Structure and Function in Agroecosystem Design and Management - Chapter 4 pot

Certainly, models of weed infestation, population growth, andcontrol have served as a valuable framework for organizing biological infor-mation on weeds and for developing weed control s

CHAPTER 4

Ecological Management of Crop-Weed Interactions Chris Doyle, Neil McRoberts, Ralph Kirkwood, and George Marshall

CONTENTS

Introduction 62

Ecological Consequences of Modern Weed Control Systems 63

Weeds in the Ecosystem 63

Weed Adaptation to Management Practices 64

In Search of New Approaches to Weed Management 64

The Role of Mathematical Models in Predicting Weed Population Dynamics 65

Spatial and Temporal Dynamics of Weed Populations 66

The Dynamics of Weed Invasion and Spread 66

Predicting Weed Invasion 67

Seed Dispersal 68

The Dynamics of Weed Population Density 69

Optimum Weed Management 73

Extrinsic Factors Affecting Weed Populations 73

Weed Control Decision Thresholds 74

Timing of Control 76

Optimal Weed Management 77

Integrated Weed Management 77

Required Advances in Modeling Weed-Crop Interactions 78

Biological Control of Weeds 79

Weed Adaptation to Management Practices 80

Adaptation to a Single Control Measure 81

Adaptation to Integrated Weed Management Systems 83

61 0-8493-0904-2/01/$0.00+$.50

Conclusions 84References 85

INTRODUCTION

In recent years, two very different approaches to controlling weeds havedeveloped On the one hand, there has been the introduction of herbicide-tolerant crops in North America with their specific reliance upon herbicides.Clearly, however, the widespread application of such techniques will alterthe dynamic equilibrium which normally exists in vegetation Thus, a keyresearch issue must be the long-term ecological consequences of the regularuse of nonselective herbicides on the community structure of seminaturalvegetation (Willis, 1990) In direct contrast, in response to both public andindustry concerns, there has been the development of sustainable systems ofcrop production, in which the emphasis has been on minimizing herbicideuse Instead, a mixture of biological, chemical, and mechanical methods arecombined to control weeds, pests, and diseases to provide stable long-termprotection to the crop (Lockhart et al., 1990; Swanton and Weise, 1991;Gressel, 1992; Wyse, 1994; Holt, 1994; Viaux and Rieu, 1995) Fundamental tothis latter approach is a sound understanding of weed demography and ofthe efficacy and impact of different control methods Although the twoapproaches represent very different strategies to weed control, both require

an understanding of the population biology of weeds, including ary aspects (Jordan and Jannink, 1997), and the dynamics of weed popula-tions Accordingly, this chapter summarizes current understanding on thesematters, including the effects of crop rotation, tillage systems, and herbicideuse on weed communities

evolution-However, one of the most striking developments in regard to researchinto improved management systems, with reduced dependency on herbi-cides, has been a move towards systems type investigations Thus, Kropff et

al (1996) have stressed that the complexity of the population dynamics ofweeds and of the crop-weed interactions necessitates the use of mathemati-cal models Certainly, models of weed infestation, population growth, andcontrol have served as a valuable framework for organizing biological infor-mation on weeds and for developing weed control strategies (Mortimer et al.,1980; Doyle, 1991; Colbach and Debaeke, 1998) In particular, they havehelped to identify information gaps, set research priorities, and suggest con-trol strategies (Maxwell et al., 1988) Furthermore, their value has arguablyextended beyond being simply useful research tools Several key questions inweed control cannot be answered using conventional field trials because ofthe constraints of cost, time, or complexity (Doyle 1989; 1997) As such, mod-els have come to serve as experimental test beds Accordingly, this chapterwill deliberately treat the ecological management of crop-weed interactionsfrom a modeling and systems perspective

ECOLOGICAL CONSEQUENCES OF MODERN WEED

CONTROL SYSTEMS Weeds in the Ecosystem

Any ecosystem, made up as it is of an integrated community of theorganisms present and their controlling environment, evolves over time into

a relatively stable community Interactions at the physical, chemical, and logical levels lead to the establishment of dynamic interrelationships amongthe species within the community and a degree of stability (Willis, 1990).However, most crop production systems directly aim to produce monocul-tures, as in arable crops, or simple mixtures of species, as in grass leys, inorder to maximize crop yield or economic profitability This means disturb-ing the “natural” vegetation of an area, either by introducing new species orselecting out specific species at the expense of others Weed control strategiesare concerned with controlling the unwanted species—a weed being defined

bio-as “a plant growing where it is not wanted” (Buchholtz, 1967; Roberts et al.,1982) Thus, the ingress of weeds into an area used for cropping is intrinsi-cally an adjustment towards a more natural plant community

