THE DESIGN OF BIOLOGICAL MONITORING
SYSTEMS FOR PEST MANAGEMENT

. Dissertation for the Degreé 'of-Ph; D.
< MICHIGAN STATE UNIVERSITY
, STEPHEN MELWOOD WELCH
1977

 

 

 

 

This is to certify that the

thesis entitled

iriE DLLSIGN OF bIOLOGICAL
MONITOfiING SYSTiI’ZD‘ FOR
PEb‘l‘ I‘iANhGEI’GENT

presented by

Stephen Melwood Welch

a...

has been accepted towards fulfillment
of the requirements for

Ph. D. degree mm

 

MMZW

Major professor

Date 1 Feb 77

G7 639

 

ABSTRACT
THE DESIGN OF BIOLOGICAL

MONITORING SYSTEMS FOR
PEST MANAGEMENT

BY
Stephen Melwood Welch

With the rising world population and the increased
value of food and fiber production, losses due to agricul-
tural pests have become intolerable. This has led to the
emergence of sophisticated philosophies of pest control
including pest management. Biological monitoring is an
important component of management systems which has not .
received adequate analysis in the literature. This thesis
formulates a design procedure for biological monitoring
systems which incorporates biological, economic, and
stochastic factors and time delays.

Such a system is viewed as having a hierarchical
structure. One or more decision makers receive data from
a sampling point located within a geographical monitoring
unit. A regional system is composed of a set of these
units. Monitoring resources are allocated among the units
by a regional controller so as to meet system goals.
Important time delays exist at the regional level, at the
monitoring unit level, and at the decision making level.
Information flowing between levels is subject to noise

which can degrade overall system performance.

Stephen Melwood Welch

Biological factors include (1) the biological demand
for monitoring, (2) distributions of target species, (3) the
biological interpretation of monitoring results, and (4) the
biological effect of time delays. Biological models are
discussed as a method of formalizing this information.

The stochastic discussion combines the effects of
spatial and sampling variation with time delays to assess
the reliability of monitoring data. Bayesian statistics are
employed to show how likelihood distributions are altered
by these processes. Examples are drawn from the population
dynamics of the European red mite, Panonychus ulmi (Koch).

The economic analysis of biological monitoring proceeds
from two points of View, that of the decision maker who must
profitably use the data he pays for and that of the monitor
who expends resources to acquire the data. Utility theory
is used to relate the decision maker's losses to his decisions
and perceived likelihoods. The monitor's economics are
viewed as an investment for which a return can be calculated
via a discounted cash flow analysis.

The logistics of monitoring are studied by decomposing
total activity into a series of actions each with its own
time delay.- Methods for the separate analysis of each action
are presented.

The most important portion of the thesis demonstrates
.mathematical linkages between the four classes of factors
just discussed. There are, in actuality, only two degrees

of freedom among these four variable types. This makes it

Stephen Melwood Welch

possible to construct a chart on which the performance of
design alternatives can be determined graphically. Such
a chart is constructed for an organism like the European
red mite.

The last chapter summarizes the design procedure and
presents arguments demonstrating the broad applicability

of the method both within agriculture and outside it.

THE DESIGN OF BIOLOGICAL
MONITORING SYSTEMS FOR
PEST MANAGEMENT

BY

Stephen Melwood Welch

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Zoology

1977

© Copyright by
STEPHEN MELWOOD WELCH

1977

DEDICATION

To the six most important people in my life:
Mary Lou, Jack, Virginia, Chris, Jack, and Grace

ii

ACKNOWLEDGMENTS

My thanks go first to my major professor, Dr. William
E. Cooper, and also to Dr. Brian A. Croft who have given
me much encouragement, support, and ideas for this study.
I also wish to thank the other members of my committee
Drs. P. David Fisher, R. L. Tummala, and D. J. Hall for
their comments and advice. Dr. M. J. Dover provided
invaluable assistance with that most foreign of languages,
English. In addition, I am indebted to Dr. Dean L. Haynes
who, although not directly involved with my thesis, was
in large part responsible for the milieu of ideas which

made this thesis possible.

iii

Chapter

II

III

IV

VI

VII

VIII

LIST OF TABLES,

TABLE OF CONTENTS

LIST OF FIGURES

INTRODUCTION.

GENERAL ORGANIZATION OF A MONITORING-
MANAGEMENT SYSTEM

A.
B.
C.

The decision making level . . . . O . .
The monitoring unit level
The regional level.

BIOLOGICAL ASPECTS OF DESIGN, , , , . . , ,

A.
B.
C.

D.

The biological demand for monitoring. .
Distribution studies. . . . . .
The extrapolation of population
processes through time. . ... . . . . .
Biological models . . . . . L . . . . .

STOCHASTIC ANALYSIS OF MONITORING SYSTEM
DESIGN. 0 O O O O O O O O C O O O O O O O C

THE ECONOMICS OF THE DECISION MAKER . . . .

MATHEMATICAL RELATIONS BETWEEN DESIGN
FACTORS O O O O C C O I O O O O O O O O D C

THE ANALYSIS OF SYSTEM TIME DELAYS. . . . .

A.
B.
C.

Transmission of the trigger event . . .
Transportation to the sampling site . .
Collection of the sample (or data) and
processing. . . . . . . . . . . . . . .
Transportation to the processing site .
Transmission of results to the decision
maker . . . . . . . . . . . . . . . . .
Accomplishment of the control action. .

THE ECONOMICS OF THE MONITORING SERVICE . .

SYNOPSIS OF DESIGN PROCEDURE. . . . . . . .

LIST OF REFERENCES. . . . . . . . . . . . .

iv

Page

vi

ll
14
18
22
24
24
26
32
33
44

66

75
92
92
94

95
104

107
108

115
128

139

Tables

Table

Table

Table

Table
Table

Table

Table

Table

Table

Table

Table

Table

10.

11.

12.

LIST OF TABLES

Schedule of decision maker's costs. . .

Some representative variables from

'each of the four important design

parameter classes . . . . . . . . . . .

The decomposition of total monitoring
delay 0 O O O O O O O O O O C O O O O 0

Road classification system. . . . . . .
Inter-subarea distance matrix (miles) .

Inter-subarea time factor matrix
(hours per mile). . . . . . . . . . . .

Partition of a mite sampling protocol
into discrete actions and the required
times 0 O O O O O O O O O O O O O O I 0

Definition of variables in the timing
equation (7-2) I I O I O O O O O O O O 0

Simplified investment screening
algorithm . . . . . . . . . . . . . . .

Discounted cash flow analysis of the
full system (FS). . . . . . . . . . . .

Discounted cash flow analysis of the
reduced system one (RS I) . . . . . . .

Discounted cash flow analysis of the
reduced system two (RS II). . . . . . .

76

93
96
97

98

102

103

118

121

122

123

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

10.

11.

12.

LIST OF FIGURES

A simplified block diagram of a
closed-loop management system. . . . . .

A detailed diagram of a pest
management system. . . . . . . . . . . .

The migration of M, fascifrons (Stal)
into WisconSin O O O I O O O O O O I O O

 

PETE description of a variegated
cutworm phenology model. . . . . . . . .

An automatically generated pest
warning from the PETE system . . . . . .

The cumulative distribution of red
mite densities at the assumed time
of first detection . . . . . . . . . . .

The cumulative waiting time
distribution from a simulation

study of a mobile van-based mite
counting service . . . . . . . . . . . .

The prior density function from
equation (3-4) . . . . . . . . . . . . .

A comparison of the posterior
effect of a uniform versus a more
complex, model-based prior distribution.

The change in a likelihood function
resulting from the extrapolation of
data taken at a point over an

extended spatial area. . . . . . . . . .

A phase plane plot showing simulations
of three interactions of the European
red mite (horizontal axis) with
Amblyseius fallacis (vertical axis). . .

A counterexample for Theorem 2 . . . . .

vi

12

29

40

42

47

49

52

54

63

72

81

Figure

Figure

Figure

Figure

Figure

Figure

Figure

l3.

14.

15.

16.

17.

18.

19.

The function V(v) graphed by
assigning the parameter values
of chapter III . . . . . . . . . . . .

Contour lines of sampling intensity
and maximum allowable time delay

as a function of risk and monitoring
unit size. . . . . . . . . . . . . . .

The cumulative density functions
of travel time per day for two
different levels of demand . . . . . .

The total processing time for mite
samples as a function of total mite
density and prey-predator ratio. . . .

The mean waiting time for service
as a function of desired accuracy. . .

A continuum of technologies indexed
by desired sampling accuracy . . . . .

The return on investment for three

mite monitoring systems plotted on
a nomogram showing system performance.

vii

87

89
99

105
110

113

125

INTRODUCTION

With the rising world population and the increased
value of food and fiber production, the losses due to
agricultural pests have become intolerable. This situation
has been aggravated by the spread of resistance to chemical
biocides and the resultant failure of many pest control
systems developed over the last 25 years. This has led to
the emergence of more sophisticated pest control method-
ologies and their incorporation into systems of pest
management. Luckmann and Metcalf (1975) citing Geier (1966)
describe pest management as

"(1) determining how the life system of a

pest needs to be modified to reduce its
numbers ... below the economic threshold;

(2) applying biological knowledge and current
technology to achieve the desired modification
...; and (3) devising procedures for pest
control suited to current technology and
compatible with economic and environmental
quality aspects ..."

There are three basic components of any pest management
system: a monitoring component which provides data, a
decision making component which determines a control strategy
based on the monitoring results, and an action component
which implements the control decision. In previous types

of control systems these components often have operated in

an "open-loop" fashion. That is, relevant states of the

2

crop ecosystem (be they pest status or cumulative damage
or just calendar date) were sensed in a rather crude
manner, a control decision made, and then implemented with
only limited concern for long-range effects. Pest manage-
ment recognizes that these components cannot be considered
outside the context of the crop or agro-ecosystem. This
system integrates the effects of control inputs with
biological and physical factors in ways which can subsequently
be monitored. This results in a "closed-loop" system as
shown in Figure 1. The closed-loop topology clearly suggests
that control is an ongoing process where today's actions can
influence tomorrow's decisions for good or for ill.

This realization has resulted in a significant altera-
tion in the conceptualization of management systems and a
clear need for new types of analysis to cope with design
and implementation problems (National Academy of Science,
1969; Luckmann and Metcalf, 1975; Tummala £5 21., 1976).
Various authors have grappled with pieces of the problem,
especially as regards the decision making and implementation
components. Headley (1971) and, later, Hall and Norgaard
(1973) examined the relation between population biology and
control in a deterministic sense. Others, particularly
Carlson (1969a, 1969b, 1970, 1971) have dealt with stochastic
and Bayesian approaches to decision making. As yet there
has been little analysis of modern monitoring systems for
pest management with the exception of physical factors in

the environment (g.g., Haynes gt a1, 1973).

Figure l. §_simplified block diagram of a closed-100p
management system.

 

 

 

 

55508-83 . L

 

 

 

H A

 

m2<mo0ma
zo_.6< oontzoz

 

 

 

 

 

AI A

022.32 +
-zo_w_om_o

 

 

 

 

 

 

5

The purpose of this dissertation is to describe an
encompassing technique for the design and analysis of
systems for monitoring biotic as opposed to physical
parameters. Of necessity, monitoring activities must be
considered in the context of the entire management system.
Information from the monitoring component undergoes a
number of transformations as it is processed around the
control loop of Figure 1. It is impossible to know how
useful the data are without knowing their intended uses.

Examination of Figure 1 suggests four classes of factors
which, between them constitute an adequate description of
a management system. They are: biological processes within
the agro-ecosystem, stochastic features of the system being
I observed and of the monitoring component, the economics of
monitoring and decision making, and the time delays of the
entire control 100p particularly as affected by the level
of technology. The biological input specifies the dynamics
of the system being controlled while economics is required
to describe the objective function (i.g., goal) of the
control process. The quality of the information on which
decisions are based can only be assessed if the stochastic
elements of the system are understood. Finally, the
dynamics of the complete closed-loop system cannot be
specified unless the time delays of the management process
are known.

The basic ideas behind this thesis emerged in the

period between 1973 and 1976 as a result of the author's

6

work with the management of phytophagous mite populations
in orchards (Croft gt gt., 1976b), the development of
extension data delivery systems (Croft gt gt., 1976a), and
the analysis of general modeling problems (Welch gt gt.,
in prep.). This experience is reflected in the specific
examples used herein, but the discussion will make clear
how to apply these techniques to a wide variety of systems.

A note on the format of the thesis is also necessary.
The normal dissertation proceeds in chronological order
from problem statement and literature review through materials,
methods, and results, to conclusions and future outlook.
This outline is adequate for field studies or reports on
specific topics. In this thesis, the contribution being made
is a synthesis of a variety of separate but related subjects.
The synthesis is original even though the raw ideas may not
be new. For this reason, the discussion is organized topically
rather than chronologically.

The first topic is a general topology for an operational
pest management system. Basically it consists of the four
components of Figure l but elaborates them in a way that
emphasizes biological monitoring activities. The system is
outlined in a hierarchical manner which demonstrates that
pest management is an activity which is distributed in space
and time. In particular the types of activities and functions
carried out at three levels (a decision making level, a
monitoring unit level, and a regional level) are defined and

discussed.

7

The second chapter focuses on biological aspects of
monitoring design. Topics include the biological require-
ments for sampling, the need for studies of the distributions
of target species to aid in statistical design, and the
extrapolation of population processes through time. Biolog-
ical modeling is introduced as a method of integrating data
so it can be applied at several points in the design process.
The specific data sets that modeling requires as well as
useful criteria for "good" models are also identified.

The following chapter deals with the stochastic elements
of systems design. By applying the common language of
Bayesian probabilities to the design problem, this chapter
serves an integrative function. The specific discussion
centers on how to combine spatial variation, measurement
error, and time delays to determine the probabilities of
various ecosystem states as seen by the decision maker. This
chapter also begins an extended example concerning the dynamics
of the European red mite, Panonychus ulmi (Koch), in predator-
free systems. The example is intended to demonstrate
monitoring analysis calculations in cases where pests are
subject to sudden exponential outbreaks. The methods
Presented are general enough to be applied to the less
Common case where significant natural enemies exist, but the
aUthor felt that the extra complexity would detract from the
example ' s illustrative value .

Chapter IV begins the discussion of economics. For
conVenience the treatment is broken into two chapters (IV

and ‘VII). Chapter IV deals with the economics of monitoring

8
as perceived by the decision maker. Because pest management
decisions are made at risk the costs of monitoring, control,
and damage are distributed random variables. Various methods
are presented to interrelate these variables with results
of the stochastic analysis to arrive at measures of the
utility of monitoring.

The fifth chapter demonstrates an important mathematical
relationship which exists among the classes of variables
discussed in chapters II, III, and IV. Two theorems are
proved showing that there are only two degrees of freedom
between typical variables describing allowable time delays,
monitoring unit variability, system workload, and economic
risk. A chart or nomogram is proposed on which, for a given
system, knowledge of any two variables will allow the
prediction of the other (with one minor exception). ‘Such a
chart is Constructed for a predator—free European red mite-
system.

The application of the nomogram is further developed in
the next two chapters. Chapter VI discusses system time
delays. Total delay is decomposed into discrete processing
activities each of which is separately analyzed. The nomogram
is used to give a direct readout of the effect on system
performance of alterations in these delays. By way of example,
it is shown how a 14 percent increase in resolution could,.
in a hypothetical mite monitoring system, cause a ten—fold
increase in economic risk due to increased time delays.

Chapter VII, resuming the economic discussion, presents

the viewpoint of the monitoring service. The establishment

9

of a monitoring system is viewed as an investment whose

utility must be judged. A screening program which calculates
a return on investment via a discounted cash flow analysis
(Park, 1973) is presented. This is combined, via the nomogram,
with the constraints on system performance developed in the
preceding chapters to make the final choices on technology,
price structure, etc.

Chapter VIII is a synopsis of the design procedure
outlined in the body of the dissertation. Following standard
system design methods (Manetsch and Park, 1974) it begins
with an analysis of management needs. Next the designer
constructs several alternative methods of meeting these needs.
These designs are then modeled so that they may be optimized,
evaluated, and the best one selected. This stage involves
the types of biological, statistical, economic, and timing
studies discussed in earlier chapters. At some point during
this process, one or more of the alternatives will be subjected
to field testing. The chapter describes the types of
auxiliary data (travel times, grower acceptance, etc.) which
Tnust be taken to complete the analysis. The nomogram of
chapter V provides the mechanism for interpreting this data.
Once the best design has been chosen the last step is imple-
mentation. By this time, because of the extensive field
work and contact with all affected parties, the selected
alternative should be seen as an effective pest management
tool, Even after implementation, however, the system must be

Periodically reevaluated so it can adapt to changing conditions.

10
In conclusion, the dissertation emphasizes the broad applica-
bility of this approach to a variety of other agricultural

and resource management tasks.

CHAPTER I

GENERAL ORGANIZATION OF A MONITORING-MANAGEMENT SYSTEM

The methods employed for monitoring a biological system
never exist in isolation; they are always part of some larger
structure which utilizes the data to some purpose. Often
the information collected by monitoring will be subjected to
processes of interpretation and extrapolation. Each such
operation will affect the utility of the data. On the one
hand each manipulation will make the data more meaningful
or more widely applicable. However, the variances associated
with the data are generally increased by these activities
making the results less reliable. 'Only by studying the
monitoring component within the context of its overall system
will the designer be able to maintain a favorable balance
between meaningfullness and reliability. For this reason
this chapter is devoted to the construction of a generalized
management system. This schema will be so ordered as to
reveal the important transformations of biological monitoring
data.

A management system can be conceived as having three
hierarchically organized levels each with its own activities
and characteristics (Figure 2). We shall refer to these as
tbs! decision making level, the monitoring unit level, and the

reB‘ional level. Briefly, the decision maker is the ultimate

ll

Figure 2.

12

A detailed diagram of a pest management system.
Each decision maker—haE control over a portion
of the extended agroecosystem. He acts on
information from a sampling program which
monitors conditions at a point somewhere
within a geographical unit containing one or
more decision makers. Sampling activities

are optimized at a regional level to meet
system goals such as profit, efficient service,
etc. Important time delays are (l) the time
required to respond to a request for sampling,
(2) the time necessary to transmit the
monitoring results to the decision maker, and
(3) the time needed by the decision maker to
interpret and act upon the monitoring data.

