Headley 7 elaborated on the economic threshold concept by considering the d i g ferential cost of pest control relative to the level of control achieved... 1 and the control cost functio
Trang 1G R A S E L A 1977 Sticky p a n e l s as t r a p s for
M u s c a a u t t u n n a l i s J Econ E n t o m o l 70:
549-552
9 R O B I N S O N , J v , a n d R L COMBS, J R
1976 I n c i d e n c e a n d effect of H e t e r o t y l e n c h u s
a t t t u n l n a l i s o n t h e longevity of face flies in
Mississippi J Econ, E n t o m o l 69:722-724
10 STOI:FOLANO, J G., J R 1967 T h e s y n c h r o n i -
zation of t h e life cycle of d i a p a u s i n g face
flies, M u s c a a u t n m n a l i s , a n d of the n e m a t o d e ,
H e t e r o t y l e n c h u s a u t u m n a l i s J l n v e r t e b r
P a t h o l 9:395-397
11 S T O F F O L A N O , J G., J R 1968 D i s t r i b u t i o n
of t h e n e m a t o d e H e t e r o t y l e n c h n s a u t u m n a l i s ,
a p a r a s i t e of t h e face fly, in New E n g l a n d
w i t h n o t e s o n its origin J Econ E n t o m o l
61:861-863
12 S T O F F O L A N O , J G., J R 1970 l ' a r a s i t i s m of
H e t e r o t y l e n c h u s a u t u m n a l i s Nickle ( N e m a -
toda, S p h a e r u l a r i i d a e ) to t h e face fly, Musca
a u t u m n a l i s De G e e r ( D i p t e r a : Muscidae)
J N e m a t o l 2:324-329
13 S T O F F O L A N O , J G., JR., a n d W R N I C K L E
1966 N e m a t o d e p a r a s i t e ( H e t e r o t y l e n c h u s sp.) of face fly in New York State J Econ
E n t o m o l 59:221-222
14 TESKEY, H J 1969 o n t h e b e h a v i o r a n d ecology of t h e face tly, M u s c a a u t u m n a l i s (Diptera: Muscidae) Can E n t o m o l 101:561-
576
15 T H O M A S (; D., a n d B P U T T L E R 1970 Seasonal p a r a s i t i s m of t h e face fly hy t h e
n e m a t o d e H e t e r o t y l e n c h u s a u t u m n a l i s in central Missouri, 1968 J Econ E n t o m o l 63:
1 (.t22 - 1 9 2 ~
16 T H O M A S , G D., B P U T T L E R , a n d C E
M O R G A N 1972 F u r t h e r s t u d i e s of field
parasitism of t h e face fly by t h e n e m a t o d e
H e t e r n t y l e n c h u s a n t u m n a l i s in central Mis- souri, with n n t e s on t h e g o n a d o t r o p h i c cycles
of t h e face fly E n v i r o n E n t o m o l 1:759-763
17 T R E E C E , R E., a n d T A M I L L E R 1968
O b s e r v a t i o n s on H e t e r o t y l e n c h u s a u t u m n a l i s
in r e l a t i o n to t h e face fly J Econ E n t o m o l 61:45~-456
Nematode Economic Thresholds: Derivation, Requirements,
and Theoretical Considerations
H FERRIS t
Abstract: D e t e r m i n a t i t m a n d use of e c o n o m i c t h r e s h o l d s is considered essential in n e m a t o d e pest
m a n a g e m e n t p r o g r a m s T h e e c o n o m i c efficiency of control m e a s u r e s is l n a x i m i z e d w h e n t h e difference h e t w e e n t h e crop v a l n e a n d t h e cost of pest control is greatest Since t h e cost of
r e d u c i n g t h e n e m a t n d e p n p n l a t i o n varies w i t h t h e m a g n i t u t l e of t h e r e d u c t i o n a t t e m p t e d , an
e c o n o m i c (optimizing) thresholtI can be d e t e r m i n e t t g r a p h i c a l l y or mathematically if t h e n a t u r e
of t h e r e l a t i o n s h i p s b e t w e e n degree o f control attd cost, a n d n e m a t o d e densities anti crop v a l u e are k n o w n E c o n o m i c t h r e s h o l d s t h e n vary a c c o r d i n g to t h e n e m a t o d e c o n t r o l practices used,
e n v i r o n m e n t a l influences on t h e n e m a t o d e d a m a g e f n n c t i o n , a n d e x p e c t e d crop yields a n d values A p r e r e q u i s i t e of t h e a p p r o a c h is reliability of n e m a t o d e p o p u l a t i o n a s s e s s m e n t tech-
n i q u e s Key Words: Pest m a n a g e m e n t , p o p u l a t i o n d y n a m i c s , control costs, d a m a g e f u n c t i o n s ,
s a m p l i n g , o p t i m i z i n g t h r e s h o l d s
In any pest m a n a g e m e n t program, an
obvious concern is not only the type of con-
trol measure to be used, relative to pest and
environmental considerations, b u t also the
necessity for such control Economic thresh-
olds are variously defined (1, 3, 14, 18) b u t
might be smnmarized as the p o p n l a t i o n
density of a pest at which the value of the
damage caused is equal to the cost of con-
trol T h u s , at densities up to the economic
threshold, there would be no (or negative)
Received for publication 3 April 1978
Associate Nematologist, I)epartment of Nematology, Uni-
versity of California, Riverside California 92521 I thank
I)r W A Jury, Soil Physicist, Department of Soil and E n -
v l r o n m e n t a t Sciences, University of California Riverside,
for enlightening discussions on tile mathematical c o m p l l t a -
economic advantage to pest control since control costs would exceed crop loss due to the pest T h i s i m p o r t a n t concept has been largely ignored in nematology for several reasons: 1) lack of i n f o r m a t i o n on the rela- tionship between n e m a t o d e densities and
p l a n t damage, and damage functions gen- erally; 2) difficulties in assaying n e m a t o d e densities in a field; 3) work involved in arriving at the decision; 4) ready availabil- ity of low-cost pesticides
Headley (7) elaborated on the economic threshold concept by considering the d i g ferential cost of pest control relative to the level of control achieved Chemical reduc- tion of the pest p o p u l a t i o n by 50% may
be relatively inexpensive, whereas a 99%
Trang 2342 fournal of Nematology, Volume 10, No
reduction, if possible, m a y be astronomical
in cost T h u s , there is an o p t i m u m level of
control at which profits (crop value less
n e m a t o d e control cost) will be maximized
T h e d o s a g e / c o n t r o l curve for nematicides