Historically, weed control measures have been pursued to minimize thedamage done by weeds to crop yields and quality Weed control practices havetypically involved a combination of periodic habitat disturbance through cul-tivation and crop rotation and more recently the widespread use of herbicides

On an ecological level, these practices have acted as a very powerful force

in the interspecific selection of weed flora through the mechanisms of adaptation, evolution, and alien immigration (Mortimer, 1990) Plant species

pre-may be pre-adapted in the sense that they are resident in a natural plant

com-munity within dispersal distance of a crop and come to predominate within thecrop as a consequence of a change in management practices The successfulinvasion of a crop by a species from the natural habitat, therefore, depends on

a match of the life history characteristics of the weed to the habitat provided bythe cropping system As such, the combination of management practices andthe pattern of crop development through time results in interspecific selection,leading to particular species becoming “weeds” (Cousens and Mortimer, 1995).However, management practices may give rise to interspecific selection as aresult of evolutionary processes Where agricultural practices are continuedfor a sufficient length of time and sufficient genetic variation occurs within aspecies, locally adapted races of weeds are likely to arise (Mortimer, 1990).Finally, where intensive agriculture is practiced, it is common for species notendemic to the area to be present as weeds While additional species are con-tinually being introduced into agricultural environments, both inadvertently

by industry and consciously by seed firms, few alien species succeed in lishing themselves as damaging weeds However, as with pre-adaptation,changes in land management practices are often a critical ingredient, as wit-

estab-nessed by the spread of Rhododendron ponticum in the U.K (Mortimer, 1990).

Weed Adaptation to Management Practices

The ability of weeds to adapt to changes in management practices is tainly one explanation for the persistent nature of crop yield losses to weeds,despite technological advances (Ghersa et al., 1994; Cousens and Mortimer,1995) Thus, observations by Fryer and Chancellor (1970) suggested that thecontinued and widespread use of herbicides had markedly altered the com-position of grassland weeds, but it was doubtful that it had led to the eradi-cation of any weed species In a specific experiment to examine the effects ofseveral herbicides on species composition over a 5-year period, Mahn andHelmecke (1979) noted that, while the different herbicide treatments changedthe density and dominance of individual weeds, there was no change in thespecies present in the community Likewise, in a much longer trial involvingherbicides on wheat, run over more than thirty years, Hume (1987) observedthat no weeds were eliminated and no new species were able to invade thecommunity The only changes in community structure were changes in therelative abundance of species Thus, fundamental to successful control ofweeds is an ability to predict the evolutionary dynamics of weed popula-tions, as shaped by human and natural factors (Jordan and Jannink, 1997).However, to make such predictions, a better understanding of the traits,and especially the variation of those traits, that confer adaptation to weedmanagement practices is needed (Hartl and Clark, 1989) Focusing on theevolutionary dynamics and mechanisms will allow questions of practical sig-nificance in regard to ongoing weed adaptation to be addressed (Jordan andJannink, 1997) These include the speed with which weed adaptation canerode the efficacy of non-chemical control methods Insofar as weed adapta-tion proceeds at a pace that negates technological advances in control, thenfuture research may need to concentrate on ways of impeding adaptation,raising the issue of whether it is possible to design management systems thatinhibit weed evolution

cer-In Search of New Approaches to Weed Management

It is clear from the preceding discussion that, despite the high level ofcrop management and the array of options at the disposal of farmers, weedscontinue to be a major problem As Cousens and Mortimer (1995) noted,some grass weeds have become increasing problems in cereal crops, requir-ing new herbicides or major changes in cropping to ensure continued pro-ductivity Herbicide resistance is also on the increase As a result, it is widelyaccepted that programs in which weed control is almost exclusively achieved

by herbicides can be very unstable (Swanton and Weise, 1991; Gressel, 1992;Zimdahl, 1993; Wyse, 1994; Shaw 1996) This acknowledgment, coupled withincreasing public concern about the levels of chemicals being used and theirpotential environmental effects, has led to a renewed emphasis on long-term

weed management and the integration of a range of environmentally safeand socially acceptable control tactics (Thill et al., 1991) Consequently, thefocus of much recent weed research has become the study of how crop yieldsand weed interference are affected by changes in cropping management,including tillage methods, the timing and rates of herbicides, cover crops,and planting patterns (Swanton and Murphy, 1996) However, the efficacy of

what has become termed integrated weed management (Thill et al., 1991; Elmore

1996) clearly depends on a thorough understanding of the populationdynamics of weed communities and their constituent populations In partic-ular, it requires an understanding of