 

 

l3

    
   
       

c2293

   

Ectootu
C0300

c2203

    

 

-
”I! 30:50 22.23.. L

  

2:9: .oEmEco.__>co maocoooxm II“

cEmm “ .Emm

£053on .960 n Em _

h

 

tonotmcoo

 

  
   

ucoEmc

_20E=mw mEEom E0605 .609:

 

Em" “ :muI

[30:60 20:8th

  

_2moo oczotmao oEEEom w_n_Eom

fill 335 _0EoEco.__>cm 80560on

E29808 .960 _

 

4m>MJ :2: 02532 20_m_owo

4w>m4 ...—2: 0255:205—

Eotuoa .63.:
280 058.63 05380.... oEEom

 

t I. >220

 

 

 

 

 

 

.05 o
@5503 o
3.68.. o
052.6 a
cozooozo
8503.. o

 

 

 

    

_
_._u>m._ ..qzoaum

l4
recipient of monitoring outputs who converts the data into
action programs and sustains the resultant benefits or losses.
The monitoring unit is a geographical area containing a
sampling point which services one or more decision makers.
At the regional level, monitoring resources are allocated
among the monitoring units so as to best achieve system goals.
We shall now discuss each of these levels in detail.

The decision making level. This forms the lowest level
of the system. Each decision making unit consists of a parcel
of land (or other production unit) plus a decision maker who
makes the control decisions for that parcel. It is an
important defining property of these units that all subsections
of the unit behave and are treated identically.

In Figure 2 these units are diagrammed as parts of an
extended agro-ecosystem. In addition to the control inputs
from action programs, the parcels receive exogenous environmental
inputs such as solar radiation, temperature, precipitation,
etc. It is the purpose of the monitoring component to
provide the decision maker with "acceptably accurate" data
on "relevant aspects" of the agro-ecosystem in a "timely
manner". Precise meanings of the quoted phrases will emerge
in the course of the dissertation.

Because the thrust of this thesis concerns monitoring we
Will treat the decision making process in an aggregated sense.
That:is, the "decision maker" is taken to consist of all
ihkiividuals and organizations who mediate the conversion of
r“(mitoring outputs into action programs. Croft gt gt. (1976a,

P21) give a breakdown of these groups for Michigan integrated

15
pest management. Two exceptions to this aggregation must be
noted. Organizations such as testing laboratories which
process raw sample materials are properly considered as part
of the monitoring component. Another special case is when
one individual or group makes distinct decisions for two or
more production units. In this instance each unit is considered
to have a separate decision maker.

The activities of the decision maker, however lumped,
form the single most important transformation which the moni-
toring data undergo. For this reason it is incumbent to
discuss the various types of decision rules in use in pest
management and identify some common class on which to base
the analysis.

The simplest and earliest rule was "there (is) no good
bug except a dead bug" (Stern, 1973). Better procedures are
based on the relationship between pest density and potential
damage. Shotwell (1935) was one of the earliest to describe
such a relation. He set up a rating system based on visual
counts of grasshoppers and determined that at 15 individuals
per square yard, 40 percent of the cropland could suffer
some loss. Formally, this type of rule states that control
measures should not be instituted below that density at which
the marginal cost of control just exceeds the marginal damage.
This is called the economic injury level (Stern gt gt., 1959).

Because it takes time to reach a control decision and
then act (see delay 3 in Figure 2) a useful modification of
this rule has come into vogue. A new term, "economic threshold",

has been introduced which is defined as "the density at which

16
control measures should be applied to prevent an increasing
population from reaching the economic injury level" (Stern
gt gl., 1959). It has long been recognized that thresholds
and injury levels are dependent on meteorology, host maturity ,
and other characteristics, and the cost of control. The
economic threshold is additionally dependent on the manner
(t.g., time delay) in which the control is applied. The
dependence of damage on these factors will be discussed
further in the next chapter.

Another refinement in decision rules was achieved with
the recognition that there may be several distinct decision
periods through the course of a season and that the outcome
of one period can affect later decisions. One example of
such a breakdown is the traditional spray calendar based on
crop phenology. It is possible to specify early season
application rules which control impacts on non-target species
so as to achieve payoffs later on. Croft (1975) describes
such a program for plant feeding mites on apples.

Mathematical techniques such as dynamic programming
(Shoemaker, 1973a) can be used to quantify this idea. This
method adjusts the losses perceived in a given period to
reflect the results of possible decisions made during that
period. This adjustment is the sum of control costs plus
terminal costs for an optimal strategy beginning in the
next period based on current outcomes (Wagner, 1975). A
major defect of this technique is that, except in very simple
cases, the formulations are so complex that they burden the

largest computers (Shoemaker, 1973c).

17

All of the decision rules discussed to this point have
been essentially deterministic in that they either utilize
average ecosystem behavior or rely on specific realizations
of stochastic variables. In practice, of course, great risk
attends all pest management decisions. One method to take
risk into account is statistical decision theory (Carlson,
1970). This method explicitly notes three important charac-
teristics of pest management decisions: (1) they are
selections among finite sets of alternatives, (2) they have
as their goal the maximization of some objective function
(see chapter IV), and (3) the decisions have associated
probabilities of error.

The decision theoretic approach partitions the possible
monitoring results into sets which correspond to distinct
control alternatives. The management decision is to implement
the strategy corresponding to the set into which the actual
monitoring outcome falls. The sets are constructed so as to
maximize the probability of optimal results.

It is evident that this procedure contains the other
rules as special cases. Rules involving thresholds can be
dealt with by partitioning monitoring results into two sets,
those above and those below the threshold. Most multi-period
decision methods assume finite sets of alternatives and are
therefore amenable to the same treatment. By adopting a
statistical decision theory approach we shall be able to
link biological, spatial, temporal, economic, and stochastic

parameters via the common language of probabilities. For

this reason, we shall follow this paradigm in what follows.

18

The monitoring unit level. A monitoring unit consists

 

geographically of one or more decision making units. The
defining characteristic of the monitoring unit is that it
contains just one sampling point which serves all the decision
makers in the unit. These data may be transformed in some
standard way for all users or tailored to their individual
needs.

The events which take place at this level deal solely
with monitoring and occur in a sequence we shall call the

sampling cycle. The first event is the determination that

 

the time to sample has arrived. How this happens depends on
the system design. One method is to sample at certain I
pre-specified points in chronological or physiological time.
Provided that the sampling interval is short enough, precise
population tracking is possible. Biological rate functions
determine the sampling rates one should use. According to
the sampling theorem (Bekey and Karplus, 1968) accurate
reconstruction of a signal is not possible unless that
signal is sampled at a rate at least twice as fast as its
most rapid fluctuation. Unfortunately, this is often not
possible in practice. An acceptable substitute is to sample
at a rate several times (at least twice) as fast as the most

rapid fluctuation of major amplitude. Oscillations more

 

rapid than this will appear as spurious low frequency compon-
ents in the data but their small amplitude will make them
unimportant.

The disadvantage of fixed period sampling is that much

effort may be expended while nothing of significance is

l9

occurring. Other methods attempt to allocate resources to
those periods ("windows") of particular interest. Usually
this involves keying the observation to some biological or
physical event (or "trigger") to which a knowledge of the
target species attaches a special meaning. Triggers should
have three properties: (1) they should be observable,
(2) they should bear a reasonably direct relationship to
the ultimate ecosystem variable of interest, and (3) they
should occur early enough to permit the monitoring-management
system to respond to the conditions the triggers herald.

There are many possible types of triggers. For example,
in an experimental mite monitoring program (Welch, 1976)
anecdotal observations on the presence of mites made by
growers in the course of their normal activities served as
the monitoring stimulus. Sampling can also be linked to
observable phenological stages of the host crop or of some
other indicator plant. To aid in this a network of phenolog-
ical stations has been set up in the northeastern United

States based on the Persian lilac (Syringa persica). Hopp

 

gt gt. (1972) reports that by 1971 498 "standard phenological
gardens" had been established in 28 states plus Quebec.
Careful observations were being made relating lilac develop-
ment to environmental parameters. Tying these parameters

to pest biology would permit observations of the lilac to
serve as a sampling input. Jones (1976) describes an apple
scab monitoring program triggered directly by the environment.
Two conditions are required for scab infection: the presence

of a spore innoculum and wet foliage. In this program, leaf

20

wetness meters trigger rotary spore traps automatically.
The traps are then examined by technicians who are also
"triggered" by rainfall. The level of spore discharge is
converted to a control recommendation by use of a Mills
chart (Mills, 1944; Mills and LaPlante, 1951).

Two other important types of trigger are the predictive
trigger and the post-control trigger. In situations where
the biology of a system is well understood it is sometimes
possible to predict when the population will require monitor-
ing. In the next chapter we shall discuss how this can be
achieved with biological models. In post-control monitoring,
sampling is scheduled to occur at some specified interval
after a control measure has been applied. This can be used
either as a check on the success of control or as input to
the next stage of some multiperiod decision process. What
both of these methods have in common is that time delay 1
(Figure 2) is eliminated. This is because the "trigger" in
both systems occurs before the sampling is actually required.
This forewarning can make it much easier for the monitoring
resource allocator to function efficiently.

Typically, however, some delay will occur, the length of
which depends on system design and available resources. A
general result from queuing theory (Baily, 1964) states that
delay increases exponentially as the average triggering rate
approaches the rate of service. One of the major design goals
is to determine the level of resources needed to satisfy
demand (see the next chapter) without excessive delay

(chapters V and VI).

INN

21

The next step is to collect and process the sample:

It is very difficult to discuss specifics in this area
because of the wide variety of sampling schemes available
(Cochran and Cox, 1957; Pielou, 1974; Kirk, 1968) and the
hundreds of economic species to which they can be adapted.
Instead, we shall treat this component as a "black box" by
focusing on the important characteristics of sampling

inputs and outputs. That is, we shall view the sampling
program as consuming resources and generating a distribution
describing the likelihood of various ecosystem states (see
chapter III). In this we shall follow the "Bayesian"
philosophy of Savage (1954, 1962) who argues that this
distribution encodes the total result of a measurement
procedure and that a detailed knowledge of sample design

can add nothing beyond this. This approach enables us to
deal with factors like quality and utility of results without
requiring assumptions on such points as sequential versus
fixed size designs, absolute versus relative measures, and
so on. These topics are adequately treated elsewhere.

The last step of the sampling cycle is to transmit the
results of the operation to the decision makers contained
within the monitoring unit. This can be done in any expedient
fashion from simply handing the decision maker the results of
a procedure conducted at the site of production to the use
of various electronic media (Haynes gt gt” 1973: Croft gt gl.,
1976a). As will be discussed in chapters VI and VII, there
are important time delays and costs associated with any

possible method. It is crucial that these be explicitly

22
accounted for in the system design.

The regional level. The highest or "regional" level

 

of a management system consists of the geographical union
of all monitoring units. Organizationally it is the level
at which the whole system is operated. There are five major
types of activities which take place at this level: (1) the
acquisition of the resources needed for monitoring and data
transmission, (2) the distribution of these resources to
meet demand, (3) the determination of the prices charged
end users for these resources, (4) all necessary accounting
and record keeping, and (5) advanced planning.
In chapter VII we Shall study design budgets of resource
needs. These resources include materials and labor and
their costs can be divided into capital and operating costs.
How these resources are allocated determines sampling delay.
The designer must choose a distribution algorithm which
minimizes this delay. There are numerous appropriate opera-
tions research methods (Wagner, 1975) which can be applied.
Pricing decisions require a detailed understanding of
market conditions, financial position, and organizational
character. The designer, however, is only responsible for
a general evaluation of system potential. This often involves
a rough screening of alternative price structures. In
chapter VII we shall adopt the point of View that a monitoring
system is an investment whose desirability must be determined.
The record keeping and planning functions are quantita—
tively important to the designer only as they contribute to

system overhead costs. Speaking qualitatively, however, they

23
are essential to smooth system operation. Good records
are necessary to track the finances and efficiency of an
organization. Records of monitoring results are of use
not only to the decision makers for whom they are intended
but also as biological input to the planning function. This
planning capability is required because improvements in
technology are always occurring as are shifts in demand,
resource costs, and other market parameters. The organization
must continually strive to anticipate these costs and adapt
to meet them (Scanlan, 1974).

A conceptual structure such as Figure 2 can be applied
to a wide variety of actual programs. It is not necessary
that all of the functions described here be carried out by
visibly distinct groups or individuals. For example, a
grower might do his own monitoring when he felt it was
necessary. In such a system, functions at the regional,
monitoring unit, and decision making levels would all be
accomplished by the same person. Nevertheless, by separating
these components as we have done, we are in a better position
to analyze the outcomes and value of such a procedure. The
rest of this dissertation is devoted to the particulars of

this analysis.

CHAPTER II

BIOLOGICAL ASPECTS OF DESIGN

One of the major characteristics of modern pest

management is a reliance on sound ecological principles
(Luckmann and Metcalf, 1975). As a primary management
component, biological monitoring requires a thorough know-
ledge of target species biology. There are three major
design areas where biological data are needed: (1) assaying
the biological demand for sampling, (2) distribution and
dispersal studies for statistical design, and (3) the
extrapolation of population processes through time. We
shall discuss each of these in turn.

The biological demand for monitoring. As time passes,

 

a target population will develop and, perhaps, disperse
throughout the monitoring region. Local populations will
reach stages requiring monitoring at various points in time
and space. This is the "triggering" referred to in the last
chapter. The spatial and temporal distributions of these
trigger events constitute the biological demand for
monitoring. This demand is an important determinant of the
overall pattern of monitoring resource allocation: clearly,
it is undesirable to expend resources where they are not
needed. Biological demand forms the baseline from which
actual demand (conditioned by economics, logistics, and the

distribution of decision making units) can be calculated.
24

25

Two simple methods of determining biological demand
are projection from historical records or calculation from
target species phenology. For example, in a study by the
author to project the demand for phytophagous mite monitor-
ing, historical data on mite densities from 146 Michigan
apple growers (Croft, unpub. data) were examined. The
monitoring trigger was a population density of 3 to 10 mites
per leaf (well below the nominal economic threshold of 15
per leaf). It was assumed that growers could detect such
populations in the normal course of their activities. The_
relative frequency of triggering was determined by date for
each of the seven areas of the state for which records were
available.

Another method can be used when something is known of
the developmental rates of the species, perhaps as affected
by environmental parameters. In this case reference to
weather charts or other data sources permits the construc-
tion of maps which show the distribution of triggering
(Fulton and Haynes, 1975). The developmental data can be
based on either laboratory or field experiments although
the latter are preferable. The problem with this phenolog-
ical approach is that it fails to take the spatial distri-
bution of the species into account. That is, the conditions
for triggering might be correct at some point but the species
might not actually be present. For this reason the method
is most useful for species which are either ubiquitous or
whose spatial distribution is at least partially known.

Once biological demand has been calculated it should be.

26
expressed as a time-varying rate or as a probability of
triggering per unit area or per decision making unit. This
permits the calculation of demand for various hypothetical
or actual distributions of decision makers. Thus, the
approximate scale of the project can be established early
in the design so that unrealistic goals may be avoided.

Distribution studies. The selection of proper statis-

 

tical techniques demand an understanding of the properties

of the target species distribution. In this section we shall
examine two common types of studies and certain biological
mechanisms which cause variation in space.

The first type of study attempts to develop a reason-
able hypothesis about the (possibly time-varying) distribu-
tion of individuals among sampling units. This may range
from a simple test for non-normality or heteroSkedasticity
to fits of any of a number of discrete distributions (g.g.,
Poisson, negative binomial, etc.). The purpose of such
studies is to facilitate the selection of estimators or
transformations, if necessary, or tests.

An example of this type of study is work done by the
author with B. A. Croft and M. J. Dover (Croft gt gt.,

1976b) on the distribution of Panonychus ulmi (Koch) and

 

Amblyseius fallacis (Garman) on apple tree leaves. Visual

 

counts of approximately 66000 leaves taken 10 per tree
under a wide range of commercial orchard conditions were
analyzed. The goodness-of-fit of the negative and positive
binomial, Neyman A, Poisson, logarithmic, and several other

distributions were determined (Gates, 1972; Bliss and Owen,

27

1958; Elliot, 1971). It was found that, in the density
ranges over which most management-oriented monitoring would
take place, the negative binomial provided an acceptable
fit. This information was then used to derive sample size
equations applicable in orchard blocks up to 10 acres in
size.

In the second type of study, one desires to know how
the sample variance is partitioned between samples and
subsamples. For example, in the design of a sampling pro-

cedure for red spider mites (Oligonychus coffeae) on tea

 

in India (Sen, 1971) bushes were selected from certain rows
of particular sections of various tea estates. Pilot studies
estimated the division of total variance between estates,
between sections within estates, between rows within sections,
and between bushes within rows. A cost function based on

the total time required for monitoring was devised and then
optimized to achieve the best tradeoff between bushes, rows,
sections, and estates.

Both of these types of studies examine variation in
space. Two primary determinants of this variation are
dispersal behavior and response to variation in the environ-
ment. This includes both abiotic factors such as weather
and biotic inputs like the resource base and natural enemies.~
The effect of dispersal is to attenuate spatial variation.
This is because the presence of a highly dispersable stage
at one location is likely to imply its presence nearby thus
indicating a high spatial correlation. Examination of two

species with widely different dispersal capabilities, the

28
European red mite and the six-spotted leafhopper, Macro-

steles fascifrons (Stal), demonstrates this. Dispersal in

 

the red mite is limited to walking about on the leaf surfaces
within a single tree. This can result in great density
variations from one tree to the next. Certain spray prac-
~tices like alternate row middle application can cause
significant variation even within a single tree (Hull gt gt.,
1976). This makes red mite sampling in large blocks diffi-
cult at low densities (Croft gt gt., 1976b).