is linear within certain limits (13); how-
ever, the cost of achieving higher dosages
may be multiplicative Similar observations
have been m a d e for insect control, such
that costs (c) may be described by:
a
where a is a constant a n d P is the level to
which the p o p u l a t i o n is to be reduced Tile
level of control usually achieved is 80 to
90% (23) for which the cost will be an
a p p l i c a t i o n overhead (B) a n d a cost of
material (A) from which a hypothetical,
unsuhstantiated model for the cost of con-
trol (y) can be developed:
y = (A x Q ) ( N / P ) + B [2]
where A is the cost of m a t e r i a l r e q u i r e d to
reduce the p o p u l a t i o n to a p r o p o r t i o n Q,
N is the p o p u l a t i o n in the field, a n d P is
the level to which the p o p u l a t i o n is re-
duced Q u a n t i f y i n g this relationship, if the
cost of m a t e r i a l (A) to reduce the field
p o p u l a t i o n to 0.1 is $150, with an applica-
tion overhead (B) of $50, and the starting
p o p u l a t i o n (N) in the field is 1,000, then
tile cost of r e d u c i n g the p o p u l a t i o n to 250
n e m a t o d e s / v o l u m e of soil would be:
(150 x 0.1 x 1,000/250) + 50 = $110
Now, in a t t e m p t i n g to m a x i m i z e prof-
its from n e m a t o d e control, consider Sein-
horst's (20) d a m a g e function y = CZW - T)
r e l a t i n g crop value (y) to n u m b e r s of nema-
todes, where C represents p o t e n t i a l crop
value, Z is the p r o p o r t i o n of the p l a n t
n o t d a m a g e d by one n e m a t o d e , P is the
n e m a t o d e p o p u l a t i o n level, and T is the
tolerance level below which d a m a g e is not
measurable Assume these p a r a m e t e r s to
have values C = 1,000, Z = 0.995 a n d T =
20 (line A in Fig 1) and the control cost
function to have values given above (line
B in Fig 1) T h e p o p u l a t i o n level at which
the crop value less the cost of suppressing
the p o p u l a t i o n to that level is maximized,
is the p o i n t at which the rate of decrease in
control cost per n e m a t o d e (line D, Fig 1)
is closest to the rate of decrease in c r o p
, October 1978
value per n e m a t o d e (line C, Fig 1) In other words, with the two c o n t i n u o u s models, crop value (line A) and control cost (line B), the o p t i m i z i n g threshold occurs at the p o i n t where the difference hetween the functions is at a m a x i m u m
T h i s is the point at which the difference between the slope of the lines is at a mini-
m u m I f the derivatives of the functions intersect, it is a difference of zero I f tire derivatives do not intersect below the
p o p u l a t i o n level in the field, the o p t i m i z i n g threshold for the m a n a g e m e n t or control practice u n d e r consideration is above the
c u r r e n t p o p u l a t i o n level (N), so the p o i n t
of m i n i m u m difference in slope is at N a n d this control o p t i o n is rejected N o t e that with a n o t h e r control a p p r o a c h , the thresh- old m i g h t be below N, d e p e n d i n g on the shape a n d position of the control cost func- tion In the case of the d a m a g e and control cost functions considered, the respective derivatives are:
a n d
dpdy _ C In Z (Z ~v - a'~) [3]
T h e p o i n t of intersection of these lines is
d e t e r m i n e d graphically (lines C a n d D, Fig 1), or by e q u a t i n g the derivatives a n d solving for P N o t e the correspondence of the o p t i m i z i n g threshold with the maxi-
m u m p o i n t on the line depicting the difference between the d a m a g e and control cost functions (line E, Fig 1)
Using the above values in the crop value and control cost functions, the op- timizing threshold is 61 n e m a t o d e s / v o l u m e
of soil (point F, Fig 1), which can be achieved by a control e x p e n d i t u r e of
$295.90, including the $50.00 a p p l i c a t i o n overhead (point G, Fig 1) T h e t r e a t m e n t should result in a c r o p value of $814.23 (point H, Fig 1) a n d a net profit of $518.33 (point I, Fig 1) N o t e t h a t the f l m c t i o n used for crop value, y = C Z ( F - ~ ) , calcu- lates gross crop value w i t h o u t considering
p r o d u c t i o n overheads (M) N e t crop value would be given by y = CZ~ r ' - ~ M, as-
s u m i n g no change in p r o d u c t i o n overheads relative to yield T h e a d d i t i o n of the con- stant causes no change to the derivative of tire function or to the p o i n t of intersection
Trang 3of the cost a n d d a m a g e derivatives a n d
hence to the threshold estimate It will,
however, cause a shift in curve A (Fig 1)
restdting itt a reduction M in the c r o p value
estimate and the benefit of treatment T h e
p r o d u c t i o n overheads should be considered
in the d a m a g e function since they m a y
shift it so m u c h that it does not intersect
the control cost function, and the t r e a t m e n t
will never be profitable T h i s concept can
be visualized by considering constant crop
p r o d u c t i o n overheads of $600 in Fig I
I n Fig 1, a field p o p u l a t i o n of 1,000
n e m a t o d e s / v o l u m e soil was assumed; the
effect of a lower N value (say 150) is to
shift the control cost function to the left
(line A, Fig 2), whereas a greater N (say
3,000) shifts it to the right (line B, Fig 2)
T h i s results in points of intersection of the
derivatives at C a n d D, respectively (Fig
2) p r o d u c i n g economic threshold estimates
of 22 and 125 for the control practice con-
sidered
By m a n i p n l a t i o n a n d consideration of
the curves in Figs l and 2, some principles
relating to economic thresholds b e c o m e ap-
parent:
I < 2 ~ ~ t : : ' i
J
FIG 1 Determination of the economic threshold
hy maximizing the difference (curve E) between
the nematode-damage function (curve A) and the
