SeinFit, a Computer Program for the Estimation of the Seinhorst ...

J o u r n a l of Nematology 29(4):474-477. 1997. © T h e Society of Nematologists 1997.

SeinFit, a Computer Program for the Estimation of the Seinhorst Equation N. M. VIAENE,1 P. SIMOENS,2 AND G. S. ABAWI1 Abstract: A c o m p u t e r p r o g r a m , "SeinFit," was created to d e t e r m i n e the Seinhorst equation that best fits e x p e r i m e n t a l data o n the relationship between preplant n e m a t o d e densities a n d p l a n t growth. Data, which can be e n t e r e d m a n u a l l y or i m p o r t e d f r o m a text file, are displayed in a data window while the c o r r e s p o n d i n g g r a p h is shown in a g r a p h window. Various options are available to m a n i p u l a t e the data a n d the g r a p h settings. T h e best-fitting Seinhorst equation can be calculated by two m e t h o d s that are b o t h based o n the evaluation of the residual s u m of squares. D e p e n d i n g o n the m e t h o d , a range o f values for different parameters of the Seinhorst equation can be chosen, as well as the n u m b e r o f steps in each range. Data, graphs, a n d values of the parameters of the Seinhorst equation can be printed. T h e p r o g r a m allows for quick calculation of the danaage t h r e s h o l d d e n s i t y - - o n e of t h e p a r a m e t e r s of the Seinhorst model. Versions written for Macintosh or DOS-compatible m a c h i n e s are currently available t h r o u g h the Society o f Nematologists' World Wide Web site ( h t t p : / / i a n r w w w . u n l . e d u / i a n r / p l n t p a t h / nematode/SOFTWARE/nemasoft.htm). Key words: c o m p u t e r p r o g r a m , crop loss assessment, d a m a g e threshold, m a n a g e m e n t , n e m a t o d e , SeinFit, Seinhorst equation, yield loss.

Several m e t h o d s have b e e n used to relate n e m a t o d e p o p u l a t i o n densities in the soil at p l a n t i n g a n d yield of host-plants (Barker a n d Olthof, 1976). T h e m o d e l developed by Seinhorst (1965), c o m m o n l y referred to as the Seinhorst equation, has b e e n used frequently since its publication. T h e m o d e l is of the form: y = ym, for x~< t,

(1)

Y=Ym" m + y m " (1 - m ) • z(X-t), for x> t

(2) where: y = c r o p yield or o t h e r plant growth parameter; x = the n e m a t o d e p o p u l a t i o n density (often referred to as P); t = the n e m a t o d e p o p u l a t i o n density below which yield reduction c a n n o t be m e a s u r e d (= the tolerance limit or d a m a g e threshold density, in m a n y articles also r e p r e s e n t e d as T); Ym = m e a n crop yield where the n e m a t o d e density is below the tolerance limit (t); m = a constant, usually between zero a n d one, such that

Ym " m is the yield at the highest possible nematode density; and z = the sloped e t e r m i n i n g p a r a m e t e r (value between zero a n d one). T h e Seinhorst m o d e l has the advantage that one of its p a r a m e t e r s (t) indicates the d a m a g e t h r e s h o l d density, i.e., the minim u m n e m a t o d e population in the soil that inhibits plant growth (Barker a n d Olthof, 1976). Traditional calculation o f the Seinhorst equation that best fits the e x p e r i m e n tal d a t a is r a t h e r d i f f i c u l t a n d t i m e c o n s u m i n g because the m o d e l is segmented. Moreover, three parameters, o f which o n e occurs in the exponential p a r t of the equation, m u s t be d e t e r m i n e d . T h e r e f o r e , a prog r a m (SeinFit) was written to e n a b l e researchers to calculate the best-fitting Seinhorst curve in a matter o f minutes. In this paper, we describe the data entry and options available in the SeinFit p r o g r a m , explain how the calculations are p e r f o r m e d , and p r e s e n t guidelines for p r o g r a m use. M A T E R I A L S AND M E T H O D S

Program language and computerrequirements: Received for publication 13 November 1996. 1 Former Graduate Research Assistant and Professor, Department of Plant Pathology, New York State Agricultural Experiment Station, Cornell University, Geneva, NY 14456. 2 Former Research Support Specialist, Department of Soil, Crop and Atmospheric Sciences, Cornell University, Ithaca, NY 14853. E-mail: [email protected] The authors thank P.J. McLeod for reviewing this article.

