ten acres were used in the land constraint.
The last set of constraints to be considered is the percentage of diet permitted for each food. These values were obtained from Marsden and Martin (1949). Corn must be between 30 and 50 percent of the diet. Wheat should never be more than 55 percent of the diet. Oats are suggested to be 10 to 50 percent of the diet but when combined with barley the addition should not be more than 60 percent. Barley and wheat added together should be less than 70 percent. It is recommended that milo be less than 40 percent of the diet.Marsden and Martin (1949) also recommend a mix of at least 2 different feeds. Korschgen (1973) stated that most individual foods are nutritionally deficient but that combinations of foods made up for deficiencies. This model ensures this mix because corn and oats are always planted along with other feeds. A limit is therefore put on feeds not mentioned implicitly by the model.
The Matrix
Using the above data we can then design the matrix to be used as the model. Table 3 shows this matrix and is summary of the above data. Values for crops are in acres. The objective function value Z is in dollars, and the coefficients are in dollars per acre. Nutritional values are on a percentage basis, the land constraint is in acres, and the percent in diet is calculated on an acre basis. This is the model to be solved.
RESULTS AND DISCUSSION
Running the linear programming problem as it was first set up (Table 3) resulted in an infea_ible solution. Looking at the output (Figure 1 See Giles for xerox copies of LINDO runs and complex tables too lengthy and difficult to present here.), it was noticed that the surplus variable in row 6 had a value of -.09. The reason is that this constraint cannot be met. Turkeys need calcium in at least one percent of their diet. Because of two constraints on corn in the model,calcium will nevef be satisfied. According to (Marsden and Martin 1949), corn should make up 30 to 50 percent of the food mix. Corn is made up of only 0.0l% calcium and none of the other plantings are rich enough in calcium to supply the amount needed for turkeys. Therefore, calcium will never be satisfied because of the constraint for the amount of corn needed.
The calcium constraint was dropped from the problem.It was determined that calcium would be supplied in the insects that are eaten by turkeys. A sufficient amount, 10 percent of the diet, (Korschgen, 1967), of insects is eaten by turkeys and will supply the calcium needed because insects are comprised of 1-17 percent calcium (Beck and Beck, 1955).
| Table 4. Optimum composition of a turkey food plot found using linear programming (program Lindo) | |
| Planting | Acres |
| Corn | 3.0 |
| Oats | 1.0 |
| Wheat | 0.0 |
| Barley | 0.0 |
| Milo | 0.0 |
| Cowpeas | 0.0 |
| Clover | 6.0 |
| Chufa | 0.0 |
| Table 5. Shadow prices calculated by linear programming for the model's constraints | |
| Constraints | Shadow Prices |
| Protein Needed | 0 |
| Fat needed | 0 |
| NFE needed | 0 |
| Crude fiber needed | 0 |
| Phosphorus needed | 0 |
| Land plot size | 13.75 |
| Max. corn allowed | 0 |
| Min. corn allowed | 31.25 |
| Whest allowed | 0 |
| Min. oats allowed | 4.25 |
| Max. oats allowed | 0 |
| Wheat and barley allowed | 0 |
| Oats and barley allowed | 0 |
| Milo allowed | 0 |
This model was set up with a few assumptions. It is assumed that the turkeys will eat these crops. It is assumed that turkeys will eat these foods to satisfy their nutritional requirements and not their preference. The nutritional requirements are based on a maintenance diet.It is assumed that the nutrients in the individual plants are additive.It is also assumed that proper planting procedures are followed and that one hundred percent of the seed planted grow.
Based on the model and its assumptions, the optimum food patch is composed of three acres of corn, one acre of oats, and six acres of clover. Clover is an extremely good turkey food because it is inexpensive to plant and it satisfies nutritional requirements. Corn and oats are in the food mix because of the minimum required of each in the plot. The other foods are not optimal because they are too expensive for the nutrition they provide.
This model has some limitations. It does not include energetics. Calcium is not included because the seed mix will never have enough due to other constraints. The model does not include turkeys' preference of food. The model also does not include the yield of planted crops or the other costs involved with planting the plots. Another limitation is that seasonality is not considered. Different crops are planted in different seasons and this was not considered here.
This model is a suggestion of methods for attaining optimum food plots. Future research should be done in order to increase the knowledge of food plots. The optimum size, depending on the number of animals using the food plot, has to be determined. This model arbitrarily uses ten acres because optimum size and number of turkeys were not considered. But if the number was known, an optimum size for that number will be used in the land constraint. Other research that needs to be done is finding the turkeys' food preference.In this model, the palatability of food was used. But even if a food is palatable, a turkey might prefer another food. A model that uses nutritional value relative to food preference would be the best model for determining a food plot.This model would allow a turkey to receive its nutrients from the food it prefers.
This model is a starting base for all other related models. The coefficients for cost can easily be changed, which is needed since costs are dynamic. The seeds can also be changed when research is done to determine the foods preferred. The constraints can also be altered. This model can be used as a suggestion for other species, seasonal diets, and regions in the world. Other projects can include natural foods rather than just planted foods Obtaining the optimum mixture of food plots will be a useful tool for wildlife managers, and future research should be done to improve this model and to obtain relevant information for other models.
References
Beck J.R. and D.O, Beck. 1955. A Method for Nutritional Evaluation of Wildlife Food. J. Wildl. Manage. 19(2):200.
Crampton, E.W. and L.E. Harris. 1969. Applied Animal Nutrition. W.H. Freeman and company, San francisco. 735 p.
Hewitt, Oliver H, (ed). 1967. The Wild Turkey and its Management. The Wildlife Society, Washington D.C. 589 p.
King, Thomas R. and Harold E. McClure. 1944. Chemical Composition of Some American Wild Feedstuffs. J. Agriculture Research 69 (1) : 33-47.
Korschgen, Leroy J. 1967. Feeding Hapits and Food in Oliver H. Hewitt (ed). 1967. The Wild Turkey and its Management. The Wildlife Society, Washington P.C. 589 p.
___ 1973. April Foods of Wild Turkeys in Missouri. in Glen C. Sanderson et al. 1973. Wild Turkey Management. University of Missouri Press. Columbia, Missouri. 355 p.
Larson, J.S. 1966. Wildlife Forage Clearings on Forest Lands--A critical Appraisal and Research Needs. Masters Thesis, Virginia Polytechnic Institute and State University. Blacksburg, Virginia. 143 p.
Marsden, Stanley J. and J. Holmes Martin. 1949. Turkey Management. The Interstate. Danville, Ill. 774 p.
Mosby, Henry S. 1973, The Changed Status of the Wild Turkey Over the Past Three Decades in Glen C. Sanderson et al. 1973. wild Turkey Management. University of Missouri Press. Columbia, Missouri. 355 p.
Schorger, A.W. 1966. The Wild Turkey: Its History and Domestication. University of Oklahoma Press. Norman, Oklahoma. 625 p.
Sanderson, Glen C. 1973. Wild Turkey Management. University of Missouri Press. Columbia, Missouri. 355 p.
Smart, Charles W., Edward B. Rayburn, Oscar T. Sanders. 1972. Formulation of an Optimum winter Food-Patch Mix for Bobwhite Quail. Proceedings, First National Bobwhite Quail Symposium. pp. 366-372.
Stoddard, Herbert L. 1963. Maintenance and Increase of the Eastern Wild Turkey on Private Lands of the Coastal Plain of the Deep Southeast. Tall Timbers Research Station. Tallahassee, Florida. 49p.
Virginia Commission of Game and Inland Fisheries. 1942. The wild turkey in Virginia, Education Div., Richmond, VA 45p.
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