The six-spotted leafhopper, an aster yellows disease
vector, presents a completely different picture. Although
this species overwinters locally in the egg stage throughout
its range, it is the influx of migratory adults each spring
which must be monitored. The migratory phase begins when
the grain cr0p host plant becomes fully headed (Drake and
Chapman, 1965). Because crops in the south develop more
quickly than their northern counterparts, migratory adults
can arrive in Wisconsin before local nymphs can mature.
Because the migration proceeds on a broad front as determined
by weather (Huff, 1963) monitoring for this pest could be
done with a comparatively wide mesh grid (see Figure 3).

A major cause of biological variation is variation in
underlying environmental parameters as mediated by species
physiology and behavior. Environmental variation has
several scales ranging from macro-effects such as north-to-
south climate gradients to meso-level phenomena like lake
shore effects and the rural effects of cities. The most

important form of variation and the one most difficult to

Figure 3.

29

The migration gt M. fascifrons (Stal) into
Wisconsin. The squares are placed to indicate
how a fairly wide mesh grid of sampling points
might be sufficient to track the advancing
population front. The contour lines, taken
from Drake and Chapman (1965), show the
migration after successive time periods.

 

 

 

31

deal with is, however, microhabitat variation. These
effects occur on a scale measuring from a few centimeters

to several hundred meters. While larger scales of variation
can be dealt with deterministically, microvariation must,

as a matter of practicality, be handled statistically.

There are numerous eXamples of microvariation and its effect
on monitoring in the literature. Fye gt gt. (1969) showed
that temperatures inside common forms of emergence cages can
vary significantly from temperatures outside. Observations
by Richardson (pers. comm.) have demonstrated that the

temperatures experienced by codling moth larvae, Laspeyresia

 

pomonella, inside apples can vary as much as 9°F from the

 

north to the south side of the same tree.

The response of a species to environmental variation
can either augment or reduce its effect. For example,
Haynes and Tummala (1976) present data from Gage and Haynes

(1975) which show that Tetrastichus julis (Walker), a

 

cereal leaf beetle parasite, can emerge up to 100 degree-
days (base 48°F) earlier in oat stubble than in straw as
measured by an external reference. This is presumably due
to microhabitat variation between the various grasses. On
the other hand, by seeking the sun in early morning and the
undersides of leaves later in the day, the tobacco hornworm,

Manduca sexta, on Jimson weed is able to keep its body

 

temperature very close to that of the air (Casey, 1976).
This would tend to moderate the physiological effects of
microhabitat temperature variation.

The important point of these examples is that the

32

variation perceived by the monitoring component results from
a complex set of biological interactions. On balance we can
identify two major classes of species. For a large class of
organisms factors such as dispersal dominate, thus permitting
monitoring units to be physically larger. For others devel-
opmental factors are more important necessitating much more
intensive monitoring.

This is certain to affect the organization of the
monitoring system. Dispersive species might well be best
handled by regional networks where the average decision maker
would have little contact with the sampling technicians.
Instead, they would receive pest advisories similar to the
present weather advisories. The other class of species
would require monitoring in the production unit itself thus
promoting more direct contact. Obviously, intermediate
systems would also have their place.

The extrapolation gt population processes through time.

 

Often the relation between the quantity of interest and the
quantity actually monitored is an indirect one. For example,
when attempting to forecast locust migrations, one measures
the egg densities of preceding generations. Even when the
quantity of interest is directly measured, time delays can
confound the issue. This is because the state of a popula-
tion at the time monitoring is triggered may well be
Significantly different from the population state actually
Sampled. Different still might be the state of the popula-
tion when subjected to the ultimate control measure. Beyond

this is the relationship between current pest activity and

33
terminal damage. The elucidation of all these effects
requires the extrapolation through time of population
processes significant to man. This is necessary to evaluate
the terminal effects of various possible magnitudes of
monitoring system error.

To answer questions like these, the designer must have
access to some form of biological model. This model may be
a quantitative mathematical model, a mental conception of
the species, or some experimental preparation which can be
used as a surrogate for the real population (g.g., a growth
chamber simulation). If it is a quantitative model it may
or may not be distinct from the decision rules we have
discussed previously. In any case, it must be based on a
careful biological study of the target organism's popula-
tion dynamics. In the following chapters, several design
applications of models will be discussed.

Biological models. In a sense all science consists of

 

the construction of models. In any branch of inquiry these
models will appear, evolve, and disappear as new techniques
and perceptions become available (Kuhn, 1970). The intro-
duction of life tables from the field of human demography
caused such an alteration in the field of entomology. Life
tables provided three crucial features which any model must
have: (1) a systematic method of recording data and, there-
fore, (2) a specific impetus to certain avenues of research,
and (3) a body of methods (in this case, mathematical) for
manipulating the data in certain ways deemed useful. I

As time passed and-the techniques of systems science

34
were applied to ecology and entomology (Tummala, 1976),
it became evident that there are better ways to conceptualize
life histories than the life table although these still
retain their descriptive value (Harcourt, 1970). Such a
synthesis has been developed by the author in work on a
generalized phenological model (Welch gt gt., in prep.).
This structure incorporates data similar to life tables
plus other information relevant to pest management with a
more advanced formulation of population dynamics.

Biological data about a species can be classified by
stage of the life cycle. For some species these stages may
be distinct developmental steps while for others like host
crops they may be arbitrary but easily recognizable morpho-
logical units (Chapman and Catlin, 1976). Stages may be
defined as capable of being monitored, controllable, damaging,
a combination of these, or neutral. A neutral stage is of
no particular relevance to pest management except as a
developmental delay between more interesting stages.

If a stage can be monitored, a list is compiled of the
types and, if known, the efficiency of the monitoring
methods. For phenological modeling one would monitor the
occurrence of important events such as first or peak adult
emergence or the onset of larval damage as detected by
examination of the host crop.

For controllable stages, the types and costs of control
are tabulated. The efficiency of each method (g.g., percent
mortality) is noted. It is quite possible for a particular

measure to affect a number of stages, perhaps differently.

35
In this case it is necessary that all effects be listed.
Since one of the purposes of phenological modeling is to
schedule control, it is necessary to note how far ahead
field personnel must be alerted in order to implement the
control measure.

For damaging stages the types and effects of damage are
noted. An important point which is often ignored is that
damage is inherently integrative. This is because, over
some range at least, the damage a species does per unit time

is proportional to pest activity. We can therefore write

(2-1) D = f(D,P)

{LID-I
r1'

where damage (D) and pest activity (P) are functions of time.
If activity depends on environmental parameters as well,

then t might denote physioloqical time. If significant host
self-repair capabilities exist then a term of -g(D) may be
appended.

This suggests that damage potential should be expressed
in units such as pest-days. For example, one study attempted
to express the effect of phytophagous mites on apples in
terms of the reduction in yield per mite-day (Hoyt and Burts,
1974). In another case involving the Colorado potato beetle

(Leptinotarsa decemlineata), it was found useful to consider

 

a potato plant canopy to consist of 3000 beetle-consumption
days (Sarrette, pers. comm.).

Of course the most important data about a stage concerns
its contribution to the species' population dynamics. For

anygiven species these will be known to a greater or lesser

36
precision. Great disparities in the quality of data on a
species serves notice where research is needed. The classes
of data are deve10pmental, reproductive, and demographic.
Developmental data primarily include the stage durations.
These may be in units of days, degree-days, or other
measures such as "days-with-average-temperature-above-a-
threshold". For well studied populations, data on develop-
mental variances may also be included. It is a common
phenomenon for the maturity distribution (or some analogue
such as size) to undergo a progressive spreading as develop-
ment proceeds. Data on this rate of spread can also be
tabulated. Reproductive data may be expressed as depending
on the maturity of the reproducing stage or on environmental
parameters. Depending on the state of knowledge, reproduc-
tion can be specified as a time-varying rate, as some pro-
pagule complement, or just as an arbitrary relative number.
Reproduction is an important component even for purely
phenological models because of the dramatic effect it can
have on events like peak hatch, etc. Demographic data
include information on non-reproductive factors affecting
the population size. Examples are immigration, emigration,
and mortality. In addition, there may be factors which alter
the effective size of a population without changing its numbers.
An example is diapause which removes individuals from the
active population without killing them. These processes
can be phenologically significant in that they can, for
example, alter emergence curves by changing the shape of the

maturity distribution. This has, in fact, been observed in

37

the codling moth, Laspeyresia pomonella (L.), (Riedl gt gt.,

 

1977).

The final type of information is used to relate the
species to the pest management community. These data include
regions where the species is found and which personnel in
those regions are responsible for it. Note is taken of the
forms of warning these individuals require to institute
effective management and what inputs to the model they
supply. Also important is the general time frame during
which the pest is dangerous. For example, an asparagus
pest may feed on the plant all season but cease to be of
economic significance after the crop has been harvested.
Data in this class set the spatial, temporal, and institu-
tional limits on the applicability of the model.

Quantitative models can be developed quite easily once
the data are in this form. It is necessary only to select a
suitable mathematical formalism. The author found the
following useful in selecting among the various structures
available for the phenological modeling project mentioned
previously:

(1) the model should permit description of the

population as a maturity distribution which
changes with time, say x(z,t);

(2) whenever possible (see below), the model should
be formally linear in x(z,t);

(3) preferably, the formalism would allow the
convenient compartmentalization of developmental,
reproductive, and demographic factors;

(4) well developed methods should exist for
numerically solving the model equations.

Criterion 1 permits factors to be incorporated which are

38
functions of maturity within a stage such as insect ovi-
position or distributed mortality. Models satisfying criterion
2 have an advantage in that they may employ either absolute
or relative densities or activities as determined by the
current state of biological knowledge. Linear models are
by no means a necessity but may be used (1) when convincing
data indicate true linearity or (2) when data are too sparse
to justify the assumption of specific forms of nonlinearity.
Thus, linear models are particularly useful when little is
known about the organism. The advantages in terms of clarity
and ease of modification granted by criterion 3 are obvious.
A model which violated criterion 4 would have little practi-
cality due to the cost of the many computer runs needed to
analyze a monitoring system. Although it was not needed in
the phenology project, a fifth requirement would be ease of
coupling species together. This would be important in the
analysis of prey—predator or host-parasite systems.

The model selected by the author for the generalized
phenology project (called PETE for Predictive Extension
Timing Estimator) is based on the forward Kolmogorov equations
(Barr gt gt.). A computer software package was designed
and implemented which enabled the computer to determine all
necessary model parameters from a species description such
as that in Figure 4. This allows biologists working with
descriptive data to generate computer models without the need
for computer programming.

These models can be used for system operation as well

as system design. For example, PETE has the capability of

Figure 4.

39

PETE description gt g variegated cutworm
phenology model. The model begins with the
initial maturity distribution shown. Simulation
starts with a field observation of first adult.
Eggs are laid after a preoviposition period. A
nominal oviposition rate is used because little
is known about cutworm reproduction. The model
cycles through the developmental stages, each of
which introduces the indicated delay. Warning
messages are transmitted one week before each
occurrence of larvae. The computer substitutes
the data indicated by brackets, < >, into the
message text. After four generations the
simulation stops.

 

 

 

4O

cozoEmmno Em:
0:35.583

.>.._m<..56wm max}: ._I_
Len—tn. mDO> XOwIO mw<mi_n_ .ASV mh<0

hzmmmDO V 20 wo<2 m._.<.2_._.ww .ZO_._.<._..w ImI
..._.<m>> A 3v 295‘va MIL. >m Dm>mwm mm.
..r2300 2. Ag m + w._.<0 thoawmav DZ<

A 8v 0 I m._.<o Duhoawmn. V me>>._.wm m<waa<
.55“. O._. kauwaxw mm< w<>m<4 EEOEDO
Dwk<0mE<> ZO_._.<mmzw0 A A8 ZO_._.<mmZm0V

£3.20QO a
835 03200? 2
moommmE to?

 

 

 

 

 

 

 

 

 

 

 

 

wt... .9 -
93o _N , braflorm 7mm DO 0.5
$32 t .62... 823
322016 m . Am no mom ,
....... ..\. T ooze
UOCOQ .9 >091

 

 

mcozobcmo 58
..2 o co_.6_:E_m
2w 2 .966

I

 

 

Iran 8 om.

IT

 

woom

 

 

 

41
integrating the population description with real-time
weather data from up to 37 field stations in Michigan's
lower peninsula to produce predictive monitoring triggers.

Such a trigger, for variegated cutworm, Peridroma saucia

 

(Hubner), is shown in Figure 5. These triggers can be
transmitted directly to the field staff via modern data
communications techniques. From Michigan State University
this is possible through the Pest Management Executive (PMEX)
system (Croft gt gt., 1976a) which was designed and imple-
mented by the author and John Howes.

This chapter has stated the needs of the monitoring
system designer for biological data. These needs touch on
virtually every aspect of population biology, so the use of
biological models is advocated to help organize these data.
Because of the elaborate nature of some models it is natural
to ask how detailed and complete these models must be. The
answer is that system design can only be based on the best
information currently available. One of the major purposes
of the model is to assess the effects of monitoring errors.
By repeated runs of the model it is also possible to determine
the sensitivity of the model to errors in its own parameters.
By extension, the effects of these on system performance can
also be tested. As always, however, in the final analysis
it requires an act of human judgment to determine whether a

system is well enough known to allow design to proceed.

Figure 5.

42

 

Ag automatically generated pest warning from

the PETE system. This type of alert is used to
direct the attention of extension specialists and
agents to particular problem areas in a pre-
dictive, management—by-exception mode.

 

 

43

.>4m<._30mm was”: ...—(ltd

m30> XOMIO ww<wIE .onmw .Omm mums—whawm

20 was). 3.52..er .ZO_._.<._.w mth<m>>

mz_._<w m1... >m Dm>mmw waZDOO Z_

05— ft”? mum—zwhawm DZ< mgr .Ihm mmmEMHdwm

me>>._.wm m<wma< ...mm..... 0... DMHOMQXw mm< w<>m<._

2m0>>._.30 ow._.<0m_m<> ZO_._.<mmzm0 I._.v

3.5050 20 .Nmé fit. ._.< ...wa I OZ_Zm<>> hwma 0_._.<_20.r3< whma waE

CHAPTER III

STOCHASTIC ANALYSIS OF MONITORING SYSTEM DESIGN

In this chapter we shall present a detailed examination
of the stochastic aspects of monitoring and show how the
various sources of random error combine with time delays to
create total error.

We begin by considering two points A and S in the
monitoring unit. At some point in time t=tO the sampling

point (S) achieves state A which triggers monitoring.

s,to

Before monitoring can occur, however, time delay Tl elapses
during which the system evolves. We can represent this

process by constructing a probability density function

1 _
p(As,t1IAs,to) where tl—to+rl. Such a distribution can be

determined via simulation studies using a biological model
as outlined in the last chapter.

Monitoring produces an observation xs. It is desirable

to express our new knowledge of AS t in terms of what we
' 1

know about the sampling design and the system being monitored.

From Bayes' theorem we have
p(XsI)‘s,tl)p(>‘s,tl)
(3-1) pHs,t Ixs) = .

l fp<xS|Mp<A>dA
This theorem, along with the controversial concept of

"personal probabilities" (Savage, 1954, 1962), forms the

 

l. The notation p(AIB) reads "the probability of event or
condition A given that event or condition B has occurred."

44

45
basis of Bayesian statistics. A good, non-partisan review
of the subject is given by Binder (1964). One of the major
tenets of this theory which we shall utilize is that the
posterior distribution, p(As,tlIXs)’ expresses the total
result of the measurement.
s,t1)

encodes all available information on the sampling protocol

Similarly, the bivariate distribution p(xS|A

and the underlying distribution among the sampling units for

a given AS For example, consider an organism for which

rtl'

a two stage sampling design has been constructed which
involves n subsamples for each of m samples. Suppose that

As t is to be estimated by is, the grand mean over all
I
1

subsamples. Further, assume that a one-way analysis of
variance has revealed the variance of sample means around
the grand mean to be 012 and the within-sample variance to
be 022. Straight foreward calculation and the application

of the Central Limit Theorem (Feller, 1968, vol. 2) yields

_ . 2 2
(3-2) p(XS|As’tl) — N(xS , ASItl’ (a1 + 02 )/nm)
where N(x,u,02) denotes a Gaussian distribution with mean u

and variance 02. In this example the underlying distribution

2 2
't1 and (01 +02 )

while the sampling protocol is encoded by 1/nm.

among the sampling units is denoted by As

Among the factors on the right hand side (RHS) of

(3-1), we have yet to discuss p()Is

) which is called the
Itl

prior distribution. If As t and T1 are exactly known, then
' o
(3-3) pus,t ) = p(A ll ) .

1 S'tl

s,tO

In general, however, triggering may not occur at a precise

46

value of A. Even if it does, we may expect the waiting
time for monitoring (T1) to be a distributed random variable.
If we call this distribution pl(r), then a more realistic
prior is
(3'4) pmsnco) = fowl). p”s,t+rI"s,to)p”s,to)pl(TI‘IAsn-bd'r
where p(As’to) is the probability of a certain state triggering
monitoring and tl=to+1.

Work done by the author on the design of a mobile van
for monitoring within orchard densities of the European red
mite (Welch, 1976) provides an example. The trigger for
sampling was an observation by a grower that mites were
present. On the assumption that growers can first detect
mites at densities between 3 and 10 per leaf, examination of
historiCal records yielded p(AS'tO) as shown in Figure 6. To
determine p1(r) simulations of system logistics (discussed
in chapter VI) were undertaken. For a market assumed to
contain 315 growers the curve in Figure 7 was obtained.
Restricting ourselves to predator-free systems, we can
describe the species dynamics by a simple exponential growth

model

I'T)

(3-5) p(1 ) = 6(1 1 e

A ..
s t + I t s t +
I O T S, 0 I O T S'to

where r was taken as .135 per day. This model (with differ-
ent r values) can be used for a variety of pests during
those outbreak phases preceding economic injury. In real
systems, population growth rates may be reduced by (l) the

effects of exogenous factors such as weather or predators or

47

Figure 6. The cumulative distribution of red mite densities

 

 

gt the assumed time of first—detection. This

corresponds to p(>.S t ) in the text.
I
o

 

 

 

48

 

L J l I l l L I

ll
QQQNQQVWN-z

uoIIoung AIIsuag eAlloanJnQ

 

Density of Mites When Detected by Grower

49

Figure 7. The cumulative waiting time distribution from g
simulation study of a mobile van-based mite
countifig service.——This is delay 1 in Figure 2
and corresponds to p1(r) in the text.