474

T h e SeinFit p r o g r a m was written in C++, with Metrowerks CodeWarrior (Metrowerks, Austin, TX). It is a "Fat Binary": a standalone a p p l i c a t i o n c o n t a i n i n g b o t h 680x0 a n d PowerPC native code for o p t i m u m perf o r m a n c e on b o t h Macs a n d PowerMacs.

SeinFit: Viaene et al. 475 T h e p r o g r a m r e q u i r e s 487 kilobytes o f m e m o r y a n d 300 kilobytes of disc space. Results can be printed on any printer. A DOS version, written in C++ with T u r b o C++ (Borland International, Scotts Valley, CA), also has b e e n developed. An HP p r i n t e r (Hewl e t t - P a c k a r d , Boise, ID) s u p p o r t i n g t h e PCL-5 language is required to print the results f r o m the DOS version. User interface: Data pairs (x, y) can be either e n t e r e d manually in a spreadsheet-like data window ('New Data') or i m p o r t e d f r o m a text file ( ' I m p o r t Data'). T h e f o r m a t o f the data can be c h a n g e d using the ' C o l u m n Form a t ' option. Any data point can be selected or unselected for use in calculating the Seinh o r s t e q u a t i o n or plotting on the g r a p h (Fig. 1A). In addition to the plotted data points and the graph, the following items can be displayed in the g r a p h window: the fitted Seinhorst equation; the value of the m e a n yield (Ym) at x --< t; the values of the p a r a m e t e r s m, z, a n d t; the coefficient of d e t e r m i n a t i o n (r2); a n d the sum of squares (Fig. 1B). T h e p r o g r a m automatically recalculates the Seinhorst equation and updates the g r a p h w h e n the 'Auto U p d a t e ' option is selected after changes are m a d e in the data

- I ~ ....

window. T h e thickness of the lines a n d dots in the g r a p h can be chosen, as well as the scale a n d the m i n i m u m a n d m a x i m u m values of the x a n d y axis. Specific values can be given to the parameters m, z, and t, with the option 'Manual' f r o m the Curve Fit m e n u . These values are used to draw the g r a p h a n d calculate the c o r r e s p o n d i n g Seinhorst equation, coefficient o f d e t e r m i n a t i o n (r2), a n d s u m o f squares once the " P l o t " b u t t o n is clicked. T h e Curve Fit m e n u contains two m o r e options to calculate the equation and draw the graph, based o n the two calculation methods described hereafter. A ' H e l p ' file contains an explanation of all the m e n u options a n d the calculation methods, as well as a description o f the Seinhorst model. T h e data, the values of the parameters of the Seinhorst equation, a n d the g r a p h can be printed. Calculation methods: Two m e t h o d s can be selected to calculate the Seinhorst equation. T h e 'Double Partial Derivative M e t h o d ' was described by Ferris et al. (1981). In this iterative p r o c e d u r e , the r e s i d u a l s u m o f squares is evaluated over a r a n g e of t values covering the initial n e m a t o d e population-

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Fro. 1. Display o f two windows of the SeinFit p r o g r a m o n a Macintosh c o m p u t e r . A) Data window. T h e data points (x,y) can be selected to a p p e a r o n the g r a p h (Plot check box), a n d to be u s e d in t h e calculation o f the best-fitting Seinhorst equation (Fit check box). B) G r a p h window. Dots c o r r e s p o n d with t h e data in the data window. T h e best-fitting Seinhorst equation, t h e values o f its parameters (m, z, t), the m e a n yield (Ym), the coefficient of d e t e r m i n a t i o n (r~), a n d the s u m of squares are shown in the g r a p h window (x = p r e p l a n t n e m a t o d e density, y = yield or o t h e r plant growth parameter).