• the factors that determine the rates at which weeds spread;

• the rates at which they increase when they reach a given location;

• the maximum extent to which they will increase; and

• the ways in which the spatial spread and abundance of weeds can

be minimized and reduced (Doyle, 1991; Cousens and Mortimer,1995)

For this reason, it has become fashionable to talk of the need to employ asystems approach to the study of weed control (Müller-Schärer and Frantzen,1996; Swanton and Murphy, 1996) The problem, as a number of researchers(Cousens and Mortimer, 1995; Swanton and Murphy, 1996; Jordan andJannink, 1997) have pointed out, is that research into integrated weed man-agement (IWM) has not progressed beyond description However, to be ofpractical use, IWM must move from a descriptive to a predictive phase AsCousens and Mortimer (1995) have underlined, most studies of weed popu-lation dynamics are capable only of providing information on the outcomes

of management changes, but not on the processes involved Equally, fewstudies on integrated weed management have as their specific aim finding asolution to specific weed management problems Finally, the emphasis ofmuch work on natural communities is the prediction of long-term changes.However, Cousens and Mortimer (1995) argue that, not only is predictinglong-term behavior of natural systems difficult, but it is also not what thefarmers are interested in They are concerned with the short- to medium-termconsequences of their management actions and with plant communities thatmay be in a state of unstable equilibrium Given this, it is interesting to askthe quality of our current ability to predict changes in weed populations

The Role of Mathematical Models in Predicting Weed Population Dynamics

Linking management changes to models of crop-weed interactions,which include such issues as weed population dynamics and the ecophysicalbasis of competition, permits the prediction of future weed problems and

their solutions, together with the economic risks and benefits involved(Doyle, 1991; Doyle, 1997) Accordingly, the following discussion focuses on

the ability of mathematical models to predict the changes in weed populations

and the consequences of changes in weed management The first part siders the contribution of quantitative models to the understanding of thespatial and temporal dynamics of weed populations Central to this is anappreciation of the types of factors driving population change At any givenpoint in time, the state of a given weed population can be defined in terms ofits spatial limits, its total size, its density, and its composition From themoment that environmental and management changes occur, alterations inthe state of the population will occur; it is the dynamics of these changeswhich are of interest

con-Nevertheless, comprehending the changes in the spatial distribution andabundance of weeds is only one element of weed management It is necessary

to understand how different management practices influence the size andspread of weed populations Accordingly, the second part of the chapterlooks at the various attempts to use biological and ecophysical models toexplore the efficacy of integrated weed management systems However, inso-far as weeds adapt to management conditions, there is also a need to predictweed evolution (Jordan and Jannink, 1997) Thus, the third and final part ofthe chapter considers our ability to predict the speed with which weeds canadapt to control measures and whether management systems can bedesigned which impede weed evolution

SPATIAL AND TEMPORAL DYNAMICS OF WEED

POPULATIONS The Dynamics of Weed Invasion and Spread

As in medicine, prevention rather than cure is likely to be the most effective strategy, so understanding how and why weeds invade a given areaand being able to predict the pattern of spread is fundamental to control(Doyle, 1991) However, only very recently has any attention been paid topredicting the process of weed invasion As late as the middle of the 1980s,Mack (1985) reported that there were no mathematical models simulating thespread of weeds Part of the reason for this lack of models was that spatialprocesses were given very limited consideration in weed management mod-els, which were almost exclusively concerned with the temporal dynamics ofweeds However, in the last decade there has been an increased interest inunderstanding the processes involved in the spread of weeds at both thenational and regional level and within fields The former has been driven by

cost-a concern to limit the geogrcost-aphic sprecost-ad of unwcost-anted plcost-ant species, while thelatter gained impetus from the pressure to reduce herbicide usage andincrease the efficacy of any chemical control

