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Estimation of endogenous phosphorus loss in growing and finishing pigs fed semi-purified diets^1,2

Department of Animal and Food Sciences, University of Kentucky, Lexington 40546

	Abstract

Top Abstract INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION LITERATURE CITED

 
Thirty-six barrows were used in a series of 3 P-balance experiments in which growing and finishing pigs were fed highly digestible, semi-purified diets at or below the dietary available P requirement to estimate the effect of BW on endogenous P loss. Experiments 1, 2, and 3 were conducted with pigs averaging 27, 59, and 98 kg of BW, respectively. In each experiment, pigs were placed in metabolism crates and allotted by weight and litter to 3 dietary treatments. The basal diet consisted of sucrose, dextrose, cornstarch, and casein fortified with minerals (except P) and vitamins. Diets 1, 2, and 3 in Exp. 1 were the basal diet with 0, 0.078, or 0.157% added P, respectively, from monosodium phosphate. In Exp. 2 and 3, diets 1, 2, and 3 were the basal diet with 0, 0.067, and 0.134% added P, respectively, from monosodium phosphate. Within replicate, pigs were fed equal amounts of feed twice daily. Pigs were adjusted to treatments for 7 d before a 6-d, marker-to-marker collection of feces and urine. Phosphorus intakes for pigs fed the 3 diets ranged from 1.73 to 3.91 g/d in Exp. 1, from 2.18 to 5.32 g/d in Exp. 2, and from 1.96 to 6.26 g/d in Exp. 3. Fecal P excretion and P absorption increased linearly (P < 0.05) with increasing P intake. In the 3 experiments, urinary P excretion (g/d) was low for pigs fed diet 1 (0.010, 0.011, 0.019) and diet 2 (0.013, 0.058, 0.084) and was low for pigs fed diet 3 in Exp. 1 (0.037); however, urinary P was greater in pigs fed diet 3 in Exp. 2 and 3 (0.550 and 0.486, respectively). When P absorption (Y, g/d) was regressed on P intake (X, g/d) in Exp. 1, 2, and 3, the relationships were linear (P < 0.01): Y = –0.110 + 0.971X (R² = 0.999), Y = –0.156 + 0.939X (R² = 0.998), and Y = –0.226 + 0.8919X (R² = 0.982), respectively. Thus, our estimates of endogenous P loss at zero P intake were 110, 156, and 226 mg/d for 27-, 59-, and 98-kg pigs, respectively. When these Y-intercepts were regressed on BW, the relationship was Y = 63.06 + 1.632X (R² = 0.996), where Y = endogenous P loss in mg/d and X = BW in kg. Based on these data, we estimate the endogenous P loss of pigs fed highly digestible, semi-purified diets to increase by approximately 1.632 mg for each 1-kg increase in BW from 25 to 100 kg.

Key Words: endogenous • phosphorus • pig

	INTRODUCTION

Top Abstract INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION LITERATURE CITED

 
Estimation of dietary influences on P excretion in growing pigs is often confounded by the inability to partition total P excretion into indigestible dietary P and endogenous P. In addition, modeling P requirements for growing pigs includes a factor referred to as maintenance P, which is a reflection of endogenous P excretion from the feces and/or urine. This endogenous P excretion has been estimated to be approximately 7 mg/kg of BW; 6 mg/kg of BW are attributed to endogenous fecal P output, and 1 mg/kg of BW is attributed to urinary P (Jongbloed and Everts, 1992). Although the endogenous excretion of P may be a small percentage of the total P requirement for growing and finishing pigs, the value of determining this portion of the requirement is essential to understanding true P digestibility associated with dietary ingredients, as well as contributing to the factorial estimation of P requirements.

Endogenous P has been estimated by numerous methods, including feeding P-free diets (Peterson and Stein, 2004) and radiolabeled P (Fernandez, 1995). Another method that has been used to estimate the endogenous excretion of P, or P at zero P intake, is the regression method (Fan et al., 2001). This technique includes feeding multiple diets to growing pigs that are formulated at and below the dietary requirement for P to obtain linear relationships of P intake to P absorption. Very few estimates of endogenous P excretion by growing pigs at varying BW exist in the literature.