 

 

 

 

 

0.

50

 

l l l I l J

I ll
QQNQQVWN

uoIIoung Atgsuaa aAItolnuInQ

 

l2

Waiting Time for Service (Days)

51

(2) by internal effects like intraspecific competition.
Exponential growth provides a conservative baseline for
estimating the behavior of systems subject to the former
effects; generally the latter processes occur too late to
be significant to management. Solving (3-4) for various
values of Asltl yields Figure 8.

One of the common criticisms of Bayesian statistics is
the requirement of knowing this distribution. The counter-
argument relies on the "principle of stable estimation"
(Ward gt gt., 1963). This principle states that if we have
no strong preferences for particular values of A and if the

sampling design yields a strongly peaked p(xslx ) then

S,t
the form of the prior distribution has little effeit on the
posterior density function.

It would seem likely that this principle might apply to
many biological monitoring situations because of the large
variances typical in the field. Indeed, in our previous
example the prior was quite uniform; the peaked appearance
is due to the ZOO-fold vertical magnification. To examine
the effect in this instance, posterior densities were calcu-
lated from the prior of Figure 8 and from a uniform prior
covering the same range of mite densities. The distribution
p(xS|AS’tl) was based on equation (3-2) with xs=ll. The
variances 012 and 022 were calculated from Croft gt gt.
(1976b) and the assumption was made that m=200 leaves were
collected n=l per tree. Figure 9 illustrates that the non-

uniform prior based on grower characteristics and time delays

had little statistical effect in this instance. While this

Figure 8.

52

The prior density function from equation (3-4).
The calculation assumes that the distributIoHs
of Figures 6 and 7 are employed and that a
simple exponential outbreak model is appropriate
for the developing population. This curve
estimates the likelihood a mite counter would
attach to various mite densities before the
field had been seen.

53

UOIIouna KIIsuea KIIIICIDQOJCI

mNLOIOQ'I'ON—o
QSQQQQQQQQO
{UUIIIIIUU

 

44

1

i

35

30

20

Number of Mites per Leaf

 

I L I I I I l I I —0

<5. m. 00. I» (0. In. sr. In. N. -: 0.
uogtoung Mysueg aAIIolnuInQ

Figure 9.

54

A comparison gt the posterior effect gt g uniform
versus g more complex, model—based prior
distribution. The similarity of these two curves
indIcates that the principle of stable estimation
seems to hold for European red mite monitoring.
That is, it makes very little difference whether
a designer uses the distribution of Figure 8 or
replaces it with a constant.

55

OAOF
- .-~\-Model-based Posterior

0.35 -

,0
OJ
0

.0

N

U!
I

Probability Density
0
N
9

t
\
I
l
I
\
I
t
I

 

 

 

0.! 5 -
0. l 0 - \
\\
0.05 - \._ Uniform-based
\\ Posterior
0.00 I ‘ ‘\ " i L J
8.00 10.00 l2.00 l4.00 l6.00 l8.00 20.00

P0pulation Mean Density

56

greatly simplifies the statistical design, it does not mean
that these factors can be dropped completely from the analysis;
these delays can still be of great biological significance
as we shall see.

Once the statistics of monitoring at point S have been
worked out the problem of extrapolating these results to
point A, elsewhere in the monitoring unit, arises. This
situation can be modeled by decomposing the relationship
between Aa and As into deterministic and stochastic parts

as follows

(3-6) Ia = aAS(As) + 8AS(AS)EAS.

In this equation 8A8 is assumed to be a random variable with

zero mean and unit variance. The distribution of EAS depends
on the particular pair of points being considered. For
example, suppose 1a and As denote some measure like mean
instar number. If location A was significantly warmer than
S, we might expect 5 to be predominantly positive whereas the
reverse would be true if S were the warmer spot.

In spite of this problem, it is possible to calculate
the expectation and variance of the biotic state at some
point selected randomly from within monitoring unit R. We

shall denote these quantities as E(AIAS) and Var(A|As)

respectively. We begin by noting

(a) EIAaIAS) = aASIAS)
(3-7) (b) Var(Aa|AS) = 8AS(AS)2

(C) piAIAS) = [R p(>\a=AIAS)p(A)dR.

57
In (3-70) A denotes some small element dR of R and p(A) is
the probability of choosing that point. In the last chapter
it was noted that the distribution of decision makers has
important effects on sampling. The distribution p(A) is
the mechanism by which this effect can be calculated. For
this discussion, however, we shall assume that decision
makers are distributed homogeneously within R so p(A)=AR”l

where AR is the area of R. This yields

(3-8) BUIAS) pr(AIAs)dA

_ -1 _
— AR 1.fo p(Aa—AIAS)deA.

By switching the order of integration and using (3-7a) we

have
(3-9) Bull ) =A-lf a (A )dRé-A

s R R AS 3 '
From an elementary identity we have

_ 2 ‘ 2
(3-10) Var(I|Is) — A p(AIlS)dl - (A) .
Substitution and simplification yields
(3-11) Var(>.l). ) = A I‘ll (a (A )2 + B (1)2) dR-(I)
s R R AS 5 AS 5 '

If we were fortunate enough to have complete knowledge

and e for all A in R, we could determine the

Ofo. 8

AS’ AS' AS
exact form of the A distribution but, in general, this will
not be the case. A result from information theory, however,
suggests that it would be proper to assume p(AIAS) to be

normally distributed. This is because, among all distributions

with a given mean and variance, the Gaussian distribution

58

maximizes entropy (Mardia, 1972). Since entropy can be
interpreted as average uncertainty (Young and Calvert, 1974)
this assumption will lead to designs which err on the side
of conservatism.

As an aside, the application of this same principle to

the conditional distribution of a particular Aa yields

_ . 2
(3-12) p(AaIAS) — NIAa . aASIAS). BASIAS) ).

This lends a certain amount of support to the idea of using
regression techniques in the experimental determination of
a and 8 as some authors have done (Bohnam and Eye, 1970;
Fulton and Haynes, in press).

In the previous chapter comments were made concerning
several biological mechanisms which affect the a's and 8's.
These included dispersal and developmental rates particularly
as modified by environmental variation. A further factor
which might be mentioned is "distance". This might be the
actual number of miles between A and S or some other index

of size such as area or similarity. If dA denotes this

S

distance measure for A and S we can make some plausible
statements about the asymptotic behavior of the a's and 8's,

namely

(a) 11m aAS(AS)=ls (b) lim aAS(As)=E(Aa)
d +0 d +00
(3_13) AS AS

(C) lim BAS(AS)=0 (d) lim BAS(AS)=Var(Aa)1/2

dAS+O dAS+m

59

These relations simply say that a and 8 yield the sample
values at the sampling point while at infinity 1a and AS are
independent (t.g., the best prediction of Ga is the mean of
Aa). We shall have cause to refer to these limits below.

The formulas (3-6) through (3-13) imply knowledge of the
actual state Is. To calculate the probabilities of various
Aa's based on an observation xS we use the equation

(3-14) p(I Ix ) = [p(i I). )p(>. Ix )d).
t1 5 t1 s,t1 S,t1 s S,tl

s t ) is the normal distribution whose parameters
' l

were constructed in (3-9) and (3-11) and where PMS t Ixs)
I
1

where p(xt IA
1

is from (3-l).

Let us now continue our red mite example. We shall
assume that as winter ends the density of mites in the
monitoring unit can be characterized by some low value Po'
Because of the limited abilities of red mites to disperse,
we shall assume that differences in mite densities found
later in the season are due to different temperature histories.
Let us suppose that the monitoring unit is small enough so
that the average temperatures at two points in a monitoring
unit of size d are the same. However, let the variance

between points be _

BX)

(3-15) 8 = 0(1-e

AS(Ts)

where x is their separation. These assumptions are consistant

with the limits in (3-13). Equations (3-9) and (3-11) yield

60
(a) E(TITS) = T8

1

(3-16) (b) V(d) é Var(T|Ts) =

02 {1+(8d)-l(eBd-4)e8d

+(Bd)-2(4(eBd-lI-(eZBd-ll/Z)}.

For simple exponential growth (such as might characterize
an outbreak phase of many pests) we have the well known

lln R where R is the rate of replacement and

relation r = G-
G is the generation time. If we assume that R is a fixed
propagule complement unaffected by longevity and that the
rate of development G-1 is proportional to temperature (T)

above a threshold (Th) then we have
(3-17) r = kIT-ThI-

If As and A are the densities of mites a sampling point S

and at a random point in the monitoring unit we have

_ t _ - ‘
(3-18) AS — PO exp( I; k(TS Th)dt ) - Po exp(rst)

where

t
I; k(TS-Th) dt.

H
II
and

(3-19)

Similar relations hold for A. Algebra yields

(3-20) lnA - lnAS = (r - rs)t.

 

l. The appropriate application of L'Hospital's Rule will
show that

lim V(d) = 0
d+0

61
In the derivations which follow, it is important to note
that As is a population parameter and, therefore, a constant.
On the other hand, A is a random variable since it results
from the random selection of a point from within a monitoring

unit. Taking expectations on both sides of (3-20) gives

(3-21) E(ln A - 1n AS) E(ln A) - ln AS

tE(r - rs)

t _
k I; E(T - TS) dt — 0.
Therefore,
(3-22) E(ln A) = 1n A .

Taking variances on both sides of (3-20) gives

Var(ln A)

tZVar(r - is)

(3-23) Var(ln A - ln AS)

= k2 jgt Var(T - TS) dt = 2tV(d).

Substituting for t from (3—18) yields

(3-24) v é Var(ln A) = k S V(d)

 

 

where TS denotes an average value. Assuming normality for
1n A means that A has a lognormal distribution with density

function

1/2

(3—25) p(AIAS) = (ZNV)- exp((ln(As/A))2/(2V))/A.

62

To calculate a numerical example a plausible value for
o of 11 was selected based on 77 years of July temperatures
for Grand Rapids, Michigan (point S). A value of T5 of
72.3°F was determined from the same source. The parameter
8 was set to -.12 on the gg_ggg assumption that temperatures
from two places five miles apart would be within five degrees
(°F) of one another 68 percent of the time. Because measure-
ments of this have not, in actuality, been made in the field
on this small a scale the results of this example may not be
realistic. It must be remembered that the point of this
example is how the different types of variation are coupled
to achieve an estimate of system performance. To continue,

developmental thresholds for the life stages of P. ulmi

 

(Welch, unpub.) were averaged to give a Th of 50°F. By
using the previous value of r, equation (3-17) was solved
for k. P0 was set to a nominal .5 mites per leaf. Assuming
the same sampling design used previously and the principle
of stable estimation, we obtain the density function shown
in Figure 10 for xS=ll. The increase in the size of potential
confidence limits caused by extrapolation over an entire
monitoring unit is evident.

In this chapter we have studied how time delays in
measurement and extrapolation through space can degrade the
value of a measurement. The first step involved the use of
Bayes' theorem to link measurement outcomes with the likeli-
hood functions of various relevant ecosystem states. It was
demonstrated how the principle of stable estimation can be

used to eliminate the troublesome need for a prior distribution.

63

Figure 10. The change tg g likelihood function resulting
from the extrapolation gt data taken gt g point
over gg extended spatial area. The figure
demonstrates that the variance associated with
an estimate increases when one tries to extrap-
olate from a single point (the peaked curve) to
all of a monitoring unit with finite spatial
extent (the broad curve).

 

 

 

 

 

 

64

0.40 ~

0.35 -

Q

01
O
T

.0

N

U"
I

 

 

.0
N
O
I

0.I5-

Probability Density

0.I0b

 

0.05 -

 

 

 

00%.0 4.0 l2.0 ISO 200 24.0
Population Mean Density

65
During this discussion methods of extrapolating distributions
through time via conditional probabilities were presented.
The problem of spatial extrapolation was handled by parti-
tioning estimators into deterministic and stochastic portions.
Means and variances were calculated in terms of this partition.
In the next chapter we shall show how these parameters are
affected by delays between monitoring and decision making
and how they are incorporated into the decision maker's

economic objective function.

CHAPTER IV

THE ECONOMICS OF THE DECISION MAKER

In the final analysis, the evaluation of any system must
rest on a firm economic base. As might be expected much work
has been expended on relating biological phenomena, economic
decisions, and risk (Headley, 1972, 1975; Hall and Norgaard,
1973; Carlson, 1970). There are two distinct viewpoints
which must be recognized. On the one hand is the decision
maker who has to balance the cost of monitoring against the
value received. This view is of importance to the designer
who has to sell his product in a skeptical market. On the
other hand, the financial prospects of the monitoring service
are important because an impractical venture is sure to fail.
This chapter will deal with the economics of decision making
while chapter VII will examine the monitoring service.

The decision maker receives data xS from the monitoring
component and makes decision D = D(xs). He then implements
this decision and is subject to loss
(4-1) L(D,xs)= fA l(D,xS, At3)p(At lxs) d At .

3 3
The distribution p(At3le) describes the probability of
various possible ecosystem states at time t3 = to+rl+12+r3

when control is actually implemented (see Figure 2). By

analogy with equation (3—4) we calculate

66

67
(4-2) p(A Ix ) = I”! p(A IA )p(A Ix )p(T) dA (11
t3 8 0 A tl+r t1 t1 S tl

where t = t1+r. Multiple runs of biological models can be

3
used to assess these probabilities.

The loss function 1(D,xS,A) is more complicated. A
useful breakdown of costs is shown in Table 1. It is
important to note that each of these costs may be a random
variable. For example, while the cost of monitoring could
be a fixed (non-random) charge, it could also be dependent
on the time required for sampling and thus, roughly, on xs.
In cases where monitoring units contain many decision makers,
each may pay some fraction of the cost or all may benefit
from some public subsidy. Public policy might adjust this
subsidy according to user characteristics to encourage
utilization by particular parties. The cost of control,
$2(D), depends on the type of control implemented. It is
even possible that different decision makers may pay different
prices for the same decision. This can happen, for instance,
if certain decision makers can realize economies of scale
in the bulk purchase of control materials. Finally, the cost
of damage depends on the state of the agro-ecosystem and the
decision taken. This has obvious stochastic elements.

Because these variables are distributed it is difficult
to construct a convenient loss function in terms of the
variables directly. A better approach is to base the loss
function on their distributions. To do this we introduce the
idea of utility as developed by the neoclassical economists.

Many factors which enter into human decision making cannot

68

Table 1

Schedule of decision maker's costs

 

I. Cost of management
A. Cost of monitoring $1(xs)
B. Cost of control $2(D)

II. Cost of resultant damage $3(D,A)

 

69

be measured in dollars because they are not market commodities.
Typical examples are the desire to avoid risk or the value
which goods have in use as opposed to exchange. Utility
theory (Scott, 1973; Nicholson, 1972) provides mechanisms for
taking these factors into account. One of the major defects
of utility theory is that utilities, in general, are not
directly measurable. Fortunately for this application, one

of the exceptions is when it is possible to make probability
statements about the various possible outcomes.

There are two methods in common use for constructing
utilities from dollar distributions. The first is simply to
take the expected value of the distribution. This is (roughly)
equivalent to saying that over some range of values an
individual is indifferent to a choice between receiving one
dollar with certainty versus receiving x dollars with

probability l/x. Under this method we have
(4-3) 11(DIXS.>\) = E($1(Xs)) + E($2(D)) + E($3(D,X)).

This method can be applied to the analysis of the mobile
mite counting van mentioned previously. In the initial study,
expected costs equalled the sum of a fixed monitoring charge
plus the expected costs of control and damage. This latter
was found by multiplying the cost of significant damage
times the probability of non-control (PNC) given the monitor-
ing results. Unfortunately, subsequently to this analysis,
an error was detected in the calculation of damage cost. This
error, however, has been corrected in the account which

follows.

70
Because the quantitative relation between mite damage
and yield is biologically obscure, an indirect method must
be used to assign a dollar value to the phrase "significant
damage". Such a value may be calculated from the following
assumptions:

(1) mite damage is cumulative so the cost of damage
must include a measure of the contribution to
future damage potential;

(2) five consecutive years with populations peaking
above 15 red mites per leaf so damages a tree
that the grower is forced out of the fresh
fruit market into the process market;

(3) one year of vigorous, mite-free growth is
sufficient to allow the tree to repair previous
mite damage;

(4) each future year can be considered statistically
as an independent Bernoulli trial (Feller, 1968,
vol. 1) where the probability of damage is given
by r, the economic risk of the monitoring-
management system (PNC is the probability of
damage this year).

Assumption 2 implies that, at 1975 prices, the grower

would sustain a loss of $656.20 per acre (Hines, 1976) after
five years of damage or $131.24 per consecutive year. Taking

the other assumptions together, we have, by the binomial

theorem

(4-4) cost of damage =
4

131.24 + 2 (A) rn(1—r)(4'n) (131.24n).
n=0
That is, the cost of damage equals the damage this year plus
the expected cost of damage over the next four future years.
A more economically complete argument would discount these

future costs but, for the sake of simplicity, we shall not

consider this point. Rearranging terms and using the rule

71
for the expectation of a binomially distributed random

variable yields
(4-5) cost of damage = l3l.24(l + 4r).

This formula shows that, by reducing the risk of cumulative
damage, we can lessen the impact of damage when it does
occur. As an example, examination of historical records
(Croft, unpub. data) reveals that growers using a particular
monitoring—based, integrated control scheme (the RS II
system of chapter VII) exceeded 15 mites per leaf on an
average of r = .11 of the cases in any one year. Substituting
this value in (4-5) yields a cost of damage of $189 per acre.
To evaluate the probability of exceeding 15 mites per
leaf given a particular monitoring outcome a biological
model was used. Each sample was taken to represent a point
in the prey-predator phase plane. The area of the plane where
most samples fall was divided into a grid of 300 points. The
model was run using each of these points as initial conditions
and it was determined for each run whether or not red mites
peaked above 15 per leaf. If so, the point was assigned1 a
value of 115(A) = 1; if not, I15(A) = 0. Figure 11 illustrates
this for three initial points. The probability of non-control
was then ascertained for particular values of X8 by

(4-6) PNC(XS) = fp(At3IxS)I15(At )dA

3 t

3

 

l. Statisticians would term 115 an "indicator function".