control-cost function (curve B) T h e optimizing
threshold is the population level at which the
derivatives of the damage function (curve C) and
the control-cost function (curve D) intersect
N e m a t o d e Economic T h r e s h o l d s : Ferris 343
I) T h e economic benefit a n d practical suitability of a control or m a n a g e m e n t practice is related to the m a g n i t u d e of the area u n d e r tile d a m a g e function (consider- ing p r o d u c t i o n overheads) less the area tmder the control cost function; or the ditference between the integrals of tile two functions If this difference is negative, the
p o p u l a t i o n is below the economic threshold tot that practice
2) T h e o p t i m i z i n g threshold is the popu- lation level at which the derivatives of the two fnnctious are equal
3) For m a n a g e m e n t practices resulting
in a n y t h i n g less than pest p o p u l a t i o n eradication, the control cost function shifts, relative to the d a m a g e function, w i t h dif- ferent field p o p u l a t i o n densities
4) If the derivatives of the cost a n d
d a m a g e ftmctions intersect at a p o p u l a t i o n level below the tolerance level, the optimiz- ing threshold will be at the tolerance level; that is, profits will be m a x i m i z e d by con- trolling the p o p u l a t i o n down to the tol- erance level or the p o i n t below which
n e m a t o d e d a m a g e is not measurable
T h e foregoing considerations relate to the economics of the current crop year, n o t
to effects on succeeding crops N o r do they
I'
' 5 L o g P i
C
FIG 2 T h e effect of initial population densities
of 150 (curve A) and 3,000 (curve B) on the magnitude of the optimizing threshold as deter- mined hy intersection of the derivatives at C and
D, respectively
Trang 4344 Journal of Nematology, Volume 10, No 4,
i n c l u d e e n v i r o n m e n t a l a n d s o c i o l o g i c a l im-
p l i c a t i o n s
N o t all p e s t c o n t r o l o r m a n a g e m e n t
p r a c t i c e s c a n b e d e s c r i b e d b y a c o n t i n u o u s
m o d e l as in Figs 1 a n d 2 T i l e use o f a c r o p
r o t a t i o n system, w h e r e b y p o p u l a t i o n r e d u c -
t i o n is i n d i s c r e t e steps a t t h e e n d of e a c h
c r o p season, r e s u l t s i n a d i s c o n t i n u o u s
m o d e l (Fig 3) I n t h i s case, t h e e c o n o m i c
t h r e s h o l d is r e a c h e d w h e n t h e a v e r a g e
cost of c o n t r o l p e r n e m a t o d e for a s t e p
r e d u c t i o n i n t h e p o p u l a t i o n c h a n g e s f r o m
p o s i t i v e to n e g a t i v e A n i t e r a t i v e p r o c e d u r e ,
r e a d i l y a d a p t a b l e to p r o g r a m m a b l e calcu-
l a t o r s a n d m i n i - c o m p u t e r s , can b e u s e d to
d e t e r m i n e t h e t h r e s h o l d level T h e a v e r a g e
cost p e r n e m a t o d e for successive d e c r e a s e s
i n the p o p u l a t i o n is c a l c u l a t e d f r o m t h e
i n c r e a s e in cost d i v i d e d b y t h e n u m b e r o f
n e m a t o d e s c o n t r o l l e d F r o m Fig 3, if tile
f r a c t i o n a l r e d u c t i o n in p o p u l a t i o n p e r y e a r
of n o n h o s t c r o p is 0.5, t h e a n n u a l p o p u l a -
t i o n series (N, P , P~, P:, etc.) w i l l b e N ,
0.5N, 0.25N, 0.125N etc A t t i m e zero,
t h e p o p u l a t i o n is N, w h i c h w o u l d r e s u l t i n
t h e c r o p v a l u e at i n t e r s e c t i o n 1, a n e t v a l u e
o f y = C , Z (N -'r~-C~ w h e r e C1 is t h e v a l u e
p e r a c r e o f t h e p r i m a r y c r o p a n d C2 is t h e
p r o d u c t i o n o v e r h e a d for this c r o p I f t h e
a l t e r n a t e n o n h o s t c r o p w e r e g r o w n , w i t h
p r i c e A, a n d o v e r h e a d A2, t h e n e m a t o d e
p o p u l a t i o n w o u l d b e r e d u c e d to 0.5N at a
cost: y - - (A~ - A2) o r C~Z ~N - ~) - C2 - A , +
A2 ( v a l u e a t i n t e r s e c t i o n 1 less t h a t a t i n t e r -
P R I M A R Y ~
CROP - " ~ X
_J
<[ A L T E R N A T E
0
' 1
rr
'4
P4 P~ 02 Pl t,,~
Log P FIG 3 Determination of the ecouomic threshold
w i t h a discontinuous-control cost model as exempli-
fied by rotation to a nonhost crop The threshold
is passed during the season in which the cost of
the step-reduction in the nematode population
passes from negative to positive
October 1978
s e c t i o n 2) If t h i s v a l u e is p o s i t i v e , t h e
p o p u l a t i o n level (N) is b e l o w t h e o p t i m i z -
i n g t h r e s h o l d for t h e c o n t r o l m e a s u r e se-
l e c t e d , a n d r e t u r n s w o u l d be m a x i m i z e d b y
g r o w i n g t h e p r i m a r y c r o p d e s p i t e t h e n e m a -
t o d e p o p u l a t i o n , o r b y s e l e c t i n g a n o t h e r
a l t e r n a t e c r o p for w h i c h t h e p o p u l a t i o n
r e d u c t i o n cost w o u l d b e n e g a t i v e a n d prof- its w o u l d b e m a x i m i z e d b y this s e l e c t i o n
If t h e v a l u e is n e g a t i v e a n d the a l t e r n a t e
c r o p is c o n t i n u e d a s e c o n d year, the p o p u -
l a t i o n w i l l b e r e d u c e d to 0.25N a t a cost for this s e c o n d r e d u c t i o n o f C~Z(°-'~¢-7)
- C2 - A~ + A2 a n d a t o t a l cost o f a c h i e v i n g 0.25 N of:
y = C~Z(~ - 7) _ C2 - A~ + A 2 + C 1 Z (°.'SN - 7)
- C2 - A1 + A2
, ' y ~
C,Z(X - 7) + C~Z(0 ~y - w~ _ 2C2 - 2Ax + 2A2
I f t h e v a l u e C~Z (°.''N - 7} _ Cz - A~ + A2 (in-
t e r s e c t i o n 3 less i n t e r s e c t i o n 4) is p o s i t i v e ,
t h e e c o n o m i c t h r e s h o l d for this m a n a g e -
m e n t p r a c t i c e was p a s s e d in t h e s e c o n d y e a r
a n d profits w i l l n o w b e m a x i m i z e d b y re-
v e r t i n g to t h e p r i m a r y c r o p A n y e x p e c t e d
a n n u a l f l u c t u a t i o n s in c r o p p r i c e s a n d over-
h e a d s can he a d j u s t e d a t each s t e p i n t h e