The purpose of these studies was to utilize highly digestible, semi-purified diets to estimate the P excreted by pigs at zero P intake, allowing for the estimation of endogenous P excretion by the pig with little or no influence from dietary ingredients. By conducting similar estimations at 3 different BW within the weight range of typical growing-finishing pigs, the effect of BW on endogenous P excretion could also be assessed.

	MATERIALS AND METHODS

Top Abstract INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION LITERATURE CITED

 
Three balance experiments were conducted with growing and finishing pigs at 3 different weights (27, 59, and 98 kg of BW). The experiments were conducted at the University of Kentucky (Lexington). In each experiment, 12 Yorkshire x Landrace barrows were allotted to 3 treatments in a randomized complete block design from outcome groups based on weight and litter. There were 4 replications per treatment. The studies were conducted under protocols approved by the University of Kentucky Institutional Animal Care and Use Committee.

Dietary Treatments
In each experiment, 3 diets (Table 1) were formulated with increasing levels of Ca and P that, when fed in equal daily amounts of feed, would incrementally increase the intake of Ca and P. Semi-purified diets were used so that digestibility of nutrients would be maximized. The major carbohydrate sources were sucrose (International Ingredient Corp., St. Louis, MO), dextrose monohydrate (Archer Daniels Midland Co., Decatur, IL), and cornstarch (National Starch and Chemical Co., Bridgewater, NJ). In each experiment, casein (acid-hydrolyzed casein, Glanbin Ingredients, Kilkenny, Ireland), which contained 6.82% lysine, 0.03% Ca, and 0.68% P, was included as a protein source at a constant level. Crystalline lysine, methionine, threonine, and tryptophan were included to meet the AA requirements (NRC, 1998). Corn oil was added as needed to make the diets isocaloric and reduce dustiness. To facilitate the passage and collection of undigested nutrients with pigs being fed such highly digestible diets, 4% cellulose (Solka Floc-40, Fiber Sales & Development Corp., Urbana, OH) and 1% sand (Short Mountain Silica, Mooresburg, TN) were added to each diet to serve as an indigestible fraction. Diets were fed in meal form.

Feces and Urine Collection
The pigs were individually penned in stainless steel metabolism crates in a temperature-controlled room. Pigs were weighed on the day that they were placed into the crates, the day that the initial indigestible marker was fed, and the day that the final marker passed at the conclusion of the balance period. The average of the 2 latter weights was termed the test weight and was used as the average weight for pigs in each study.

All pigs were acclimated to the metabolism crates for 2 to 3 d before a 7-d adaptation to their respective dietary treatments. During the dietary adaptation period, feed intake levels were equalized within replicate to that of the pig consuming the least amount of feed. All pigs were provided their daily allotment of feed in 2 feeding periods at approximately 0700 and 1600. During the collection period, refused or spilled feed (orts) was collected after each meal and either refed to the same pig at the next feeding or air-dried, weighed, and subtracted from the total feed offered to estimate daily feed intake. At the time of feeding, water was mixed with the diet at a ratio of 1 part water to 4 parts feed (wt/wt). Pigs were allowed ad libitum access to water between meals.

On d 1 and 7 of the collection period, pigs were fed their morning meal mixed with 0.5% Fe₂O₃ (Fischer Scientific), which served as an indigestible marker. Fecal collection commenced with the passage of the marker fed on d 1 of the collection period and ended with the final unmarked feces passed before that resulting from the marked meal fed on d 7. The collection of urine commenced 8 h after the feeding of the first marked meal and ended 8 h after the feeding of the second marked meal. Excreted urine was directed by a stainless steel, funneled pan beneath the metabolic crate into a 13.5-L container that contained 150 mL of 3N HCl (75 mL was used for 27-kg pigs) to prevent N volatilization. Urine was collected from the containers daily, and the volume was determined. The daily urine output was then mixed, and a 100-mL aliquant was taken and frozen. After each experiment was concluded, samples from each day were subsampled and combined in amounts corresponding to each day’s urine volume as a percentage of the total volume over the collection period.

Feces were quantitatively collected daily and frozen in plastic bags until the end of the experiment. At that time, the feces from each pig were weighed and then dried for 96 h at 55°C. Dried feces were allowed to air-equilibrate for 24 h before weighing and then were ground to pass though a 1-mm screen in a Wiley Laboratory Mill (Model 4, Arthur H. Thomas Co., Philadelphia, PA).