Figure 11.

72

5 phase plane plot showing simulations of
three interactions of the European red mIte
(horizontal axis) wIth Amblyseius fallacis
(vertical axis). The three curves are
characterized by progressively poorer initial
prey-predator ratios resulting, ultimately,
in a failure of biological control.

Predator Density

.45
O

IIFF T ‘TTIUTIrTTUUUIUIIIIIIIIIIITil'I'jj

7' r- 9° P0 S” S”
O 01 O 01 0 0|

.0
tn

73

con.
hresh.

   
    

 

I Day45

[Dayl

 

0%.

lllllllllllljlllll4llllllLlllJ

O 4.0 8.0 I2.0 I0.0 20.0 2|.O
Pest Density

74
In many cases decision makers, understandably, wish to
avoid situations where significant probabilities of great
loss exist even when these are offset by the chance of great
gain. This is termed risk aversion. A common method of
quantifying this (Markowitz, 1952) is to attach a penalty
to the loss function proportional to the variance of the

dollar distribution. Thus,
(4-7) 12(D,xS,A) = 11(D,xS,A) - A-Var($l+$2+$3).

In most cases this method of determining losses yields
optimal policies which are suboptimal according to (4-3).
The difference may be thought of as the amount the decision
maker is willing to pay to avoid risk.

One difficulty with the utility approach is that it is
sometimes difficult to interrelate it with linear programming
methods which designers may desire to use. An alternative
method without this defect has been proposed by Boussard and
Petit (1967). In this method the probability of some
"surprisingly great" loss is kept below some level. This
loss is called the "focus of loss", a term introduced by
Shackle (1949, 1961). Boussard and Petit have taken the
focus of loss to be an amount which would result in insufficient
income to cover unavoidable expenses. The general technique
is called "chance constrained programming" and has been
reviewed by Charnes and Cooper (1959) and Charnes gt gt. (1965).
We shall employ constraints of this form in an example in

the next chapter.

CHAPTER V

MATHEMATICAL RELATIONS BETWEEN DESIGN FACTORS

In this chapter we shall mathematically combine several

of the classes of factors discussed previously. These include
variability within monitoring units, economic risk, manage-
ment system time delays, and intensity of operations. There
are quite a few specific parameters which might be used as
indices of any one of these classes (see Table 2). Indeed,
a designer may desire to examine several from each class to
gain a more complete picutre. Let us suppose, however, that
.some particular combination (v,i,t,r) of variables has been
chosen, one per class, where the variable names are as in
Table 2. I

The discussion below focuses on cases when the following

relations may be assumed true.

(5-1) t = h(r:V)
(5-2I i-= 9(V.t)
3t at
(a) W < 0 (b) 'a—f > 0
(5-3) . .
31 31
(C) ‘3'; < 0 (d) E < 0

We shall take 9 and h to be defined, continuous, and
differentiable over the region of interest.

The parameter v relates to all factors which might
broaden the confidence limits assigned to particular estimates

within a monitoring unit. Many projections made in pest
75

76

TABLE 2

Some representative variables from each of
the four important design parameter classes

 

Variability within monitoring units (v)

Variance of monitored variables
Geographic size of monitoring unit
Dissimilarity index of sites within unit
Etc.

Intensity of monitoring (i)

Man-hours spent monitoring

Number of samples taken per unit time
Total monitoring expenditures per season
Etc.

Management system time delays (t)

Average time from monitoring to action
Maximum time from monitoring to action
EtC.

Economic risk (r)

Expected total loss

Probability of exceeding economic injury level
Probability of sustaining focus of loss

Etc.

 

77
management depend on determinations of biological rates
(chapter II). Uncertainty in the value of a rate at a
given sampling point or systematic variation in a rate from
point to point in space (chapter III), when integrated over
time (gt. equation 3-23), progressively degrades the value
(t.g., increases the variance) associated with monitoring
estimates.

The function 9 (equation 5-2) relates the variability
of the monitoring unit (or scale if this is correlated) and
time (specifically, the delays of Figure 2) to a measure of
the intensity of the operation. Intensity is meant to refer
generally to the inputs to sampling, that is, to sampling
effort. It might therefore include components of frequency,
sampling point density, or redundancy. However, it would
not directly measure, say, accuracy which is a characteristic
of sampling output; it gggtg measure any extra effort needed
to achieve that accuracy. The measure may be a parameter
with actual physical or economic meaning or just a relative-
index as we shall use later in this chapter.

The designer can and should minimize the effect of
monitoring unit variation by selecting units as internally
homogeneous as possible. Beyond this, however, reductions
in v can be achieved only by increasing the number of sampling
points and, thus, the overall sampling effort. This is
embodied in inequality (5-30). The other way to improve the
reliability of monitoring estimates is to decrease the delay
time over which variation is allowed to integrate. By

requiring the system to work faster, we are, again, increasing

78
the required effort. Inequality (5-3d) states this rela-
tionship.

The function h (equation 5-1) yields the maximum
allowable delay in terms of monitoring unit variability and
permissible risk level. It is determined primarily by the
biology of the organism being managed. As delays progress
and the variances of our posterior likelihood functions
increase, the more conceivable is the possibility (risk)
that the system has entered an injurious state (assuming that
the sampling trigger takes place before damage begins).
Inequality (5-3b) says that the higher the level of allowable
risk, the longer we may delay the monitoring-management
process. Inequality (5—3a) maintains that the greater the
within-unit variability (t.g., the confidence limit "spreading
rate"), the quicker we must act to avoid undue risk to portions
of the monitoring unit.

In view of the preceding paragraphs, it seems likely that
the relations in (5-3) will hold in many practical cases
although they must be verified in each specific instance.
Later in this chapter an example of such verification will
be shown. First, however, we shall demonstrate two important
results about variables satisfying (5-1) through (5-3d).

Theorem t: There exists a one-to-one transfor-

mation between the ordered pairs (r,v) and the

ordered pairs (t,i).

Proof: Consider the transformation defined by
the equations

t!

t'(r,V) h(r.VI

g(k(r,v),h(r,v))

i' i'(r,v)

79

where k(r,v) = v. We shall prove that this transfor-
mation is one-to-one by proving that its Jacobian
at' at'
3r 3v
J:
31' 31'
Or 3V

 

 

cannot vanish. Using the chain rule for differentiation
and the definition of determinants we have, after
simplification

3-2: 3_i_+fliE .. 11% n
3r 8v at av at 8r 3v .

Suppose that J = 0. Rearranging terms and canceling
at/ar which is not zero by equation (6-3b) yields

But this implies that ai/av is zero which contradicts
equation (5-30). Therefore the transformation is
one-to-one.

This result says that all four variables can be graphed
in a single plane without any point having more than one
four-tuple assigned to it. An even stronger result is

Theorem t: Specifying values for any two of the

variables v, i, r, t determines values for the other

two uniquely with one exception; given i and r it

may not be possible to solve for v and t.

Proof: Define the following four univariate functions

h (v)

r h(rx,v) h (r)

V
X X

h(r,vx)

g x(t) 9(vx,t) gtxtv) é g(v.tx)

80

where the subscript x is an "o" for given values and
an "s" for solved values. Equations (5-3a,b,c,d)
show that these functions are strictly monotone in
the region of interest and, therefore, their inverses
exist and are one-to-one. Not counting (i,r) there
are five possible pairs of given variables and we
shall treat them one by one.

 

gttgg Solution for the other pair
ro,vO tS = h(r0,vo), iS = g(vo,ts)
to'vo is = g(Vo't0)’ rs = hv: (to)
io,vo ts = g;1 (to), rs = h;1 (ts)

0 0
to'ro v5 = hf: (to)' is = g(vs'to)
io'to Vs = gt: (io)' rs = hv: (to)

If we are given i0 and r we proceed by substituting
(5-1) into (5-2) giving the system of equations

t = h(rOIV)
. _ .,
iO - i (ro,v)

where i' is defined as in Theorem 1. This system can
be solved if and only if

is unique. An example of when this fails to occur is
shown in Figure 12. Examination of this figure shows
all of the relations (5-3a,b,c,d) to be satisfied.

, The importance of these theorems is that they permit us
to construct a nomogram of particular use to monitoring system
design. This is done by plotting contour lines of any two of
the four classes of variables on a grid made up of the other
two. Theorem 2 provides the only constraints on the choice

of pairs. As the following chapters will show, such a chart

enables the designer to assess quickly the effects of various

Figure 12.

81

g counterexample for Theorem 3. In this
instance, 1 and r0 are given. Motion along

the trajectories indicated by the arrows

(a, b, c, d) demonstrates that the corresponding
inequalities in equations (5-3a,b,c,d) hold.

In spite of this, it is evident that there is

no unique solution for v and t.

 

increasing r

 

82

increasing i

 

 

 

 

increasing t

 

 

 

 

 

 

increasing n

 

 

83
time delays, technologies, pricing structures, etc.

This chapter will conclude with an example of the
construction of a chart such as we have discussed. The steps
involved are (1) the selection of a suitable set of parameters
v, i, t, r, (2) the derivation of the functions 9 and h, (3)
the proof that these functions satisfy the conditions of the
two theorems, and (4) the preparation of the chart.

For this example we shall continue our discussion of an
organism similar to the European red mite. So as not to
obscure the illustrative value of the example we shall select
measures for v, i, r, and t which are somewhat simpler than
might be justified in practice. For instance, let us define
v to be the radius of the monitoring unit and r to be the
probability of exceeding a nominal injury level (PD) of 15
mites per leaf. In this example we shall use these variables
as axes and plot contour lines for i and t. Let us suppose
that we have a method of requesting sampling which, as a
worst case, triggers at the tolerance level (P0) of 7 mites
per leaf. We define t to be the maximum delay allowed I
between triggering and the application of control. For the

intensity of monitoring we use the following gg hoc index

(5-4) i é g(v,t) = Ct-lv-z

where C is an arbitrary normalizing constant. This function
has the reasonable pr0perties that (1) it is proportional

to the minimum rate of sampling and (2) it is proportional
to the density of sampling points in the region.

To derive h(r,v) we first note that we have, from

84

equations (3-22) and (3—18),

(5-5) E(lnA) = lnAS = Est + 1n PO ,

and, from equation (3-23),

(5-6) Var(1nA) = k2V(v)t.

Since we have assumed normality for p(lnAllnAS) we have

1n PD

(5-7) r = l - erf
kV(v)1/2t1/2

- 1n Po - rst

where erf is the cumulative distribution function of a
standardized normal variate. We note that some algebra

suffices to rewrite (5-7) as

(5-8) 0 = (a + t)/(bt1/2)
where
(a) a = -:l ln(PD/Po) < 0
rs
(5-9) (b) b = —:l kV(v)1/2 < o
r
S
A _ -1
(c) c — erf (1-r)_ > 0 .

The inequalities (5-9a,b) are obvious by inspection; (5-90)
declares that we are not interested in economic risks greater

than 50 percent. Solving (5-8) yields
(5-10) tl/2 = k(cb i (c2102 - 4a)l/2)

which, from (5-9), has exactly one positive and one negative

85

root. Discarding the negative root as not meaningful gives

2 1/2)2

(5-11) t = h(r,v) = k(cb + (02b - 4a)

The next step is to show that g and h satisfy the

conditions of the two theorems. It is clear that
31 _ _ -l -3
(a) '5—‘7 - 2Ct V < 0
(5-12)
31 _ _ -2 -2
(h) FE - Ct V < 0

so (5—3c,d) hold. Differentiating h yields

Q)
,1.

(a) 3; = SflfzbV
(5-13) (h) g; = %flf3
where

(a) fl = (cb + (c2b2 - 4a)1/2) > 0
(5-14) (b) f2 = c + 02b(c2b2 - 4a)‘1/2

(C) f3 = (Crb + brc + %(02b2 - 4a)‘1/2

2 2

. (Zocrb + 2c bbr - 4ar))

and the subscript "r" and "v" refer to partial differentiation.

Since ar = br = 0 we can rewrite f3 as

(5-140') f3 = Crb + ccrbz/(czb2 - 4a)l/2

From the inequalities (5-9) we have

(a) bcz/(czb2 - 4a)1/2 > b02/ chl = -c

(5-15) . .
(b) ccrbZ/(czb2 - 4a)1/2 > ccrbz/ chl = —crb

86

or, upon rearranging terms across the inequalities

(5-16) f

This yields (5—3b) directly. To complete the proof of (5-3a)

we note that

k

2rS

-1/2 8V

(5-17) b 85

V(v)

 

Since, when the parameter values from chapter III are used,
both V(v) and its derivative are positive over a reasonable
interval (see Figure 13), we have bv and, therefore, Bt/av
negative.

The final step is to plot the contour lines of g and h.
Figure 14 shows the resultant computer generated plot when
all parameters are as before. As a simple example of the
use of this chart let us consider chance constrained pro-
gramming. In Figure 14 r is defined as the probability of
exceeding an economic injury level but it could easily have
been the chance of suffering the focus of loss (Table 2).
Under these circumstances a chance constraint could be
represented by a horizontal line as in Figure 14. Only
those designs which resulted in operation below this line
(such as point A) would be acceptable. Other alternatives,
even those with the same workload (point B) or total time
delay (point C), would not be effective. As the following
chapters will show, this type of chart can also be used to
evaluate a variety of design parameters.

In summary, this chapter has demonstrated that it is

Figure 13.

87

The function V(y) graphed gy assigning the

 

 

parameter vaers gt chapter III. This
describes the variance of a series of
temperature readings from points selected
randomly within monitoring units of
different sizes. Clearly, both V and its
derivative are positive over the range of
values shown.

 

 

88

2.5 :5 8:282 to arm
0v mm on mm ow m. o. m

1d---quq-uu-...-u-qqfiuu-.-nud-undu-uqJ

 

llllllllllllllllllLllJlllJllL

Om

OO.

 

ON.

SOUoiJDA

89

Figure 14. Contour lines gt sampling intensity and
maximum allowable time delay gg a function
gt risk and monitoring unit size: The
points A, B, and C and the 7.5 percent
chance constraint are explained in the text.

 

 

 

 

 

Economic Risk (pct)

90

Relative Sampling Intensity
50 63.8 l5.0 7.l 4.0 2.0 l.8 l.3 l.0 0.8

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

/_1 5.6
45 - / ,_....— 5,5
/'
40 P / //__., 5.4
/
35 ’ / / 5.2
30 t ///
25 h / /// 5.0
20 // 4 a
.. / .
/ /
'5 - /IB/ 4.6
/
/
5 il / / A 4.2
/l I I 1"" I In \ 3.8

 

00 5 I0 I5 20 25 30 35 40
Monitoring Unit Size (miles)

‘ Maximum Time Delay (days)

91
possible to greatly simplify relations between certain
classes of variables provided they behave in certain plausible
ways. Charts based on these relations can simplify the
analysis of system performance. In the example given, the
system is simple enough to permit analytic solution; this
may not always be the case. In these instances simulation
models can be used to construct the charts by approximation.
In the next chapter we shall see how this may be done with

system time delays.

CHAPTER VI

THE ANALYSIS OF SYSTEM TIME DELAYS

For any monitoring mission there are a variety of
suitable technological alternatives. Perhaps the most
important parameters associated with a technology are its
direct cost (including any social or environmental costs to
which the designer is responsive) and its time delays (which
may indirectly affect cost through damage as previously
discussed). In this chapter we shall decompose and analyze
the total monitoring time delay. Table 3 shows how the
sampling cycle can be partitioned into a series of discrete
actions. We shall consider each of these entries in turn.

Transmission gt the trigger event. The length of this

 

 

delay depends entirely on the nature of the trigger although
it is usually short. For example, this delay might be
effectively zero for those designs which involve sampling at
preset times or after a preset interval following an easily
observable event. In the case of the mobile mite counting
van mentioned previously, the growers were given a telephone
number to call after they first detected mites. This, too,
yields a very short delay (perhaps one day). On the other
hand, systems which rely on environmental parameters such as
heat units or rainfall to schedule sampling would, as a
minimum, be subject to any delays in acquiring these data.

92

93

Table 3

The decomposition of total monitoring
delay

 

Time delay 11

(1) Transmission of the trigger event
(2) Transportation to the sampling site

Time delay 2
(3) Collection of the sample (or data)
(4) Transportation to the processing site
(5) Processing the sample (or data)
(6) Transmission of results to the
decision maker
Time delay 3

(7) Accomplishment of control action

 

1. See Figure 2 for an explanation of delays
1, 2, and 3.

 

94
This would also be the case for sampling protocols triggered
by biological observations of some other species.

Transportation tg the sampling site. The vast majority

 

 

of biological monitoring involves the collection of materials
from the sampling site (although "materials" may mean only
some form of recording media). If there are many sites or
if sites are widely scattered sample collection can involve
significant amounts of travel time.

The simulation analysis of the mobile sampling van
provides an example of how these delays can be calculated.
It was desired in that study to determine the distribution
of travel time delay as a function of demand. There are
seven regions in Michigan where the Michigan State University
Integrated Apple Pest Management Project is active (Thompson
gt gt., 1973). Each of these regions was divided into two
approximately equal subareas and the average trip within a

subarea calculated as

(6-1) distance = %A2

where A is area. Optimal routes were selected for trips
between subareas. A matrix of inter-subarea distances was
created by hand using county and state road maps. Probable
routes were chosen according to criteria which combined
short distances with best available roads. Interstate and
state highways were given preference to other routes while
unpaved roads were selected infrequently. A similar matrix
for inter-subarea time factors (time divided by distance)

was constructed. In determining these time factors the

 

95

Michigan Department of State Highways' road classification
was used. Each road type was assigned a speed based on
previous Highway Department studies (Marino, 1972; Welch
and Marino, unpub.). The road classification, distance
matrix, and time factor matrix are reproduced here as Tables
4, 5, and 6 respectively. These tables were combined with
data on biological demand (chapter II) and processed by an
algorithm which selected sites to be visited so as to mini-
mize travel time to the next site. Figure 15 shows the
cumulative frequency functions for two situations, one in
which there are 30 growers being served in each management
region and one in which there are 45.