i t e r a t i v e process I n Fig 3, t h e t h r e s h o l d is
r e a c h e d d u r i n g t h e t h i r d year, a f t e r w h i c h
t h e cost o f f u r t h e r p o p u l a t i o n r e d u c t i o n b y this a p p r o a c h is p o s i t i v e ( i n t e r s e c t i o n 8 less i n t e r s e c t i o n 7)
G e n e r a l i z i n g t h e c o n c e p t s for t h e
d i s c o n t i n u o u s m o d e l , t h e n e t r e t u r n s
f r o m t h e p r i m a r y c r o p for a n y y e a r a r e Y, = C~Z~V~ - 7 ) - C.,, w h e r e C~ is t h e ex-
p e c t e d gross c r o p v a l u e in t b e a b s e n c e of
n e m a t o d e s , C2 is t h e p r o d u c t i o n o v e r h e a d ,
Z is t h e d a m a g e f t m c t i o n c o n s t a n t , T is t h e
t o l e r a n c e l i m i t , a n d Pk is t h e i n i t i a l p o p u l a -
t i o n at y e a r k T h e p o p u l a t i o n a f t e r k y e a r s
of t h e a l t e r n a t e n o n h o s t c r o p is g i v e n b y
Pk = N(1 - b) k, w h e r e N is t h e i n i t i a l p o p u -
l a t i o n m e a s u r e d in t h e field, a n d b is t h e
a n n u a l f r a c t i o n a l r e d u c t i o n i n t h e a b s e n c e
o f a host T i l e cost o f r e d u c i n g t h e p o p u l a -
t i o n i)y e a c h s t e p w i s e s e a s o n a l r e d u c t i o n (~bk) is e q u a l t o t h e v a l u e of t h e p r i m a r y
c r o p a t t h e p o p u l a t i o n level a t t i m e k, less
t h e v a l u e of t h e a l t e r n a t e c r o p T h u s ,
6 k = C~ Z ( P ~ - 7) _ C ~ - A~ + A 2 [5]
w h e r e Pk ' = N(1 - b) k
Trang 5]f this value is initially positive, the
field p o p u l a t i o n N is already below the
o p t i m i z i n g economic threshold for the
m a n a g e m e n t alternative u n d e r considera-
tion If yields of the p r i m a r y c r o p are n o t
acceptable at this p o p u l a t i o n level, alterna-
tive approaches should be considered, xvVhen
the function is initially negative, the popu-
lation is above the economic threshold a n d
subsequent years should be tested T i m
threshold is bridged d u r i n g the season that
the step-reduction cost function becomes
positive a n d the r o t a t i o n should revert to
the p r i m a r y crop after this season to
maximize profits T h e n , it is possible to
estimate the economic threshold by deter-
m i n i n g the p o p u l a t i o n level at which the
cost of p o p u l a t i o n reduction becomes zero,
i.e., ~bk = 0 so that C~Z (v~- T) _ C2 - A~ +
A2 = 0
C~Z(I,,_ T~ A ~ - A2 + C2
Pk = T l n Z In C1
[6]
T h e n u m b e r of years (k) to reduce the popu-
lation to Pk is derived from: Pk = N(1 - b) ~,
• ".ln, N + k l n ( l - b ) - - InPk
k = I N T E G E R ~ (/nlnPk- (1 - b) ln N ) ~ _~ [7]
N o t e that since it is not desirable to stop
the p o p u l a t i o n reduction in the m i d d l e of
a crop, k takes the value of the n e x t integer
Equations 6 and 7 can be c o m b i n e d to give
a value for the expected length of rotation:
~ l n ~ A ~ - A 2 + Ce - l n
/ In (1 - b ) ] [8]
T h i s a p p r o a c h gives initial indications o[
r o t a t i o n length w h e n there is only one
a l t e r n a t e crop, or w h e n average crop values
N e m a t o d e Economic T h r e s h o l d s : Ferris 345 are used for a series of a l t e r n a t e crops W i t h
m u l t i c r o p rotations, the a p p r o a c h w o u l d
be to d e t e r m i n e w h e t h e r the threshold h a d been bridged by p r e d i c t i n g the cost of
n e m a t o d e r e d u c t i o n in one-season steps us- ing e q u a t i o n 5 a n d substituting a p p r o p r i a t e crop values T h e same a p p r o a c h can be used for m o n i t o r i n g the progress of a single- alternate r o t a t i o n scheme at the e n d of each season by substituting actual crop prices
T h e concepts involved in b o t h the con- tinuous a n d discontinuous models can be exemplified and tested using d a t a for
Heterodera schachtii from Cooke a n d
T h o m a s o n (3) T h e d a m a g e function de-
t e r m i n e d for sugar beets in the I m p e r i a l Valley of California, using five-year average prices (3, 4) is: y = 858.42 (.99886)( P - 100), where p o p u l a t i o n levels are expressed as eggs plus larvae p e r 100 g soil A s s u m i n g that the n e m a t o d e can be controlled to the 10% level by a n in-row t r e a t m e n t of l0
g / A of 1,3-D n e m a t i c i d e at recent com- mercial a p p l i c a t i o n costs of $52.50 for
m a t e r i a l a n d $7.25/acre for application, the
p a r a m e t e r s for the hypothetical continuous control cost flmction (eqn 2) are available
If the field p o p u l a t i o n (N), m e a s u r e d by sampling, is 2,000 p r o p a g u l e s / 1 0 0 g soil, the a p p r o p r i a t e substitutions can be m a d e
in the derivative equations (eqns 3 a n d 4):
dy - 858.42 In .99886 (.99886 (v_ 100))
d P
d P
T i l e o p t i m i z i n g threshold p o p u l a t i o n for the chemical control a p p r o a c h can be de-
t e r m i n e d by finding the value of P at the
p o i n t of equality of the derivatives:
858.42 In .99886 (.99886 ,(v - 100)) = -(52.5 × 0.1 × 2000)/P 2
- 97916 (.99886( I ' - 100)) = _10500/P2
2 In P + (P~- 100) (-.00114) = 9.2802
2 In P - 0 0 1 1 4 P = 9.3942
T h i s transcendental e q u a t i o n can be solved
by iteration to yield: P = 109'.6 eggs a n d larvae/100 g soil Alternatively, the value
of P can be d e t e r m i n e d g r a p h i c a l l y as the
p o i n t of intersection of the derivatives
N o t e that u n d e r a s t a n d a r d definition of the economic threshold as the n u m b e r of nematodes at which the loss in crop value
Trang 6346 Journal of Nematology, Volume 10, No
is equal to the cost of control, the estimate
would be at a c r o p value of $(858.42 - 52.5
- 7.25) = $798.67 Substituting in the dam-
age function yields an economic threshold
of 163.3 p r o p a g u l e s / 1 0 0 g soil, so that the