Chemical Analysis
Casein was analyzed for AA, Ca, and P before formulating the diets. Representative samples of diets and dried fecal samples were analyzed for DM and N (FP-2000, Leco Corp., St. Joseph, MI) concentration. Phosphorus concentration in feed and fecal samples was determined by gravimetric procedures after wet ashing. Urinary P was determined by colorimetric spectrophotometry. Calcium concentration in feed and fecal samples was determined by atomic absorption spectrophotometry after wet ashing. All procedures were according to procedures of the AOAC (2003). Amino acids in the casein were analyzed by ion exchange chromatography after acid hydrolysis. Methionine and cysteine were oxidized to methionine sulfone and cysteic acid by treatment with performic acid before hydrolysis. Tryptophan was analyzed after alkaline hydrolysis. Amino acid assays were conducted at the University of Missouri Experiment Station Chemical Laboratories (Columbia), and the other assays were conducted at the University of Kentucky.

Statistical Analysis
The data in each experiment were analyzed as a randomized complete block design (Steel et al., 1997) using the GLM procedure of SAS (SAS Institute, Inc., Cary, NC). The statistical model included the effects of block, diet, and block x diet (error). For the estimation of endogenous P loss at zero P intake, P absorption and P intake were analyzed for linear and quadratic relationships using regression analysis. For all other variables, orthogonal polynomials were used to partition treatment responses into linear and quadratic components. Unless stated otherwise, an level of P < 0.05 was considered statistically significant.

	RESULTS

Top Abstract INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION LITERATURE CITED

 
The analyzed CP, Ca, and P concentrations of the diets were close to the calculated levels, as shown in Tables 2, 3, and 4. Analyzed P contents of the 3 diets were 0.12, 0.19, and 0.26%; 0.09, 0.15, and 0.22%; and 0.06, 0.14, and 0.20%, for the 3 experiments, respectively.

All pigs were visibly healthy throughout each of the 3 balance studies. Average BW of pigs in Exp. 1, 2, and 3 were 27.2, 59.2, and 98.4 kg, respectively. All pigs gained weight during the course of the experiments; ADG of pigs in Exp. 1, 2, and 3 were 0.81, 1.27, and 1.41 kg/d, respectively (Tables 5, 6, and 7). Pigs consumed 1,488, 1,483, and 1,491 g/d of diets 1, 2, and 3, respectively, in Exp. 1; 2,384, 2,398, and 2,401 g/d of their diets in Exp. 2; and 3,227, 3,171, and 3,152 g/d of their diets in Exp. 3. Although pigs were meal-fed, feed intake averaged 98, 96, and 102% of estimated ad libitum intake (NRC, 1998) during Exp. 1, 2, and 3, respectively.

The P balance data for pigs in the 3 studies are shown in Tables 5, 6, and 7. As designed, P intake increased linearly (P < 0.05) as P content of the diet increased in each experiment. Across experiments, P intakes for diets 1, 2, and 3 averaged 44, 80, and 115% of the NRC-1998 estimated requirement for daily bioavailable P.

As pigs consumed increasing levels of dietary P, excretion of P in the feces increased linearly (P < 0.01) with increasing P in Exp. 2 and 3. A similar pattern was evident in Exp. 1, but the linear trend was not significant. Phosphorus absorption increased linearly (P < 0.01) with increasing P intake at each BW studied. When P absorption was calculated as a percentage of P intake, the efficiency of P absorption increased linearly (P < 0.01) with increasing P intake for 27- (Exp. 1) and 59-kg pigs (Exp. 2); however, in 98-kg pigs (Exp. 3), the response was quadratic (P < 0.01).