The only type of system lacking transportation delays
is one which (1) has transducers located permanently at the
sampling site and which (2) transmits its data automatically
to the site.of processing. However, while many automatic
systems exist for measuring biologically relevant physical
parameters (Haynes gt gt., 1973; Klein gt gt., 1968; Atmar
and Ellington, 1973) most biological parameters still require
manual sampling.

Collection gt the sample (gt data) and processing.

 

 

 

Included in these categories (3 and 5 in Table 3) are all

the manipulations required by the sampling protocol. Examples
might be capturing specimens, drying or disecting them,
counting them, etc. To analyze this type of delay, it is
necessary to decompose the protocol into a series of steps

and determine how the length of each step varies with work-

load, desired accuracy, and so on. In many cases the

 

96

Table 4

Road classification system

 

 

 

Category Definition Assigned Speed

Freeway Divided highway 55 mph
limited access

Multilane, Multilane, divided, 55 mph

divided free access

Paved, 2 lane Two lane roads 45 mph

upgraded to state
highway standards

Bituminous Two lane roads 45 mph
surfaced not upgraded to
roads state highway
standards
Gravel roads Roads with gravel 25 mph
surface

Improved dirt Roads with dirt ------
roads surface

Unimproved Two tire tracks ------
dirt roads

 

97

Table 5

Inter-subarea distance matrix
(miles)1

 

 

Subarea l 2 3 4 5 6 7

l 2.8

2 7.5 2.8

3 120.0 109.0 3.8

4 122.0 111.0 12.0 4.0

5 125.0 114.0 14.0 14.0 4.6

6 138.0 126.0 26.0 28.0 15.0 4.9

7 121.0 110.0 17.0 8.0 27.0 29.0 4.2
8 128.0 117.0 24.0 13.0 35.0 41.0 12.0
9 148.0 137.0 87.0 79.0 99.0 112.0 89.0
10 163.0 152.0 101.0 94.0 114.0 127.0 93.0
11 209.0 198.0 136.0 123.0 149.0 162.0 125.0
12 224.0 213.0 140.0 127.0 153.0 166.0 129.0
13 42.0 31.0 97.0 98.0 109.0 122.0 102.0
14 43.0 32.0 98.0 99.0 110.0 123.0 103.0

8 9 10 ll 12 13 14

l

2

3

4

5

6

7

8 4.1

9 68.0 4.8
10 81.0 14.0 4.9
11 113.0 56.0 48.0 3.8
12 117.0 72.0 65.0 16.0 3.7
13 111.0 127.0 140.0 188.0 205.0 3.1
14 111.0 121.0 134.0 183.0 193.0 5.9 3.0

1. Matrix is symmetric. Distances within a subarea are

assumed to be one half the square root of the area of

the subarea.

Subarea

\DmflmthNH

11
12
13
14

\OflNIONU'IIhUJNl-J

...:
O

11
12
13
14

98

Table 6

factor matrix

Inter-subarea time
(hours per mile)

 

l

.0278
.0278
.0185
.0188
.0188
.0192
.0187
.0187
.0187
.0191
.0193
.0187
.0185
.0186

.0245
.0222
.0222
.0233
.0245
.0183
.0184

.0278
.0186
.0188
.0188
.0191
.0188
.0190
.0188
.0191
.0199
.0201
.0187
.0188

.0222
.0222
.0222
.0267
.0184
.0187

.0222
.0222
.0232
.0231
.0230
.0222
.0192
.0197
.0222
.0222
.0183
.0184

10

.0222
.0222
.0222
.0184
.0187

.0222
.0235
.0236
.0292
.0222
.0192
.0197
.0222
.0222
.0183
.0194

11

.0222
.0222
.0184
.0187

.0236
.0236
.0229
.0334
.0195
.0199
.0233
.0267
.0185
.0186

12

.0222
.0184
.0187

.0236
.0255
.0232
.0196
.0196
.0242
.0267
.0187
.0187

13

.0222
.0222

.0245
.0245
.0222
.0235
.0233
.0242
.0187
.0187

14

.0222

 

99

Figure 15. The cumulative density functions gt travel
time per day for two different levels gt
demand. The distributions were generated
by a simulation of the logistics of a mobile,
van-based mite counting service.

100

 

 

00k 00.x
0 o
\ \
680.: 669. .
on 0s
-Ibh- n-h - p-
0 00
m. m. m. m. m. m... 4. w. 2. I. m
l000000000

35:02.... 028.3an

0.

Travel Time Per Day (hours)

101

protocol will consist of well established techniques. Even
if the techniques are new with the system being designed,
there is almost always a period where the new and the old
methods are operated side by side. It is during these
periods that the basic timing data can be taken. This can
be done by simply adding to the data notebook a notation for
each sample as to how long the various processing steps took.
The designer will then be in a position to determine the
contribution of the protocol to total delay.

An analysis of mite sampling will serve as an example.
The current method of choice for mite counting is to take a
leaf sample, mechanically brush the mites on to a sticky
glass plate, and count sectors of the plate under a low
power binocular microscope (Morgan gt gt., 1955). The time
involved in these activities was partitioned as shown in
Table 7. The right-hand column shows the times for each
action. These were determined from multiple linear regres-
sion fits of data taken during time—motion studies of mite
counting (Croft, unpub. data). With these values we can
construct the f0110wing predictive equations for collection
and processing delays

(a) collection delay =
.25 + .00833(NTR) + .00167(NTR)(NLV)
(6-2) (b) processing delay =
.00449 + (NTR-NLV)(.00067 + (A)(M))
where
(c) M = .00005(NES)(ER) + .00034(NAS)(AF).

The variable definitions are given in Table 8. In actual

use NAS and NES can be determined from sample size curves

102

.moEHu common ummcoH ca mcfiuasmou mowuflmcoo Hausa :H moconommao umoum 050 OD
000 manmnoum ma mafia m0 momma 030 on» How moEflu mcflpcsoo a“ oocoumwmwo 036 .H

 

mnns\.mue
man\.mnn
mmm~\.mnn

.mn:

H

omma\.mnn
oouu\.mun
.mus

oaxovm. muflmcoo uoumooum ou Hmcofiuuomoum muouomm Avv
mHonoom. wuflmcoo anon on HocoHonomonm mnouomm Amv
MIoaxObw. mo>moa* ou HocoHuuomoum muouoom Amy
mtoaxmvv. muouomm ooxflm lav
mo>moa 0:500 Op mafia
oatha. mo>moa# on Hmcowuuomoum muouomm Amv
Mmoaxmmm. moouu# on HMGOHNHOQOHQ muouomm ANV
coaxomm. muonomm ooxflm AHV

mo>ooa on» xowm ou oEHB

 

moEHu consumes can can mc0fluoo ououomflo
000w Hooououm mcmeEam oqu n no cofluwuumm

s wanes

103

Table 8

Definition of variables in the
timing equation (7-2)

 

AF
ER
NAS
NES
NLV
NTR

The
The
The
The
The
The
The

relative area of one plate sector

per leaf density of predatory mites

per leaf density of phytophagous mites

number of plate sectors counted for predators
number of plate sectors counted for pest mites
number of leaves taken per tree

number of trees sampled

 

104
based on the densities of mites in the sample (Croft
gt gt., 1976b). For a sample of 200 leaves taken 5 per
tree, Figure 16 shows the processing delay for various total
densities and prey-predator ratios. In this case most of
the delay is consumed in collecting and preparing the sample.
The breaks in the curves in Figure 16 are due to the integer
nature of the number of plate sectors counted.

Transportation tg the processipg site. In most cases

 

 

samples are not processed at the same place they are
collected. Instead, they are transported to some specialized
facility or laboratory for examination. In other designs,
the sample may be examined in the field but the resultant
data require further manipulation. This may occur because
some statistical computation is necessary or the results

must be compared with previous data or run through a bio-
logical model. In any such case transportation must be
included as a component of total delay.

An example is provided by the BLITECAST computer pro-
gram developed by Krause gt gt. (1975). This program
integrates rainfall, relative humidity, and temperature to
produce a spray recommendation for potato late blight

(Phytophthora infestans). Although the data are taken in

 

the field, computer processing at a central site is necessary.
As is frequently the case when plant pathogens are involved,
any time delay is critical. For example, in one case on
record a two day delay in transmitting data to the BLITECAST
program resulted in a grower loss of approximately 50,000

dollars (Bird, pers. comm.). This testifies to the

105

Figure 16. The total processing time for mite samples
gg g function gt total mite density and pre -
predator ratio. Counting time is most like y
sensitive to the latter factor due to the
extra search time required for the counter
to find the relatively rare predators.

 

 

 

 

 

106

 

|.|8r
l.l6-
. as

75 43I\‘
5.: l.l4-
g ..
I: LIZ-
U’ b (\O
.5 \<°
g LIO- \OI\ ,gx‘xo
s - ‘5’ .0
d.’ l.08- 20/\ “i“
g ..
I3 I05.

l.04-

'.02011141111élll|1211Lllelllzjo

Total Density (mites/ leaf)

107
importance of characterizing all sources of delay.

Transmission gt results tg the decision maker. An

 

interesting dichotomy exists between information which must
be transported in physical form and that which can be
transmitted via the electronic media. Some forms of infor-
mation, such as raw biological samples, are inherently I
frozen in physical form. Other data, however, can be
freely interconverted. For example, written material can
either be mailed or sent electronically by such devices as
Code-a-phones® (telephone playback equipment), data terminal
networks, or the mass media. Although the latter methods
may have high capital costs, they often result in signifi-
cantly reduced delay times and lower operating costs.

An example of this is the transmission of pest alert
information via the Michigan State University Pest Manage-
ment Executive (PMEX) system of which the author was one of
the two principal designers. This system consists of a
statewide network of data terminals linked via the direct
Edial telephone service to a central computer at Michigan
State University. Software on this computer permits the
rapid accessing and updating of biological monitoring data
bases by pest management personnel. In addition, if
monitoring reveals results of wide interest, alert messages
can be sent directly to all affected individuals. During
the 1976 growing season over 300,000 words of information
passed through the system to more than 70 extension
personnel with concerns in fruit, vegetables, and field

crops. Because of the selective nature of the Executive

108
system, ggty those individuals interested in particular
types of data received them. The most important result of
this system from our point of view is that data which
previously took a week to ten days to reach users (prin-
cipally through the mails as the "Insect, Disease, and

"1) now reach them in a few minutes. Further

Nematode Alerts
details of the PMEX system are discussed by Croft gt gt,
(1976a).

Accomplishment gt the control action. This delay

 

 

covers the time it takes the decision maker to arrive at
and implement a control decision once he receives the moni-
toring results. Typically the designer has no control over
the length of this delay because it depends solely on how
the decision maker schedules his activities. Nevertheless,
the designer must take this interval into account because
biological interactions are unceasing.

After all seven of the delays in Table 3 have been
analyzed, the next step is to determine how they are altered
by changes in design parameters and how this affects system
performance. At this point it is appropriate to describe
an extension of the graphical technique we introduced in
the last chapter. Consider a system whose design is complete.
The operation of the system can be represented by a point

in the (v,i,t,r) plane whose exact location is a function of

 

1. Published cooperately by the Coop. Ext. Serv. and the
Departments of Entomology, and Botany and Plant Pathology,
Michigan State University, East Lansing, MI 48824.

109
the design parameters. Changes in these parameters will
cause the point to trace out some curve in the plane. Changes
in single variables or in sets of variables with only one
degree of freedom will produce a line. Changes in sets with
more than one degree of freedom will have more complex results
which can be analyzed by additional contour lines. The use
of these graphical methods can greatly facilitate the design
process.

In the analysis of the mobile mite counting van, it was
desired to determine the effect of requiring more accurate
estimates of mite density on system performance. Accuracy
was represented as one half the width of the 80 percent
confidence limits expressed as a percentage of the estimated
mean density. It was possible to relate these to delay times
as shown in Figure 17 by using the methods discussed in
earlier examples in this chapter. We can plot these data
on the nomogram by equating the average distance traveled
to reach a monitoring site with monitoring unit size.

Figure 18 shows the results. Each point on the curve was
plotted by reading monitoring unit size off the bottom axis
and delay off the righthand axis. Because of the properties
of the nomogram, however, the curve can be used to read risks
and sampling intensities for each "technology" on the
continuum. The results show that, for these technologies

at least, improving the accuracy of sample estimates far from
pays off when confidence limits are already tight. If this
example is combined with the chance constrained programming

example of the last chapter one concludes that confidence

Figure 17.

110

The mean waitipg time for service gg g
function gt desired accuracy. The data for
this figure come from the previously mentioned
logistic simulation of the mobile mite
counting service. As greater accuracies are
demanded, processing times increase generating
a system bottleneck. This leads to the
exponential rise in service wait times.

Mean Waiting-Time for Service (Days)

 

lll

 

l

5

a

 

l0 IS 20
Eighty Pct. Cont. Limits (Pct. of mean)

Figure 18.

112

g continuum gt technologies indexed gy
desired sampling accuracy. Each point on
the graph was plotted by taking the time
delay from Figure 17 and the monitoring
unit size from the original simulations
(see text). The figure illustrates that
when confidence limits are already tight
(7.5 percent) even modest further improve-
ments can dramatically alter grower risk.

 

Economic Risk (pct)

113

Relative Sampling Intensity
50 63.8 I50 7.! 4.0 2.0 l.8 |.3 l.0 0.8

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

/_.1 5.6

45~ / If 5.5
40_ ////_.1 6.5 5.4
35- ///
30)-
25- //
20-
//
l0-

I /
5- IA/

 

 

 

 

 

O l J L I l L 1
O 5 IO I5 20 25 30 35 40
Monitoring Unit Size (miles)

(-

Maximum Time Delay (days)

114

limits narrower than 7.2 percent should not he demanded of
this system. By way of comparison, field experience shows
that accuracies in the range of 20 to 50 percent are
adequate for management (Croft 33 al., 1976b).

In this chapter we have diagnosed the typical causes
of delay in monitoring systems and shown methods of relating
them to system parameters such as sample size and the

spatial distribution of demand. By use of the nomogram the

Aimpact of these delays can be assessed for various possible

design alternatives. In this manner parameter values may
be chosen so as to insure that the resultant systems operate

within their performance constraints.

._ Fig

CHAPTER VII

THE ECONOMICS OF THE MONITORING SERVICE

In chapter IV we discussed the economics of monitoring
as seen by the decision maker. In this chapter we take up
the subject from the point of View of the monitoring service.
In designing monitoring systems and choosing between alterna-
tive configurations, it is necessary to budget the activities
of those systems. Many such systems are initially funded on
capital granted the developer by various public or private
sources. At some point, however, a system which is to
continue operations must switch from developmental monies to
some more permanent source. The economics of the system
must be understood very well if the conversion is to be
seen as justifiable. By estimating the economic performance
of a system ahead of time one can choose design alternatives
which will facilitate this transition. Conversely, failure
to consider these aspects of the problem can result in initial
funding and credibility being wasted on impractical systems.

In this chapter we shall View initial capital as money
to be invested and alternative system designs as an array of
possible investment choices. To help make the investment
decision we shall adopt a slight modification of an investment
screening program described by Park (1973). This method

combines various economic components to calculate a return on

115

116
investment (ROI) via the discounted cash flow (DCF)
technique. The method requires inputs which we shall describe
using Park's terminology. Although this nomenclature has an
industrial slant, the application to agriculture is clear.

Average annual sales 93 revenues. This is simply the

 

number of samples taken times the cost to the grower of each
sample plus any "revenues" derived from other sources. These
might include public subsidy payments, sales of unused moni-
toring resources, etc.

Direct production costs. These are the per sample costs

 

of monitoring. They cover materials, any labor paid on a
piecework basis, etc.

Indirect, fixed, gr overhead costs. This category

 

includes costs which are related to time rather than to the
number of samples. Salaries and wages, capital charges,
facility rental, and so on would come under this heading.

Net investment. This is the total capital cost of

 

putting the system in operation. If the goal of the analysis
is to see how attractive the system would be to the private
sector, then any public subsidies should be deducted from
this entry. On the other hand, if the overall viability of
the enterprise is being examined, this quantity should not
reflect subsidies.

Economic project life. This is the period, in years,

 

over which it is estimated that the system will operate as
designed. It can also be defined as the period over which
the capital costs will be recovered. To simplify the

calculations we shall assume (1) that sales, costs, and tax

117
rates (as applicable) will remain constant over this period
and (2) that capital costs are amortized on a uniform
straight line basis. Park (1973) states that most projects
will have a life of five to ten years since "less than five
years is unrealistic and conditions beyond ten years can
seldom be anticipated". This last is particularly true in
an evolving discipline such as pest management.

Income tax rate. This refers to the total of all income

 

based taxes minus any applicable credits. This may be zero
for systems Operated in the public sector.

Once these quantities are known they can be entered in
the program of calculations illustrated in Table 9. The
goal of the first part of the analysis (lines 7 to 12) is to
determine net cash flow which is revenues minus production
costs, overhead, and taxes. It is also numerically equal to
net profit after taxes plus depreciation which is the
algorithm used in the table. It can be thought of as the
money in the bank at the end of the year.

From the net cash flow one can calculate the percentage
of the initial capital investment recouped each year. This
is the capital recovery rate and is determined as in line 13.
While this rate is a useful index of how fast the system will
pay off, it gives little indication of the total profitability.