476 Journal of Nematology, Volume 29, No. 4, December 1997 densities (x), unless differently specified. For every t value, an initial z value o f 0.99 is selected. Using the estimated z and t values, an m value is derived with (3SS/ 3m = 0):

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(3)

Using this m value, the partial derivative o f the residual sum of squares with respect to z is calculated as follows, and evaluated in z. 0SS 0z - X(2[yi - Ym" m - Ym" (1 - m) • z(X,- t)]. [ m - 1 ] . Ym" [xi• z(Xi-t-

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W h e n this partial derivative is positive, z is decreased by 0.01 and m and 0SS/0z are recalculated. Once the derivative is negative, a new z at mid-point of the current and the previous z is chosen, and m and 0SS/0z are recalculated. This p r o c e d u r e is repeated until the difference between the present z and the previous z values becomes less than the interval of uncertainty. Finally, the sum of squares is calculated for those t, m, mad z values. The t value with the smallest sum of squares, and the c o r r e s p o n d i n g z and m values, are saved for the best-fitting curve. In the " D o u b l e Partial Derivative" dialog box, the defaults for the uncertainty interval for z, the m i n i m u m and m a x i m u m value for t, a n d the n u m b e r o f steps f o r t can be changed. In the 'Grid Method,' the residual sum of squares is calculated for a range o f t, z, and m values. These ranges, as well as the number o f steps to be used in each of them, can be specified in the " G r i d " dialog box. The t, z, and m values returning the smallest residual sum o f squares are saved for the bestfitting curve. The calculation o f the o p t i m u m values o f m, z, a n d t, the c o r r e s p o n d i n g sum o f squares, and the coefficient o f determination are visualized when the 'Show Progress' option is marked.

RESULTS

AND DISCUSSION

SeinFit, a c o m p u t e r program, was created to describe the relationship between nematode population densities in the soil at planting and plant growth parameters, according to the Seinhorst model. As an example, SeinFit was used to relate preplant nemat o d e densities o f Meloidogyne hapla a n d weight of lettuce, as well as to determine the d a m a g e threshold density in g r e e n h o u s e and field microplot tests (Viaene and Abawi, 1996). As with any model, caution in interpretation of the results is needed. Yield and n e m a t o d e p o p u l a t i o n data are often too variable to permit estimation of the parameters with confidence (Ferris, 1984). The Seinhorst equation that fits the data best does n o t always differ m u c h from the second best-fitting equation. For example, a Seinhorst equation with r 2 = 0.97 can have a tvalue o f 2 n e m a t o d e s / g soil, whereas the s e c o n d best-fitting e q u a t i o n to the same data set has r 2 = 0.96 and indicates a damage threshold density of 3 n e m a t o d e s / g soil. The damage threshold density calculated by SeinFit should therefore be interpreted with consideration of the values o f r 2 for the Seinhorst equations that have t-values close to the t-value of the best-fitting equation. The biology o f the interaction between nematodes and host crops always should be kept in m i n d w h e n drawing conclusions a b o u t the calculated values. It is possible to obtain values of m that are higher than one, resulting in a graph that shows an increase in yield as the n e m a t o d e population density increases. A stimulation in plant growth caused by plant-parasitic n e m a t o d e s has b e e n r e p o r t e d for some crops (Wallace, 1971), but this usually occurs at low population densities. If population densities used in the experiment were not high e n o u g h to result in a m i n i m u m yield, m can be set to 0 to calculate the other parameters (z and t) o f the Seinhorst e q u a t i o n (Ferris et al., 1981). It is also possible, however, that failure to obtain m i n i m u m yields is caused by factors o t h e r than low initial p o p u l a t i o n densities, e. g. the covariation o f n o n p a t h o genie or weakly pathogenic nematodes with

SeinFit: Viaene et al. 477 unmeasured variables that also affect plant growth. Versions written for Macintosh or DOScompatible machines are currently available through the Society of Nematologists' World Wide Web site (http://ianrww .unl.edu/ ianr/plntpath/nematode/SOFTWARE/ nemasoft.htm). LITERATURE CITED Barker, K.R., and T. H.A. Olthof. 1976. Relationships between nematode population densities and crop responses. Annual Review of Phytopathology 14:327353.

Fen-is, H. 1984. Nematode damage functions: The problems of experimental and sampling error. Journal of Nematology 16:1-9. Ferris, H., W. D. Turner, and L. W. Duncan. 1981. An algorithm for fitting Seinhorst curves to the relationship between plant growth and preplant nematode densities. Journal of Nematology 13:300-304. Seinhorst, J.W. 1965. The relation between nematode density and damage to plants. Nematologica 11: 137-154. Viaene, N. M., and G. S. Abawi. 1996. Damage threshold of Mdoidogynehaplato lettuce in organic soil. Journal of Nematology 28:537-545. Wallace, H. R. 1971. The influence of the density of nematode populations on plants. Nematologica 17: 154-166.