Urinary P excretion was extremely low (0.010, 0.013, and 0.037 g/d) and did not differ significantly with increasing P intake in 27-kg pigs (Table 5). In 59- and 98-kg pigs (Tables 6 and 7), urinary P excretion was comparatively low (0.011 and 0.017 g/d; 0.058 and 0.084 g/d) for pigs fed diets 1 and 2, respectively. However, for pigs fed diet 3, daily urinary P excretion increased to 0.550 (Exp. 2) and 0.486 g/d (Exp. 3). This response pattern was quadratic (P < 0.05) in Exp. 2. The quadratic trend was not significant in Exp. 3 because of the high variability of the urinary P excretion data (CV = 167.03%). However, when the urinary P excretion of pigs fed diet 3 in Exp. 3 was tested with LSD (Steel et al., 1997), the mean of 0.486 tended (P < 0.10) to be greater than the means of the other 2 treatments. Phosphorus retention increased linearly (P < 0.01) in Exp. 1 and 2 and increased quadratically (P < 0.01) in Exp. 3 as P intakes increased toward the requirement for dietary P. When expressed as a percentage of P intake, P retention increased linearly (P < 0.01) in Exp. 1 and increased quadratically in Exp. 2 (P < 0.05) and 3 (P < 0.01) with increasing level of P in the diet. The percentage of absorbed P that was retained was high (97.8 to 99.5%) for all treatments in each experiment except for the highest P level fed to 59- and 98-kg pigs in Exp. 2 and 3. In those instances, the percentages were 88.4 and 91.4%, respectively. The lower percentages for the high-P diets in these 2 weight groups were associated with the greater amounts of P excreted in the urine and were indicative that the P intakes were slightly above the P requirement.

In each experiment, the P absorbed (g/d) for each pig was regressed on the intake of dietary P (g/d), and these relationships are shown in Figures 1, 2, and 3. From the equations, the Y-intercepts can be assumed to be the best estimates of absorption of P at zero P intake. From the equations, the absorption of P at zero P intake was –110, –156, and –226 mg/d for 27-, 59-, and 98-kg pigs, respectively. It can be assumed that negative absorption is equal to positive secretion of P into the gut and ultimately excretion in the feces.

View larger version (9K): [in this window] [in a new window]   Figure 1. Relationship of P absorbed to P intake for 27-kg growing pigs (Exp. 1).

View larger version (9K): [in this window] [in a new window]   Figure 2. Relationship of P absorbed to P intake for 59-kg growing pigs (Exp. 2).

View larger version (10K): [in this window] [in a new window]   Figure 3. Relationship of P absorbed to P intake for 98-kg finishing pigs (Exp. 3).

View larger version (9K): [in this window] [in a new window]   Figure 4. Relationship of endogenous P loss to BW in 27- to 98-kg growing and finishing pigs (Exp. 1, 2, and 3).

	DISCUSSION

Top Abstract INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION LITERATURE CITED

The most important factor for the proper utilization of regression analysis to estimate endogenous P loss is to establish a linear relationship between total P intake and absorbed P from the diet (Fan et al., 2001). In each experiment, all diets were formulated with incrementally increased levels of dietary P up to the NRC- (1998) estimated requirement for pigs at each specific BW. Pigs were also not allowed ad libitum access to feed so that the incremental increases in dietary P could be reflected in daily P intake but also so that pigs fed the highest level of dietary P would not consume a daily P level beyond the NRC- (1998) estimated requirement. In these studies, P intake (g/d) of pigs fed diet 3 exceeded the NRC- (1998) estimated P requirement by 1.5, 11, and 28% for 27-, 59-, and 98-kg pigs, respectively. The NRC (1998) estimate of the requirement for daily P is based on maximal growth rate, and the requirement for maximal tissue retention is greater than that for growth (Combs et al., 1991a, b). Strong linear relationships of P intake to P absorption were observed at all BW tested, using each individual pig as data points, indicating the marked digestive response to added P when pigs are fed approximately at or below their requirement as well as the lack of variability in pig response when they are fed highly digestible diets.

The excretion of increased urinary P has commonly been used as an indicator of excess dietary P in pigs. Typically, urinary P >150 mg/dL is considered reflective of a pig that has consumed an adequate-P diet (Jongbloed, 1987). In these studies, urinary P was low at all 3 BW in pigs fed the 2 lowest P diets. Not until the daily intake of P neared the requirement (as with diet 3 in Exp. 2 and 3) did urinary P increase appreciably. This observation supports the idea that urine may not be a route of endogenous P excretion in the pig, but rather urinary P is responsive only to increases or decreases in dietary P levels that elicit intrinsic homeostatic mechanisms to control P balance in the body. Jongbloed and Everts (1992) utilized a factorial approach to estimate P requirements for growing pigs and assumed 1 mg of daily endogenous P loss via urine/kg of BW. In our studies, a linear relationship of P intake to urinary P excretion was not observed at any of the 3 BW tested; therefore, urinary P excretion at zero P intake could not be estimated. However, if the urinary P excreted (g/d) by pigs fed the 2 lowest dietary P levels in each experiment is averaged and presented similarly to Jongbloed and Everts (1992), the daily estimated endogenous loss would be 0.43, 0.59, and 0.52 mg/kg of BW for Exp. 1, 2, and 3, respectively. These estimates indicate that urinary endogenous P loss, if it does exist, is extremely minute, and the variability in our data does not lend confidence to including endogenous urinary P excretion in any model to estimate maintenance P requirements of growing pigs.