The ROI is helpful in this regard. According to the
DCF method, the ROI is defined as the discount rate which
makes the sum of the discounted cash flows identically zero.
To interpret the ROI, suppose that the initial capital for

the project was borrowed from a bank. If the ROI exceeded

118

“mm .a .mamav xumm umuma .H

 

uxmu mom AHomv unmEumm>cw co :Hsumm
w mGwH\NH mafia mumu >Hm>oomu Hmuwmmu

I IHCQEHmQNVCfl GO GHSUQNHI I

Ha wcfla+h mafia 30Hm ammo #02

H mafiaIm mafia mmxmu Hmumm panama umz

m mafia x m mafia mmxmu mEoocH

m mafiaIH mafia mmxmu muommn uwmoum uoz

n mcwa+m mcfiH+N mafia mGOfluospwp Hmuoa
m mcfla\v mafia coaumwomummp Hmsczm mmmum>¢

I I I 30Hw ammo umz I I I
open xmu oEooaH

Emumzm mo mafia aflfioaoom

ucmsumm>GH uoz

mumoo :ofluospoum uomHflUcH

mumoo cowuospoum uomuwa

mwscm>mu no moamm Hmsccm ammum>¢

I I I I I musmcH I I I I I

 

 

COwumasoamo GoHumfluommo

va
ma

NH
AH
OH

[x

I-INM'Q'lnkO

 

mafia

 

Enuwuomam mcflammuom unmEumm>cw UmwmemEHm

m magma

119
the loan rate then, after paying off the bank, there would
be cash left over at the end of the system life. If the loan
rate was greater than the ROI then the project would end up
in debt.
Mathematically the ROI is determined from the equation
NCFi

n
(7-1) 0 == :5 -———————r
, i=0 (1+ROI)1

where NCFi is the net cash flow for year i and n is the system
life. Under the simplifying assumptions adopted above, the
ROI can be calculated from the capital recovery rate CRR from

the equation
ROI(l+ROI)n

(7-2) CRR = n
(1+ROI) - 1

 

Under the most common patterns of investment, problems of
multiple or imaginary roots for the ROI generally do not arise.
In his more complete treatment of cash flow analysis Park
(1973) gives more complete algorithms for the ROI including
methods for incorporating risk in order to obtain a probab-
ility distribution for the ROI.

To illustrate the use of the ROI we shall compare three
possibilities for monitoring mite populations with the mobile
sampling unit we have discussed previously. We shall refer
to these alternatives as the full system (FS), reduced system
one (RS I), and reduced system two (RS II). In the full
system the van is equipped with both a calculator and a data
terminal. The staff consists of two individuals who collect
and process the leaves and use the calculator to store the
data and make a control recommendation. Data are transmitted

to a centralized computer directly from the van at the end of

120
each day via the data terminal. If the computer detects
unusual field conditions which invalidate the calculator's
recommendation then a postcard with the correction is mailed
the next day. Reduced system one differs in that the data
are sent in vocally by telephone rather than by terminal.
This necessitates an extra employee at a central site who
spends a few hours each day entering data into the cOmputer.
In reduced system two only one person operates the van.
Rather than counting mites in the orchard, the samples are
refrigerated and taken to one of three field stations at the
end of the day. They are counted there the next day by
technicians who mail the recommendations to the growers on
post cards.

By use of a model incorporating biological, logistical,
and statistical factors as discussed in the previous chapters
we can predict the number of samples taken, resources used,
time delays encountered, etc. By assigning costs to these
items and conducting a DCF analysis of the results we obtain
Tables 10, 11, and 12 for F8, RS I, and RS II respectively.
These figures are based on the assumption that the systems
are operated as Cooperative Extension Service projects
employing student labor. By noting system time dealys we
can plot these three alternatives on the nomogram (Figure 19).
There is no significant difference in the performances of
FS and RS I. The results for RS II are interesting because
(1) this method has been, in fact, employed for several years
prior to and in parallel with the mite counting van and (2)

the predicted level_of risk to the grower (12 percent) is

121.

 

vb.hH
ahHm.
va.ammm
ca.v~ma
mm.mNHm

oo.mv-
anon

magma m
oo.m-HH

om.~om¢

mm.wHNH

oo.omvm
Hmuoa

 

oo.m~m
oo.oom
oo.oon
oo.oom~
oo.oomN
oo.oomv

 

oo.ovHH
oo.ovaa
om.Nmm

oo.oomH

oo.HhH
Hr.mmm
om.~
mh.mh

Nuucm

AHomv acmsumm>cfi co :Hsuom
mums aum>oomu Hmuwmmu

30Hm ammo umz

muwmoum umz

macauospwp Hmuoa
cowuawomummo Hmsccm mmmum>¢
mums xmu mEoocH

Emumhm mo mmwa oflEocoom

nozom
unwemwsqm uncumuonmq
mascouuooam msoocmaamomwz
Moumasoaao
Hac«Euou nousmeoo
ca>

ucoEumw>cH uwz

A>m0\oam a whapIcaE vaav wocm30HHa poem
Asmnxomm a name ems mecca Hmuoz
Au:\om.~m @ mu: mmmv mmonmEm pwwuaammIcoz
.mzuCOE vv mo>onEo pmwuaaam

mumoo pawnum>o can .pmxflu .uomuwch

Azmp\mm w ammo hmv mmmumno wconmoama
1.as\ooa a amass H.emmav .ucame cm> new mac
A.aw OOH w mmHmEmm mmv mpuaoumom
A.mm own a mmHQEmm mama managesm

mumoo cofiuospoum uomufio

“.mm omw w mmHQEmm mamv mmscm>mm

 

cofiumwuommo

ed
ma
NH
HHIm

LONOI‘

 

mafia

 

Ammv Emumhm Adam
on» no mfimhamca 30am ammo pmucsoomao

OH manna

l122

 

wa.m~
ommn.
vo.m5mN
vo.mwNH
mm.HmHm

oo.mowa

ouwn
mumm> m

oo.m~om

oo.ommm

om.mv~a

oo.omvm
Hmuos

 

oo.mNm
oo.oom
oo.oom~
oo.oomv

 

oo.ovaa
oa.ovHH
oo.ov~
om.~mm
oo.oomH
om.va

 

oo.HhH
Ab.mwm
om.Hm
mh.mh

Nuucm

AHomv ucoEumm>cw co cusumm
oumu >um>oomu Hmuwmmu

30Hu ammo umz

mnemoum umz

mCOquSGOU Hmuoa
coflumflowummp Hmsccm mmmum><
mums xmu mEoocH

Eoumxm mo owed owEocoom

Hmzom
ucwemflsqw kuoumnonmq
Houndsoaau
cm>
ucwsumm>cw umz

Ammp\oam w mxmpIcme «Hay moam3oHam boom
Asmn\o~w a mama amt meoou Hmuoz
105\omm 9 Hanson canoe we Hmcneums
Aun\om.~m @ mun mmmv moonQEm pmHumHmmIcoz
Amzucoe «v mmonmEo pwflumamm

Aun\om.~m w
>mp\mun m x ammo hmv ammowanomu auucm mama

mumoo vmmnuw>o can .Umxwm .uowuflch

A>Mp\mm w mmmp nmv mmmuano mcosmwame
A.Hs\ooa 9 He H.hmmmv .uawae cm> paw mam
A.am ooa @ mmHmEam many mpumoumom
A.mm 0mm a mmHQEMm mama mmaaaazm

mumoo sawuospoum uoouwo

A.aw on» @ mmameam mHmv mmscw>mm

 

cofiumfluommo

AH mm. mco Emum>m Umospou
on» ma mwmxamcm 3on ammo cmucsoomwa

AH manna

 

mafia

1123

 

mH.mm
vONw.
v5.Nth
ch.hHNN
mN.NMNh

oo.mmOH
oumu

mummx m
oo.m>~m

om.Nmmv

wh.v¢MH

oo.omvm
Hmuoe

oo.th

oo.oom
co.oomv

00.0mm

oo.ONh
om.NwON

oo.oomH

om.Hm

oo.mm
Ho.mvHH
om.Hm
mh.mh

Nuucm

.Hom. ucmEumw>cH co cusumm
mums >um>oomu HmuHmmu

30Hm ammo uoz
uHuoum umz

mGOHuospmp Hmuoa
coHuaHooummp Hasccm mmaum><
mums xmu mEoocH

Emumxm mo meH OHEocoom

um3om
ucmEmqum huouauonmq
cm>

unoEumw>cH umz

Ahmo\OHw @ mwmpIcmE mmv wocm30HHm poom
A.mo maucos v new Hmucmu oe\oom a MC mHmcHEHmB
A.mw Hn\om.Nm x
hmp\mus m x mwmp mm w my mCMHoHccomB
Amnucoe vv mahonEm pmwumHmm
mumoo cmmsum>o Dam .pmxHu .uowancH

A.mm ooH @ mmam5mm mama coaumamocaummm
A>m0\Hm w mwmp mmv mmmumso mcozmmHmB
A.HE\ooH w mmHHE H.omvHHv .uchE ca> 0cm moo
“.mm ooH 9 moHQEmm mHmv mpumoumom
A.am 0mm 9 mmHmEMm mHmV meHszm

mumoo coHuospouQ uoouHa

A.mo omw w mmHmEmm mHm. mmscm>om

 

coHumHuommo

«H
«H
NH
HHIm

LDKDI‘

 

mch

 

AHH may 03» Emumxm.nmoscmu
may no mHmNHaca 3on nmao poucsoomHa

NH OHQMB

Figure-19.

124

The return 92 investment for three mite
monitoring systems plotted 23 a nomogram
showing system performance. The key paint
here is that the most profitable system
(RS II) is also the most risky to the

grower.

 

Economic Risk (pct)

125

Relative Sampling Intensity
63.8 l5.0 7.l 4.0 2.0 l.8 l.3 l.0 0.8

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

50 /_7 5.6
45 / l 55
//’"’f A
40 / ...—-——-—'” 5.4 u>)‘
/ // s
35 / /"‘”"‘i‘ 5.2 E
so // g
/ 5.0 a,
20 / ' 43 i:
/ RS 11 / j ' g
'5 / l= 5.I°/. 4.6 E
D
l0 / 4.4 2
sJ // / FS 4.2
.// .o/.\ 9' 7:7
O l l l l 1 j 1
o 5 IO IS 20 25 so 35 40

Monitoring Unit Size (miles)

 

126

almost identical to the level actually realized (11 percent).
If we were to impose the 7.5 percent chance constraint used
in previous examples (eliminating RS II) we would be led to
RS I because of its greater return at no increase in grower
risk.

This example raises an interesting point: the system
which is best for the decision maker may not be the best for
the monitoring service. In the long run, risk levels would,
presumably, be subject to bargaining or some other adjustment
process between the decision maker and the monitor. However,
because of the complexities involved, decision makers may be
unaware of the risks attending different levels of service
from competing monitors. This lack of perfect knowledge
would complicate the approach of the parties to a mutually
acceptable equilibrium position. Additional factors which
would affect these negotiations might include the partition
of total monitoring between the public and private sectors,
general market conditions, the degree of organization among
decision makers, etc. The main point is, however, that some
"avoidable" damage will almost certainly occur during this
adjustment period, especially if it is prolonged. The extent,
nature, and sources of the certification procedures and
insurance mechanisms which might or might not be necessary
to ameliorate this effect have not yet been explored.

In this chapter we have examined a method for studying
the economics of the monitoring service. Because of its
simplicity this investment screening approach can easily be

applied to a large number of design alternatives. The

127
nomogram can be used to relate this analysis to the factors
considered in earlier chapters. When all these data are
plotted together along with the relevant constraints, the

final choice of a feasible configuration can be made.

CHAPTER VIII

SYNOPSIS OF DESIGN PROCEDURE

In the previous chapters we have discussed the factors
and types of information necessary to design the monitoring
component of a management system. As yet, however, we have
not presented a unified and integrated plan for the design
process. Such a plan is obviously needed to prevent
unnecessary waste of the designer's time and money. In
this chapter we shall discuss the sequence of activities and
methods of recording data to facilitate this process.

Work on methods of monitoring and controlling a pest
always begin with a perceived need. Often these needs are
rather vaguely defined. An outbreak of a new pest is either
observed or anticipated. In many cases it may not be known
how serious the pest is or what its potential for spread
may be. Even when a pest is known to be dangerous in a
neighboring geographic region, its behavior in a new physical
and economic environment may be difficult to predict.

The first step, as always, is biological investigation
of the pest ecosystem. The goals of this inquiry are four-
fold: (l) to provide input to a detailed analysis of
management needs, (2) to elucidate the bionomics of the pest
under local conditions, (3) to provide for the statistical,

logistical, and economic analysis of potential monitoring

128

129
protocols, and (4) to facilitate the construction of
decision making rules.

The types of biological data needed were discussed in
chapter II. These include, broadly, where the pest is found,
when it is found there, and the types of damage it does.

This last should incorporate both biological indices of
damage (g.g., 40 percent damage to the photosynthetic surface)
and, insofar as is possible, economic measures (g.g., 15
percent reduction in salable yield). Economic measures are,
admittedly, difficult to document, particularly for indirect
pests. Measures such as the percentage of yield in various
quality classes or subjective measures of crop vigor may be
more appropriate. In any case, data in some form should

be taken to relate biological and economic processes.

All of this fairly general information can be combined
into a detailed statement of management needs. This should
specify the location, volume, and nature of the affected
crops, the types, timing, and severity of damage, and a
quantitative description of the ecosystem states which must
be maintained to alleviate the problem. It should also
include the methods available to achieve these ends but not
necessarily how they are to be applied. Any constraints on
the operation of the system must be carefully described.

Also important is a description of the groups and individuals
involved in the management process since one of the design
constraints is that the system be acceptable to these

personnel.

130

At this point the designer must determine if it is
possible (feasible) to meet these needs with current technol-
ogy. .This involves a very rough look at a number of solution
types. This usually means the construction of some promis-
ing approaches to the problem; generally, at this point, too
little is known about the situation to formulate any specific
designs.

If it should develop that no alternatives with more
than a marginal value are readily apparent, then it may be
necessary to reformulate the needs. This might involve,
for instance, a willingness to accept a higher level of
damage or a method of control previously classed as unsuitable
(g.g., because of secondary effects).

Once the needs have been defined and it appears that
feasible solutions may exist, steps can be taken which aid
the construction both of the ultimate monitoring component
and of the decision algorithms it drives. These steps involve
detailed studies of the population dynamics and the formula-
tion of a model of the pest ecosystem (chapter II). These
studies may be a continuation of the needs analysis investi-
gations but generally they will contain new elements. The
types of data needed are developmental rates and reproductive
information, if applicable, of the pest. Dispersal data are
also essential for certain organisms. Particularly useful,
if obtainable, is the influence of environmental factors on
these processes. The importance of having at least some
data on these rates cannot be overemphasized. It is from

this information that the basic time constants of the

131

management system must be calculated. Fortunately, it is
not necessary that these rates be known with great pre-

cision. For example, in the construction of a successful
model of the interaction of the European red mite and the

predaceous beetle Stethorus punctum, Mowery gt_§l. (1975)

 

assumed merely that the beetle population increased at the
flat rate of five percent per day.

The investigation of population dynamics typically
requires the biological monitoring of field populations (as
may the preceding needs analysis). Monitoring methods may
be taken from the literature or from experience with similar
species or be created d3 2923 for this system. There may,
and hopefully will, be several distinct monitoring approaches.
0f necessity this monitoring must be accomplished without
the monitoring design it is meant to facilitate (except for
generic features which may carry over from previously
designed systems). The earliest steps must therefore be
exploratory and may be devoted to improving sampling
sufficiently to get reliable data to design the ultimate
monitoring-management system. The riddle of the chicken
and the egg has a certain relevance here.

Two major classes of monitoring can be distinguished
at this stage. The first contains those specialized
measurements which, while necessary for a particular exper-
iment, would probably not be made in a management context.
The remaining protocols might well be used in a management
scheme even if the preliminary experiments are only indirectly

related to decision making. A major goal of the preliminary

132
field work is to evaluate the use of these latter methods
and provide the statistical, timing, and cost data necessary
to implement an optimized monitoring component.

There are two steps which should be taken to facilitate
this process. First of all, auxiliary records should be
kept of the timing and cost of sampling. Protocols should
be decomposed into their constituent activities and timed.
This permits studies such as those described in chapter VI.
Strict accounts should be maintained of the consumption and
prices of labor and sampling materials. This record keeping
may add to the time required to process the samples. To a
certain extent this can be alleviated by only recording
rigorously a fraction of the samples and keeping less
complete or no records on the remainder. Beyond this it can
only be emphasized that it is easier in the long run to
maintain good records as one goes along than to have to go
back and make specialized studies later on.

Another related category of auxiliary data concerns
travel times to remote sites and the costs of vehicle opera-
tion. While the map-based methods of chapter VI can be-
used, better results will be achieved from data obtained by
actually traversing the management region. In cases where
the region consists of a relatively homogeneous mixture of
rural country roads and two-lane highways, records of total
distance and total time may be sufficient. In cases where
interstate or limited access freeways are involved, somewhat

more complex records may be needed.

133

A second major point is that a variety of sampling
methods, if available, should be used. Often, different
methods may not measure exactly the same thing or may measure
it with different efficiencies. For this reason certain
portions of the samples should be measured by more than one
technique. This will provide a direct comparison of the
methods on the same materials. Other portions of the samples
can be analyzed by single methods so that complete duplica-
tion of effort does not result. When there are very few
methods available (perhaps only one) or when initial screen-
ing yields one of clear superiority, then protocol variations
should be employed. That is, such parameters as sample size,
number of subsamples, etc. are altered in several combina-
tions. The total duration of a sample procedure will depend
on several independent factors. The use of multiple protocols
will give each factor a chance to express itself. Ideally,‘
to permit multiple regression studies of time requirements
(see chapter VI) there should be one more variation than the
number of activities into which the protocol has been
decomposed. Each protocol variation must, of course, be
consistent with the requirement for sound biological data.

It is important to remember that while this work is
going on, a parallel effort is designing and testing decision
algorithms. These two programs, ideally, will act to
reinforce one another. The testing of decision rules in the
field generates data useful to model building and monitoring .
evaluation; the evolving model can be used to test nascent

decision rules in ways not possible in the field.