o p t i m i z i n g technique yields a lower thresh-
old in this case However, the control cost
function was based on a hypothetical
model T h e o p t i m i z i n g a p p r o a c h (exclud-
i llg prod uction overheads) as d e t e r m i n e d by
sul)stitution in the d a m a g e function a n d
e q u a t i o n 2 would yield a crop value of
$849.07 a n d control cost of $103.05, result-
in~ in a net r e t u r n of $746.02 A s s u m i n g
9 0 % effectiveness of the control t r e a t m e n t ,
the standard a p p r o a c h would result in
reduction of the p o p u l a t i o n to 200
p r o p a g u l e s / 1 0 0 g soil at a cost of $59.75
T h e crop value would be $765.88 a n d the
net r e t u r n $706.13
A v a r i a t i o n on the control efficiency
assumptions would be p r o v i d e d by assum-
ing that the 10 g / A in-bed t r e a t m e n t
resulted in 80% control of the n e m a t o d e
p o p u l a t i o n , while 9 0 % control could be
achieved at 15 g / A broadcast T h i s w o u l d
result in o p t i m i z i n g threshold estimates of
138.3 a n d 119.8 p r o p a g u l e s / 1 0 0 g soil a n d
o p t i m i z e d profits (excluding p r o d u c t i o n
overheads) of S662.64 a n d $700.53, respec-
tively In this case, the broadcast t r e a t m e n t
m i g h t be a preferable selection
T h e University of California recom-
mends c r o p r o t a t i o n to nonhosts such as
alfalfa for H schachtii control (10, 19)
E x a m i n i n g the economics of the discon-
tinuous control model, c u r r e n t yields a n d
prices of alfalfa in the I m p e r i a l Valley (4)
p r o d u c e crop values of $589.30 with pro-
d u c t i o n overheads of $169.30 for stand
establishment and a n n u a l p r o d u c t i o n costs
of $480.56 T h e establishment cost repre-
sents an extra p r o d u c t i o n overhead which
will be p r o r a t e d over an average of three
years of the crop, i.e., $56.43 is the cost per
year Sugar beet p r o d u c t i o n currently costs
$719.13 per acre, resulting in 28.5 tons
average), a total crop value of $858.42 Sub-
stituting in the discontinuous model (eqn
6):
P~, = 100 +
(-.00114)
4, October 1978
T h e a n n u a l rate of p o p u l a t i o n decline in the I m p e r i a l Valley is a b o u t 5 0 % (I J
T h o m a s o n , personal c o m m u n i c a t i o n ) , so that the required length of r o t a t i o n f r o m eqn 7 is:
k = I N T E G E R ~ (ln 193.7 - In 2 0 0 0 ) ~
In 5
= 4 years
T h u s , a four-year alfalfa r o t a t i o n is initially indicated, b u t a n n u a l u p - d a t i n g of the economic situation based on actual crop prices m a y result in modification of this estimate as time progresses
N O N M A T H E M A T I C A L S U M M A R Y
T h e concepts e x p l o r e d are based on the premises t h a t the value of a crop can
be related to the initial p o p u l a t i o n density
of tile nematodes d a m a g i n g it, a n d t h a t the cost of controlling a n e m a t o d e p o p u l a t i o n
by a specific m e t h o d varies with tile level
of control desired T h e difference b e t w e e n the c r o p value a n d the cost of conlrol rep- resents the benefit to the grower T h e r e is
an o p t i m u m level ( p o i n t F, Fig !) to which the n e m a t o d e p o p u l a t i o n can be reduced at a cost (point G, Fig 1) deter-
m i n e d by tile shape a n d position of the control cost curve (curve B, Fig l), at which the benefits of the t r e a t m e n t are
m a x i m i z e d (point H m i n u s p o i n t G, Fig 1) Curve E (Fig 1) represents the differ- ence between the crop value and control cost lines for various n e m a t o d e p o p u l a t i o n densities, indicating the p o p u l a t i o n density
at which benefits are m a x i m u m T h i s den- sity is the o p t i m i z i n g threshold, different from the standard definition of economic threshold as the p o i n t at which returns equal control costs (7) In the case of crop
r o t a t i o n (Fig 3), where tlle p o p u l a t i o n is reduced in a stepwise m a n n e r , the o p t i m u m
n u m b e r of years for r o t a t i o n to reduce the
n e m a t o d e p o p u l a t i o n can be d e t e r m i n e d
if the seasonal r e d u c t i o n u n d e r a n o n h o s t
a n d the r e l a t i o n s h i p between n e m a t o d e densities a n d expected g r o w t h of the pri-
threshold is reached w h e n returns f r o m the
Trang 7primary crop at that p o p u l a t i o n level would
he equal to or greater than those of tile
alternate crop
DISCUSSION
A prerequisite for deternfination and
application of economic thresholds is a
knowledge of tile relationship between pest
density and expected damage Currently,
there is intense interest in developing these
damage functions because of: 1) environ-
mental and health pressures restricting
pesticide use, anti pemling legislation re-
q u i r i n g d o c u m e n t e d justification before
pesticide application (22); 2) the desirabil-
ity of regulating tile pesticide load in the
environment; 3) the legal r e q u i r e m e n t to
demonstrate d o c m n e n t e d evidence of the
benefit of pesticides d u r i n g the R P A R
process (24); 4) increasing cost and lack of
availability of pesticides relative to declin-
ing fossil fuel supplies; and 5) lower
efficiency of m a n y alternative pest control
measures T h e s e factors require considera-
tion of tile economics anti cost/benefit
analysis of pest m a n a g e m e n t programs
Data which are currently largely unavail-
able are needed for such analyses Besides
damage functions, data on costs of control
measures, and estimated yields anti crop
value for a particular field are required
Operational costs are largely calculable,
although an element of estimation and
forecasting is involved in d e t e r m i n i n g
expected yields and crop value Farmer
experience aml agricultural statistics are