The estimates of fecal endogenous P loss indicated by these data are lower than those estimated in previous studies. Studies concomitantly conducted in nursery and heavy pigs fed semi-purified diets showed fecal endogenous losses to be 130 and 1,040 mg/d in 21- and 152-kg pigs, respectively (Rodehutscord et al., 1998). However, in their study, the researchers used an assumed true P digestibility (82.5%) for both weight groups to calculate endogenous loss, and the actual apparent digestibilities were 65 and 28%. It is doubtful that the assumed true P digestibility is applicable to both weight groups, and the low apparent P digestibility for the heavy pigs brings into question the selection of ingredients as sources of P for this experiment. In a survey of data conducted by the same researchers, fecal P excretion was regressed on P intake using pigs that had consumed low-P basal diets in previous mineral balance studies. The Y-intercept of the equation from their data estimated P loss to be 280 mg/d at zero P intake. The drawback from this estimation approach is that a wide range of BW was used in the survey, and the span of P intakes seemed to be approximately 0.75 to 1.95 g/d. This is a much narrower range than used in our studies, and P intakes did not reach approximate requirement levels. Both factors make determining linearity between intake and absorption difficult, and the slope of the line may not be truly reflective of the true digestibility of the diet.

A series of papers utilizing the regression method to estimate endogenous P has been published, where semi-purified diets containing a specific test feed ingredient (i.e., corn, soybean meal) were fed to pigs to ascertain the true digestibility associated with these ingredients. In those studies, the estimation of endogenous P losses ranged from 0.2 g/d (Ajakaiye et al., 2003) in 40- to 58-kg pigs, to 0.35 g/d (Fan et al., 2001) in 7- to 20-kg pigs, to 0.4 g/d (Shen et al., 2002) in 20- to 45-kg pigs. It should be noted that these values were not given by the researchers but were calculated from the data provided in their reports to be comparable with the current studies. Although these studies were conducted using similar methodology as our studies, the ranges in P intakes (g/d) of the 4 P levels fed were narrower and did not approach the estimated P requirement for the pigs. Additionally, feed ingredients with inherently reduced P digestibilities (phytate P) were used; therefore, any estimates of endogenous P losses may not distinguish between the true endogenous excretion from the pig and that from indigestible intake P.

The estimates from our studies may be lower due to the feeding of highly purified diets, which might not have elicited the same secretion of P-containing digestive enzymes or the sloughing of P-containing cells as compared with typical diets fed in commercial situations. However, any influence of dietary ingredients directly compared with a semi-purified control diet has still to be proven and can be addressed by the apparent digestibility estimates of feed ingredients used when estimating total dietary P requirements.

Regarding the effect of BW on endogenous P loss, our data show that endogenous P estimates (g/d) increased as BW increased. The metabolic and homeostatic mechanisms seem to simply be on a larger scale; as pigs were consuming greater amounts of feed, growth rate was increased, and total body mass (specifically gastrointestinal mass) was greater as BW increased. The influence of BW on endogenous P losses has not been extensively studied. A published report by Fernandez (1995) showed no effect of BW on the daily excretion of endogenous P when using a radiolabeled P technique. It should be noted that the compared difference in weight of pigs in the studies of Fernandez (1995) was smaller (35 and 65 kg of BW) than in our studies, where the greatest increase in endogenous P loss (on a g/d basis) occurred in pigs >60 kg. It is evident from the data that although the estimated daily maintenance requirement increases with BW, it is not in constant proportion to BW. This observation is in disagreement with previous estimates of the maintenance P requirements of Jongbloed and Everts (1992). Those researchers estimated endogenous P excretion to be 7 mg/kg of BW, which included 1 mg/kg of BW for urinary P loss, and they considered endogenous P excretion to be constant across the growth curve of the pig.