134

The development and testing of decision rules can begin
as soon as the management needs have been completely specified,
although it is possible that a period of biological investi-
gation might necessarily intervene. Once actual field
testing of one or more sets of decision rules begin, there
are several types of data which should be recorded. First
of all there is, obviously, the data on which the decision
is based, what decisions are made, what control was actually
implemented, and what the result was. Also, however,
economic data should be taken. What was the cost of monitor-
ing; what was the cost of the control recommended; what was
the cost of the control actually applied; and what was the
cost of the outcome. These data are necessary to quantify
the economic aspects of the system as discussed in chapters
IV and VII. It must be remembered that pest management is
an economic as well as a biological problem. The designer
of decision making strategies should always be sufficiently
aware of conditions in the pest control market to know the
costs of his recommendations. By recording these right
along with the biological data the embarrassing alternative
of having to make later "guesstimates" can be avoided.

At several points in the previous paragraph a distinction
was made between the recommended control and the control
actually implemented. This difference becomes particularly
important when field testing is being done with cooperators
who may be unwilling or, for various reasons, unable to
follow completely the given recommendation. By recording

this information, a much better understanding of potential

135
performance can be formulated.

When cooperators are involved in pilot studies, the
opportunity also exists to determine what institutional
mechanisms and price structures will be most acceptable in
the ultimate system. In this way the market potential for
various levels of service can be estimated. Equally important,
satisfied pilot project cooperators are an invaluable aid in
getting a new system accepted once it is fully operational.
Indeed, these pilot programs should be as closely tailored
to actual operating conditions as possible so they can serve
as stepping stones to an in-place system.

As data from both the biological and control strategy
programs become available in the forms of models and decision
rules, the development of nomograms can proceed. As
mentioned earlier, it may be possible to make a beginning
based on the needs analysis alone. In this case, the initial
crude efforts may prove very useful in making gross feasibility
decisions. In any event, as soon as possible, one or more
relevant sets of (v, i, t, r) parameters should be seleCted
(chapter V). Charts construCted on the basis of these
variables can be improved as research proceeds. By showing
which alternatives appear most likely to succeed at each
stage, the charts serve to guide the design effort. Also,
of course, their use in optimization has already been
mentioned (chapters V, VI, and VII). Finally, using models,
charts, and pilot studies as winnowing agents, only one
design will remain.

The last step is implementation. By this time, through

136

field demonstrations, publications, analysis, and contact
with the affected parties, the system should be perceived
as an effective pest management tool. All that should
remain is the formal act of instituting full operation.
Even after this happens it is necessary to check system
operation periodically. This may best be done by the
regional-level system control (see Figure 2) in conjunction
with the planning function described in chapter I. This is
necessary because the system must be able to adapt to meet
any changes in its operating environment. These changes
may range from simple incremental improvements in technology
up to and including a complete replacing of the system or
the phasing out of operations.

The design process outlined here is typical of the
systems approach to problem solving (Manetsch and Park, 1974).
The procedure begins with the recognition of needs which are
then analyzed in detail. Next, a set of potentially feasible
approaches are proposed and studied. For monitoring (and‘
the corresponding decision making components) this entails
the integration of biological, statistical, logistic, and
economic factors. By the use of graphical models it is
possible to design, optimize, and, perhaps after several
iterations, to choose a suitable system.

The robustness of this design approach is its most
important characteristic. Agriculture possesses great
diversity. Hosts may be animal or vegetable; they may be
short lived or live for many years. Pests can vary in

severity, number of generations per year, damage mechanisms,

137
etc. Agricultural components may operate in the public or
the private sector. Finally, marketing arrangements range
from virtually free market conditions, through oligopoly
and government regulation. Nevertheless, no matter what the
unique properties of a given situation might be, the four
types of factors discussed in this thesis will play a
determining role.

Chapter II contained an example which showed that, while
different levels of pest spatial variation could affect the
scale of management, the design process remained the same.
Consider now two alternative marketing structures, each of
which is confronted by a pest whose dispersal behavior makes
large scale, regional monitoring preferable. Suppose that
the first structure consists of many small, undiversified
operators acting independently. Let the second market be at
the other end of the spectrum; that is, let it be dominated
by a few large, diversified, oligopolistic producers. In
contrast to the chapter II example, the main comparison here
is economic rather than biological. In spite of the
differences between the two structures, the designer must
still ask questions about risks, decision maker costs, and
monitoring service economics. Only the answers are different.
Diversification would allow the large producers to tolerate
higher levels of risk than could the small independents.
Because of the size of their operating budget, however, the
large operators may not always choose to do so. For instance,
they may realize sufficient economies of scale in the bulk

purchase of control materials to lower their perceived

138

economic injury levels. While small agriculturists may
have to turn to cooperatives or public agencies to administer
the regional management system, the large producers are more
likely to internalize these costs. They may even do so by
forming wholly owned subsidiaries which might well be
permitted to operate at a loss (which would not show on a
consolidated statement). Except, possibly, for a public
agency, this would not be a feasible design alternative for
the small producer case. The freedom to operate at a loss
would be an important element in the determination of level
of service. The appropriate form of monitoring-management
system is developed by utilizing the differing answersto
the common questions posed by the unified design procedure.

This design approach can also be applied to a variety
of situations not limited to pest management or even to
agriculture. There are a great number of problems in today's
world ranging from energy production to waste disposal where
strong interactions exist between humanity's economics and
biological reality. Figure 2 might well serve as a manage-
ment schematic for any number of these. In any such instance,
the analysis set forth in this dissertation would be
applicable. As time passes and management systems become
more complex, more automated, and more capital intensive,
and as the managed commodities become more valuable, the
importance of this and related forms of analysis can only

increase.

LIST OF REFERENCES

LI ST OF REFERENCES

Atmar, J. W. and J. J. Ellington (1973). An advanced
environmental chamber control system. Environmental
Entomology, 2:88-94.

Baily, N. T. (1964). The Elements gf Stochastic Processes.
John Wiley and Sons, Inc., New York.

 

 

Barr, R. O. et a1. (1973). Ecologically and economically
compatible pest control. In: Insects: Studies in
Pest Management. Ecological Society of Australia,
Memoirs 1, Canberra.

 

Bekey, G. A. and W. J. Karplus (1968). Hybrid Computation.
John Wiley and Sons, Inc., New York.

 

Binder, A. (1964). Statistical theory. Annual Review of
Psychology, l§:277-310.

Bliss, C. I. and A. R. G. Owen (1958). Negative binomial
distributions with a common 3. Biometrika, £§:37-58.

Bohnam, C. D. and R. E. Eye (1970). Estimation of winter-
time soil temperatures. Journal of Economic Entomology,
63:1051-3.

Boussard, J. and M. Petit (1967). Representation of farmers'
behavior under uncertainty with a focus—loss constraint.
American Journal of Agricultural Economics, 39:869-80.

Carlson, G. A. (1969a). A decision theoretic approach to
crop disease prediction and control. Unpub. Ph.D.
thesis, University of California, Davis.

(1969b). Bayesian analysis of pesticide use.
Business and Economics Section, Proceedings of the
American Statistical Association.

(1970). A decision theoretic approach to crap disease
prediction and control. American Journal of Agricultural
Economics, §2:216-23.

(1971). The microeconomics of crop losses. In:
Economic Research 9n Pesticides for Policy Decision
Making. USDA, pp 89-101.

 

 

 

139

140

Casey, T. M. (1976). Activity patterns, body temperature,
and thermal ecology in two desert catepillars
(Lepidoptera: Sphingindae). Ecology, 51:485-97.

Chapman, P. J. and G. A. Catlin (1976). Growth stages in
fruit trees -— from dormant to fruit set. New York's
Food and Life Sciences Bull. No. 58. New York
Agricultural Experiment Station, Geneva, New York.

Charnes, A. and W. W. Cooper (1959). Chance constrained
programming. Management Science, §:73-9.

Charnes, A. gt gt. (1965). Chance Constrained Programming
and Related Approaches tg Cost-effectiveness. Manage-
ment Science Research Report No. 39. Carnegie Institute
of Technology, Pittsburgh.

 

 

Cochran, W. G. and G. M. Cox (1957). Experimental Designs.
John Wiley and Sons, Inc., New York.

Croft, B. A. (1975). Integrated control of apple mites.
Cooperative Extension Service Bull. E-825. Michigan
State University, East Lansing.

Croft, B. A. gt gt. (1976). A computer-based extension pest
management delivery system. Environmental Entomology,
5:20-34.

(1976b). Dispersion statistics and sample size
estimates for the mite species Panonychus ulmi (Koch)
and Amblyseius fallacis. Environmental Entomology,
5:227-34.

 

(1976c). Modeling and management of two prototype
apple pest subsystems. In: Modeling for Pest Manage-
ment: Concepts, Techniques, and Applications. R. L.
Tummala gt gt., eds. Michigan State University,

East Lansing.

 

 

Drake, D. C. and R. K. Chapman (1965). Migration of the
six-spotted leafhopper, Macrosteles fascifrons (Stal).
University of Wisconsin Research Bull. 621.

Elliott, J. M. (1971). Some methods for the statistical
analysis of benthic invertabrates. Freshwater Bio.
Assoc. Sci. Pub. 25.

Feller, W. (1968). An Introduction tg Probability Theory
and Its ApplicaEIons, Vols. 1,2. John Wiley and Sons,
Inc., New York.

 

 

Fulton, W. C. and D. L. Haynes (1975). Computer mapping in
pest management. Environmental Entomology, 3:357-60.

141

(in press). The use of regression equations to
increase the usefulness of historical temperature
data in on-line pest management. Environmental
Entomology. ’

Fye, R. E. gt gt. (1969). Modification of temperature by
four types of insect cages. Journal of Economic
Entomology, g3:1019-23.

Gage, S. H. and D. L. Haynes (1975). Emergence under
natural and manipulated conditions of Tetrastichus
julis, an introduced larval parasite of the cereal
leaf beetle, with reference to regional pest manage-
ment. Environmental Entomology, 4:425-34.

 

Gates, C. E. and F. G. Ethridge (1972). A generalized set
of discrete frequency distributions with FORTRAN program.
Journal of the International Association of Mathematical
Geology, 3:1-24.

Geier, P. W. (1966). Management of insect pests. Annual
Review of Entomology, t1:471-90.

Hall, D. C. and R. B. Norgaard (1973). On the timing and
application of pesticides. American Journal of
Agricultural Economics, 55:198-201.

Harcourt, D. G. (1970). Crop life tables as a pest manage-
ment tool. Canadian Entomologist, 102:950-5. _

Haynes, D. L. gt gt (1973). Environmental monitoring net-
works for pest management systems. Environmental
Entomology, 3:889-99.

Haynes, D. L. and R. L. Tummala (1976). Development and use
of predictive models in the management of cereal leaf
beetle populations. In: Modeling for Pest Management:
Concepts, Techniques, and Applications. R. L. Tummala
gt gt., eds. Michigan State University, East Lansing.

 

 

 

Headley, J. C. (1972). Defining the economic threshold.
In: Pest Control Strategies for the Future. National
Academy of Science, pp 100-8.

 

(1975). The economics of pest management. In:
Introduction tg Insect Pest Management. R. L. Metcalf
and W. Luckmann, eds. John Wiley and Sons, Inc.,

New York. ‘

 

 

Hines, C. A. (1976). Michigan agricultural statistics for
1976. Michigan Crop Reporting Service, Michigan
Department of Agriculture, Lansing.

142

Hopp, R. J. gt gt. (1972). Regional phenological studies
with Persian lilac (Syringa persica). New York's
Food and Life Science Bull. No. 17. New York
Agricultural Experiment Station, Geneva, New York.

 

Hoyt, S. C. and E. C. Burts (1974). In: The Principles,
Stratggies, and Tactics gt Pest Population Regulation
and Control tg Major Crgp Ecosystems, Vol 2, p 845.
C. B. Huffaker, ed. University of California, Riverside.

 

 

 

 

 

Huff, F. H. (1963). Relation between leafhopper influxes
and synoptic weather conditions. Journal of Applied
Meteorology, 3:39-43.

Hull, L. A. gt gt (1976). Distribution of Stethorus
punctum in relation to densities of the European red
mite. Environmental Entomology, 2:337-42.

 

Jones, A. L. (1976). Systems for predicting development of
plant pathogens in the apple orchard. In: Modeling
for Pest Management: Concepts, Techniques, and
Applications. R. L. Tummala gt gt., eds. Michigan
State University, East Lansing.

 

 

 

 

Kirk, R. E. (1968). Experimental Design: Procedures for
the Behavioral Sciences. Brooks/Cole Publishifig Co.,
Belmont, California.

 

 

 

Klein gt gt. (1968). An integrated monitoring system for
water quality management in the Ohio Valley.
Environmental Science and Technology, t:764-71.

Krause, R. A. gt gt. (1975). BLITECAST: a computerized
forecast of potato late blight. Plant Disease
Reporter, gg:95-8.

Kuhn, T. S. (1970). The Structure of Scientific Revolutions.
University of Chicago Press, Chicago.

 

 

Luckmann, W. H. and R. L. Metcalf (1975). The pest-manage-
ment concept. ‘In: Introduction tg Insect Pest Manage-
ment. R. L. Metcalf and W. H. Luckmann, eds. John
Wiley and Sons, Inc., New York.

 

 

Manetsch, T. J. and G. L. Park (1974). System Analysis and
Simulation with Application tg Economic and Social Systems.
Michigan State University, East Lansing.

 

 

 

 

Mardia, K. V. (1972). Statistics gt Directional Data.
Academic Press, London.

 

 

Marino, M. L. (1972). An accessibility study of the northwest
region of Michigan's lower penninsula. An in-house study
prepared for the Michigan Department of State Highways
and Transportation, Lansing.

143

Markowitz, H. (1952). Portfolio selection. Journal of
Finance, 1:77-91.

Mills, W. D. (1944). Efficient use of sulfur dusts and
sprays during rain to control apple scab. Cornell
University Extension Bull. 630:1-4.

Mills, W. D. and A. A. LaPlante (1951). Diseases and insects
in the orchard. Cornell University Extension Bull.
711:21-27.

Morgan, C. V. G. gt gt. (1955). Methods for estimating
orchard mite populations, especially with the mite
brushing machine. Canadian Entomologist, 87:189-200.

Mowery, P. D. gt gt. (1975). Computer simulation for predict-
ing the number of Stethorus punctum needed to control
the European red mite in Pennsylvania apple trees.
Journal of Economic Entomology, t§:250-4.

 

National Academy of Science (1968). Principles gt Plant
and Animal Pest Control, Vol. 3. Publication 1695 of
the National Academy of Sciences, Washington, D. C.

 

 

Nicholson, W. (1972). Microeconomic Theory: Basic Principles

 

 

and Extensions. Dryden Press, Inc., Hinsdale, Illinois.

 

Park, W. R. (1973). Cost Engineerinngnalysis: g Guide tg
the Economic Evaluation gt Engineering Projects.
John Wiley and Sons, Inc., New York.

 

 

 

Pielou, E. C. (1974). Population and Community Ecology:
Principles and Methods. Gordon and Breach Science
Publishers, New York.

 

 

Riedl, H. (1977). Diapause and its effect on seasonal
variability of codling moth (Lepidoptera: Tortricidae)
phenology in North America. Canadian Entomologist
(in press).

Savage, L. J. (1954). The Foundations gt Statistics. John
Wiley and Sons, Inc., New York.

 

 

(1962). Subjective probability and statistical
practice. In: The Foundations gt Statistical
Inference: A Discussion. Methuen and Co., Ltd.,

 

 

 

 

Scanlan, B. K. (1974). Management 18: A Short Course for

Managers. John Wiley and Sons, Inci, New York.

 

 

Scott, R. H. (1973). The Pricing System. Holden-Day, Inc.,
San Francisco.

 

144

Sen, A. R. (1971). Sampling techniques for estimation of
mite incidence in the field with special reference to
the tea crop. In: International Symposium gg Statisti—
cal Ecology gt New Haven, 1969. Patil et gt., eds.
Pennsylvania State University Press, UniVersity Park.

 

 

 

Shackle, G. L. S. (1949). Expectations tg Economics.
Cambridge University Press, Cambridge, England.

 

 

(1961). Decision, Order, and Time tg Human Affairs.
Cambridge University Press, Cambridge, England.

 

 

Shoemaker, C. (1973a). Optimization of agricultural pest
management I: biological and mathematical background.
Mathematical Biosciences, tt:143-75.

(1973b). Optimization of agricultural pest manage-
ment II: formulation of a control model. Mathematical
Biosciences, t1:357-65.

(1973c). Optimization of agricultural pest manage—
ment III: results and eXtensions of a model. Mathemat-
ical Biosciences, t§:l-22. '

Shotwell, R. L. (1935). Method for making a grasshopper
survey. Journal of Economic Entomology, t§:486—91.

Stern, V. M. gt gt. (1959). The integrated control concept.
Hilgardia, 32:81-101.

(1973). Economic thresholds. Annual Review of
Entomology, t§:259-80.

Thompson, W. W. (1973). Michigan apple pest management
second annual report. Cooperative Extension Service,
Michigan State University, East Lansing.

Tummala, R. L. (1976). Concept of on—line pest management.
In: Modeling for Pest Management: Concepts, Techniques,
and Applications. R. L. Tummala gt gt., eds. Michigan
State University, East Lansing.

 

 

Wagner, H. M. (1975). Principles gt Operations Research with
Applications tg Managerial Decisions. Prentice-Hall,
Inc., Englewood Cliffs, New Jersey.

 

 

 

 

Ward gt gt. (1963). Bayesian statistical inference for
psychological research. Psychological Review, 19:193-242.

Welch, S. M. (unpub.). A preliminary developmental model
for Panonychus ulmi (Koch).

 

(1976). Integrated pest management -- mobile message
center speeds data to grower. In: Special Projects
Report. Michigan State University Cooperative Extension

145
Bull. EA-l. Michigan State University, East Lansing.
Welch, S. M. and M. L. Marino (unpub.). Biological

Monitoring of Panonychus ulmi and Amblyseius fallacis
in Michigan apple orchards: a simulation study.

 

 

Welch, S. M. gt gt. (in prep.). An extension-oriented
phenological modeling system applicable to a broad
spectrum of species.

Young, T. Y. and T. W. Calvert (1974). Classification,
Estimation, and Pattern Recognition. American Elsevier
Publishing Co., Inc., New York.

 

 

 

"Iilllllllllilllllllllllll“