useful
T h e models developed in this t)aper
have informational requirements which
indicate needed research emphasis in quan-
titative aspects of nematology It is useful
to examine these requirements
The damage [unction: Prediction of
yield losses in annual crops is, at least in
concept, simpler for nematodes than for
many other pests Nematodes are relatively
less motile, and crop yields can be related
to preplant p o p u l a t i o n densities (16, 20),
so that considerations of crop age or status
at the time of pest invasion are not neces-
sary However, edaphic, environmental,
cultural and varietal conditions do need to
be considered in d e t e r m i n i n g or applying
the d e n s i t y / d a m a g e relationship T h e situ-
ation is more complex in perennial crops,
N e m a t o d e Economic Thresholds: Ferris 347 where the response of the host to the path- ogen, and the effect of this response on the pathogen, is a reltection of crop history (6)
"I'he general nematode damage function involves an essentially linear relationship between plant damage and log-transformed nematode densities, with several alternatives
at its extremities (16) Equations for the relationship, based on theoretical damage considerations (20), are compatible with empirical observations, although the valid-
theoretical relationship has been questioned (25) T h e theory-based relationship allows consideration of a tolerance limit (T) below which damage is not seen T h a t concept has also been questioned (25), although it has practical validity when considered as the p o p u l a t i o n below which yield loss is not measurable T h e term "tolerance" is perhaps too limiting
Seinhorst's (20) damage function relates yield (y), on a relative scale, to initial
p o p u l a t i o n density (P) by y = CZ ¢e-T)
w h e n P > T and has the v a l u e y = 1 w h e n
P ~ T If T (measurable d a m a g e / t o l e r a n c e limit) is greater than zero, it is i m p o r t a n t
in d e t e r m i n i n g tile position of the damage portion of tile relationship and imparts greater sensitivity to this position since it
is expressed at tile low end of the logarith- mic populatior~ scale where damage per individnal is greatest Unfortunately, most
y i e l d / p o p u l a t i o n data are too variable to allow estimation of W with confidence Square root transformations of p o p u l a t i o n data have been suggested to facilitate de- termination of T (21)
Damage functions for applied use must
be based on data from field and m i c r o p l o t trials From a practical standpoint, the yield-loss portion of the relationship ap- proximates linearity Any error incurred
by tile assumption of linearity is m i n i m a l relative to the i n h e r e n t variability of field data T h e assumption allows the advantage
of using standard linear regression tech- niques to enable nonsubjective line fitting However, the existence of a t o l e r a n c e / measnrable damage limit may be over- looked, resulting in a linear damage function with a more gradual slope L i n e a r regression techniques have been used with microplot data (2)
T h e data base from which damage
Trang 8348 Journal of Nematology, Volume 10, No 4,
functions are derived is a limitation to the
confidence with which they can be used
T h e slope and position of the regression
line may be influenced by seasonal varia-
tion, crop variety and predisposition, and
soil factors T h e influence of these factors
can be d e t e r m i n e d by r e p e t i t i o n of field
experiments over several years and in dif-
ferent localities T h e damage function on a
heavy soil might be shifted to the right
(line A, Fig 4) and its slope altered from
the situation on a sandy soil (line B, Fig
4) Knowledge of this variability would
allow estimation of the position and slope
of the line in individual fields of inter-
mediate soil texture (line C, Fig 4) Similar
considerations for o t h e r influences would
allow useful estimates based on data from
extreme situations r a t h e r than from every
possibility
Data from microplots are valuable and
have been used extensively (2, 9, 17)
Microplots have the disadvantage of being
expensive and u n a d a p t a b l e to standard
cultural practices, and lack the ftdl inter-
acting c o m p l e m e n t of soil flora and fauna
However, they reduce m u c h of the ex-
traneous variability i n h e r e n t in field-plot
data Attempts were made to obtain crop-
damage data from field conditions by
exploiting the variability in horizontal
distribution of nematodes t h r o u g h r a n d o m
location of individual plots (5) Crop yields
in plots were related to the range of nema-
tode densities encountered Exact relocation
of plots proved difficult, a n d data were
variable because of textural and agronomic
variations across the field A n o t h e r ap-
U5
J
t~2
L.J
\',,->
">\\
Log Pi FIG 4 C o n c e p t u a l influence of e n v i r o n m e n t a l
factors on the d a m a g e function D a m a g e functions
m e a s u r e d at extremes (lines A and B) of climatic
o r e d a p h i c factors and estimated (line C) for
October 1978
proach is to obtain data from crops grown
in adjacent strips Direction of the strips is rotated through 90 ° in different crop years
to m a n i p u l a t e nematode densities in square plots, similar to cross-over rotation trials (15) Even in a small area of a p p a r e n t l y uniform soil conditions, growth differences occur which cannot be ascribed to nema- tode effects Precision of regression analyses
is improved by expressing yield data (0-1 scale) relative to m a x i m u m and m i n i m u m yields in stratified areas of the block of plots A variation of this approach is to use
a paired plot technique where one plot of each pair is treated with a nematicide Yield