When endogenous P estimates at different BW are compared on the basis of their concentration to BW (g/kg of BW) in the current study, there does not seem to be a constant relationship as assumed by ARC (1981). In our studies, the endogenous estimates per unit of BW were 4.04, 2.63, and 2.30 mg/kg of BW for 27-, 59-, and 98-kg pigs, respectively. Previous estimates of endogenous P loss per unit of BW ranged from 5.5 to 7.0 mg/kg of BW (Jongbloed, 1987; Rodehutscord et al., 1998) and did not change with BW. Not only are our values lower than those reported previously, the excretion of endogenous P was higher, on a concentration basis, in younger pigs compared with older or heavier pigs. Whether this is a response to age, BW, or level of feed intake is not known. It does seem that, on the basis of unit of BW, the endogenous loss of P from growing pigs is not constant and may be responsive to the stage of development of digestive functions in the gut as well as P-utilizing tissues in the body. However, per unit of DMI, endogenous P estimates varied little in these studies with values of 0.08, 0.07, and 0.08 g/kg of DMI for 27-, 59-, and 98-kg pigs, respectively. Even though P levels in the diets were reduced below the estimated requirement, DMI was maintained near or above estimated ad libitum levels (NRC, 1998). This lack of any influence of DMI on endogenous P loss is in agreement with Rodehutscord et al. (1998), but does not correspond with the differences in endogenous P associated with corn (Shen et al., 2002) or soybean meal (Fan et al., 2001; Ajakaiye et al., 2003). However, the DM fed to the pigs in our studies was highly digestible and might not have had the same effect on digestive processes as the DM from conventional feed ingredients. Therefore, it may be necessary to distinguish between dietary effects on endogenous losses and inevitable P loss that is reflective of the true maintenance requirements of the pig.

Although the primary objectives of these studies were to estimate endogenous P losses at various BW, the data collected also provide an estimation of the differences in true and apparent digestibility of P in pigs fed similar diets and various BW across the growth curve. The comparison of the slopes of the regression equations generated by the relationship of P intake to P absorption is also a comparison of the true digestibility estimates for the average of the 3 levels of P intake at each BW tested. Pigs at 27 kg averaged 97% true digestibility of P, and pigs at 59 and 98 kg declined to 94 and 89%, respectively. This reduction in the efficiency of digestion by heavier pigs is in agreement with a survey of data summarized by Jongbloed (1987). However, numerous studies have shown opposing results, where heavier pigs have shown increased digestibility of all nutrients, not only P (Kemme et al., 1997). Undoubtedly, increased intake of nutrients and antinutritive factors can influence digestion efficiency and may explain differences between BW. In these studies, pigs at 98 kg of BW consumed feed at approximately 3% of their BW, and pigs at 27 and 59 kg consumed approximately 5 and 4%, respectively.

In summary, this study indicates that endogenous P excretion of the pig can be determined by feeding highly purified diets and regressing P absorption on P intake and obtaining the Y-intercept of the linear equation. The endogenous P loss, using this procedure, is estimated to be 110, 156, and 226 mg/d for 27-, 59-, and 98-kg pigs, respectively. Thus, endogenous P loss increases with increasing BW of the pig by 1.632 mg for every 1-kg increase in BW.

	Footnotes

 
¹ Paper no. 04-07-178 of the Kentucky Agric. Exp. Stn.

² Appreciation is extended to Ajinomoto Heartland LLC, Chicago, IL, for providing the L-lysine·HCl; to Degussa Corp., Kennesaw, GA, for providing the DL-methionine; to Archer Daniels Midland, Decatur, IL, for providing the L-threonine and L-tryptophan, to Akey, Lewisburg, OH, for providing the vitamin premix, and to Bioproducts, Inc., Fairlawn, OH, for providing the choline chloride.

³ Current address: Dep. of Anim. Sci., California Polytechnic State University, San Luis Obispo 93407.

⁴ Corresponding author: gcromwel{at}uky.edu

Received for publication August 9, 2005. Accepted for publication October 31, 2005.

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