of an u n t r e a t e d plot is expressed relative to that of the treated plot of the pair, reduc- ing the effects of site variability In this approach it may be necessary to adjust for any stimulatory effects of the nematicide not associated with reduction of nematodes
The control cost function: T h i s area has received very little consideration Control costs are based on specified control recom- mendations (19), and the costs of varying levels of control have not been investigated Such control-cost relationships are necessary for optimizing approaches to n e m a t o d e pest management Some studies have e x a m i n e d levels of control achieved by varying nema- ticide dosages in closed chambers (13), b u t the a m o u n t of nematicide necessary to achieve these dosages u n d e r field conditions
is not known T h e r e is, however, some in- formation on the a m o u n t of nematicide needed to achieve a specified level of con- trol u n d e r different soil conditions (11, 12) Similar i n f o r m a t i o n is needed for o t h e r
m a n a g e m e n t practices to which a contin- uous model could be applied T h e s e might include cost of biological control agents incorporated into the soil, lengths of fallow- ing or flooding of the soil, and the levels
of control achieved
I n f o r m a t i o n for discontinuous control cost models might be available in the literature It includes, for example, relative crop values of alternate crops and rate of
n e m a t o d e decline u n d e r these crops, or degree of control achieved by, and cost of, repeated soil tillage However, there are many gaps to be filled in this knowledge
Analysis o[ nematode populations: T h e derivation and practical use of damage functions involves d e t e r m i n a t i o n of nem-
Trang 9atode p o p u l a t i o n densities Expected
p o p u l a t i o n densities on a regional basis
for use in crop-loss estimates m a y be avail-
able f r o m the records of advisory agencies
(8) However, data for regressions a n d de-
cisions on m a n a g e m e n t approaches involve
sampling, extraction, identification, a n d
c o u n t i n g of nematodes T h e reliability a n d
cost of the s a m p l i n g p r o g r a m m a y be the
l i m i t i n g factor in d e v e l o p m e n t a n d use of
tlamage functions T r e a t m e n t of the field
for insnrance purposes r a t h e r t h a n eco-
nomic threshold considerations m i g h t be a
reasonable a p p r o a c h if the cost of n e m a t o d e
assessment is too high In the o p t i m i z i n g
a p p r o a c h to economic thresholds (7), it is
useful to include a p o p u l a t i o n assessment-
cost constant in the control cost function
T h i s will n o t change the p o p u l a t i o n level
at which the difference between the deriva-
tives of the control cost a n d d a m a g e
functions is minimized, b u t it m a y resnlt
in a vertical shift in the control cost func-
tion to the p o i n t t h a t the m a n a g e m e n t
a p p r o a c h is not profitable I t is i m p o r t a n t
thresholds are corrected for e x t r a c t i o n
efficiency so that they can be a d a p t e d to
other extraction systems
C O N C L U S I O N S
Data needed for considerations of eco-
nomic a n d o p t i m i z i n g thresholds include
reliable d a m a g e functions r e l a t i n g expected
crop yields to n e m a t o d e densities a n d an
u n d e r s t a n d i n g of the influence of geo-
graphic, climatic, a n d e d a p h i c factors on
them Also r e q u i r e d are d a t a on costs of
control or m a n a g e m e n t practices, in ab-
estimates, or as related to levels of control
for o p t i m i z i n g approaches I n i n d i v i d u a l
fields, estimates of p o t e n t i a l yields a n d
expected crop values are required T h e
forecasting involved will be based on
m a r k e t trends, farm, local, a n d state av-
erages, and grower experience R e l i a b i l i t y
of n e m a t o d e p o p u l a t i o n assessment is a
prerequisite of these approaches
L I T E R A T U R E C I T E D
1 BARKER, K R., and T H A OLTHOF
1976 Relationships between nematode popu-
lation densities and crop responses Ann Rev
Phytopathol 14:327-353
N e m a t o d e E c o n o m i c T h r e s h o l d s : Ferris 349
2 BARKER, K R., P B SHOEMAKER, and 1, A NELSON 1976 Relationships of initial population densities of Meloidogyne incognita and M hapla to yield of tomato J Nematol 8:232-239
3 COOKE, D A., and I J THOMASON 1978
T h e relationship between population density
of Heterodera schachtii Schmidt, soil tem- perature and the yield of sugar beet J Nematol (in press)
4 CUI)NEY, D W., R W HAGEMANN, D G KONTAXIS, K S MAYBERRY, R K SHARMA, and A F VAN MAREN 1977 hnperial County crops: guidelines to produc- tion costs and practices, 1977-78 Univ Calif Coop Ext Circ 104 57 p
5 FERRIS, H 1975 Proposed approaches to nematode pest management research in an- nual and perennial crops, p 61-65 in: P S Motooka ted.), Planning Workshop on Co- operative Field Research in Pest Management East-West Food Institute, Hawaii 81 p
6 FERRIS, H., and M V McKENRY 1975 Relationship of grapevine yield and growth
to nematode densities J Nematol 7:295-304
7 HEAI)LEY, J C 1972 Defining the economic threshold, p, 100-108 in: Pest Control: Strategies for the Future, Natl Acad of Sci., Washington, D C 376 p
8 HUSSEY, R S., K R BARKER, and D A RICKARD 1974 A nematode diagnostic and advisory service for North Carolina N C Dept Agr Folder 3
9 JONES, F G W 1956 Soil populations of beet eelworm (Heterodera scbachtii Schm.) in relation to cropping II Microplot and field results Ann App1 Biol 44:25-56
10 KONTAXIS, D, G., R W HAGEMANN, and
I J THOMASON 1975 Sugar beet cyst nematode and its control in the Imperial Valley, California Univ Calif Coop Ext Circ 140 12 p
11 McKENRY, M V 1976 Selecting application rates for methyl bromide, ethylene dibromide and 1,3-dicbloropropene nematicides J Nematol 8:296 (Abstr.)
12 McKENRY, M V 1978 Selection of preplant fumigation Calif Agr 32:15-16
13 McKENRY, M V., and I J THOMASON
1974 1,3-Dichloropropene and 1,2-dibromo- ethane compounds II Organism-dosage response studies in the laboratory with several nematode species Hilgardia 42:422-438
14 OLTHOF, T H A., and J W P O T T E R 1972 Relationship between population densities of Meloidogync hapla and crop losses in summer-maturing vegetables in Ontario Phytopathology 62:981-986
15 OOSTENBRINK, M 1959 Enkele een voudige proefveldschemas bij het aaltjesonderzoek Meded Landbouwhogesch Gent 24
16 OOSTENBRINK, M 1966 Major characteristics
nf the relation between nematodes and plants Meded Landbouwhogesch Wageningen 66(4) : 1-46
17 P O T T E R , J W., and T H A OLTHOF 1977, Analysis of crop losses in tomatoes due to
Trang 10350 Journal of Nematology, Volume 10, No
P r a t y l e n c h u s p e n e t r a n s J N e m a t o l 9:290-295
18 R A B B , R L 1970 I n t r o d u c t i o n to t h e con-
ference, p 1-5 in: R L R a b b a n d F E
G u t h r i e (eds.), C o n c e p t s o f Pest M a n a g e -
m e n t N C State Univ Press, R a l e i g h , N C
242 p
19 R A D E W A L D , J D 1973 S u m m a r y of n e m a -
tode control r e c o m m e n d a t i o n s for C a l i f o r n i a
crops U n i v Calif Agr Ext 41 p
20 S E I N H O R S T , J W 1965 T h e r e l a t i o n b e t w e e n
n e m a t o d e d e n s i t y a n d d a m a g e to p l a n t s
N c m a t o l o g i c a l 1:137-154
21 S E I N H O R S T , J w 1972 T h e r e l a t i o n s h i p
b e t w e e n yield a n d s q u a r e root of n e m a t o d e
density N e m a t o l o g i c a 18:585-590
22 S T A T E O F C A L I F O R N I A 1977 Notice of
4, October 1978
p r o p o s e d c h a n g e s in t h e r e g u l a t i o n s of t h e
D e p a r t m e n t of Food a n d A g r i c u l t u r e p e r t a i n - ing to A g r i c u l t u r a l Pest C o n t r o l Advisors
S a c r a m e n t o , Calif 11 p
23 T H O M A S O N , I J., a n d M V M c K E N R Y
1974 C h e m i c a l control of n e m a t o d e vectors
of p l a n t viruses, p 423-439 in: F L a m b e r t i ,
C E T a y l o r , a n d J W S e i n h o r s t (eds.)
N e m a l o d e Vectors of P l a n t Viruses I ' l e n u m ,
NY 460 p
24 T R A I N , R 1976 H e a l t h risk a n d e c o n o m i c
i m p a c t a s s e s s m e n t s of s u s p e c t e d carcinogens Federal R e g i s t e r 41:21402-21405
25 W A L L A C E , H R 1973 N e m a t o d e ecology a n d
p l a n t disease E d w a r d Arnold, L o n d o n 228 p
Interaction Between Neoaplectana carpocapsae and a
Granulosis Virus of the Armyworm Pseudaletia unipuncta
Abstract: Neoaplectaua carpocapsae d e v e l o p e d a n d r e p r o d u c e d in a r m y w u r m hosts infected w i t h
a g r a n u l o s i s virus (GV) M a c e r a t e d tissues of d a u e r j u v e n i l e s f r o m GV-infecled hosts h a d suf- ficient GV to infect 1st a n d 2 n d i n s t a r a r m y w o r m s Electron-microscope e x a m i n a t i o n of d a u e r
j u v e n i l e s a n d a d u l t female n e m a t o d e s c o n f i r m e d t h e presence of GV in t h e l u m e n o f t h e
i n t e s t i n e No GV was o b s e r v e d in o t h e r tissues of t h e n e m a t o d e Key Words: DD-136 n e m a t o d e ,
n e m a t o d e - i n s e c t virus i n t e r a c t i o n , insect virus, Baculovirus
T h e mutualistic r e l a t i o n s h i p of the DD-
136 strain of Neoapleetana carpocapsae a n d
nematophilus, has been clearly established
(1, 6) Very little is known, however, a b o u t
pathogens and this nematode Lysenko a n d
Weiser (4) e x a m i n e d the microflora asso-
ciated with N carpocapsae a n d its host,
GalIeria mellonella, a n d f o u n d several
bacterial species other t h a n A nematophiIus
in the gut of the nematode V e r e m t c h u k
a n d Issi (9) r e p o r t e d t h a t the n e m a t o d e ,
N agriotos ( = N carpocapsae), which de-
veloped ill Pieris brassicae larvae infected
with the p r o t o z o a n Nosema mesnili was
also infected by the protozoan Seryczyfiska
(8) studied the defense reactions of the
Colorado p o t a t o beetle against the fungi
Paecilomyces larinosus a n d Beauveria
bassiana, a n d N carpocapsae She f o u n d
that the simultaneous exposure to the
Received for publication 30 March 1978
~Division of Nenlatology and Facility for Advanced In-
strumentation, respectively University of California, Davis
spores of either fungi a n d the n e m a t o d e increased tile n u m b e r of hemocytes in the
h e m o l y m p h over that in u n t r e a t e d beetles
W e are not aware of ally studies of insect
stndy was initiated to investigate the inter- action between N carpocapsae a n d a gran-
Pseudaletia unipuncta
M A T E R I A L S A N D M E T H O D S
G V and nematode infections: T h e
O r e g o n i a n straiu of GV, o b t a i n e d from
Dr Y T a n a d a , University of California, Berkeley, was used to infect newly m o l t e d 5th-stage larvae of the a r m y w o r m as de- scribed by Kaya a n d T a n a d a (3) T e n days after feeding on the virus, 6th-instar army- worms which showed typical signs a n d
s y m p t o m s of a GV infection a n d an equal
n u m b e r of h e a l t h y 6th-instar a r m y w o r m s were weighed Each a r m y w o r m larva was
c o n t a i n i n g ca 500 d a u e r juveniles of N
carpocapsae on m o i s t filter paper After