Predicting Weed Invasion

The simplest model to simulate the geographic spread of weeds isobtained by assuming that a species spreads outwards along a front at a con-

stant rate in all directions If the distance advanced each year is r, and suming that the spread starts from a single focus, the area A occupied after t

1980) For any given site, the level of weed infestation in year t(P t) was sumed to increase according to the exponential model:

where P 0 is the initial weed population at the site, c is the proportionate rate

of growth, as given in Equation 4.3, and s is the proportion dispersed away

from the site The model was subsequently used (1) to simulate the possible

spread of serrated tussock (Nasella trichotoma) in southeast Australia (Auld

and Coote, 1981); (2) to gauge the potential costs of an effective regional trol policy (Auld, Vere and Coote, 1982); and (3) to compare the costs of dif-ferent strategies for controlling the spread of a localised weed population(Menz et al., 1980)

con-Implicit in such a model is the assumption that weed seed is distributedequally in all directions, so the spread may be described by a series of con-centric circles However, likening the spread of weeds to the ripples from astone dropped in water involves considerable simplification of reality (Mack,1985) In practice, environmental heterogeneity and spatial irregularity arelikely to result in an uneven spread (Plumber and Keever, 1963; Rapoport,1982) Random processes may also influence the observed pattern of weeddiffusion, as Skellam (1951) noted in a seminal study, which modelled theareal spread of a plant population using random-walk techniques As a con-sequence, more recent research has focussed on identifying areas potentiallysuitable for the growth of particular weed species The earliest of these

studies, by Medd and Smith (1978), involved the development of a simplemodel to predict the growth, phenological development, and seed yield of

musk thistle (Carduus nutans) from climatic data Using the model, they were

able to determine areas within Australia that were suitable for the growthand development of the weed, including uninfested regions More recently,Panetta and Mitchell (1991) have used a computer program to analyze the climatic factors at locations where particular weed species occur in Australia

in order to describe the climatic profiles of the species and to examine thepossibility of the invasion of New Zealand by these species Others, such asPatterson et al (1979), Williams and Groves (1980), and Patterson (1990) haveused experiments under controlled environment conditions to infer the limits to the spread of particular weed species The problem with all thesemodels that use climatic data to predict spread from present occurrences isthat there is no guarantee that climate is the limiting factor (Cousens andMortimer, 1995)

However, the recent advent of geographic information systems (GIS) hasallowed the spatial distribution of weeds to be mapped against a wider range

of limiting factors, including soils, management techniques, competitorspecies, and climatic variables As a consequence, it is possible to derive amore complex picture of the environmental and ecological determinants thatfavor the growth of a particular species Such techniques have been used byPrather and Callihan (1993) to study the efficacy of eradication programs and by Wilson et al (1993) to predict the environmental consequences ofweed control Nevertheless, even these models do not strictly predictwhether a particular area will be invaded by a given weed species but rather

if it is possible

Seed Dispersal

Although the spatial diffusion models discussed may describe the spread

of weeds, they are essentially descriptive models, in that they do not reallyexplain the mechanism through which dispersal occurs As Cousens andMortimer (1995) outline, the mechanisms are complex, including dispersal bywind, animals, water, and tillage operations, as well as vegetative spread.However, quantitative studies of weed dispersal have been few and mostmodeling work has focussed on wind dispersal Thus, Smith and Kok (1984)studied the factors responsible for the direction and distance over which the

seed of Carduus nutans was spread from a single point source They found

that local seed dispersal was a function of wind velocity and the degree ofturbulence Specifically, the observed seed dispersal could be described by a

Gaussian plume model, in which the concentration of seeds (C) at a point (x,y,z) in three-dimensional space at a relative time (T) is given by

C(x,y,z,T)T

Q(t)C0(x,y,z,t)dt (4.5)

where C 0 denotes the rate at which seeds pass through the point x,y,z at time

t, Q(t) is the rate at which seed is released and T is the cumulative time since

the initial release of seed

However, the Gaussian dispersal model was originally constructed todescribe movements of molecules in a gas cloud and so implicitly assumesthat particles will continue to disperse indefinitely With heavy particles,such as seeds, this is evidently not true Thus, Johnson et al (1981) used a dif-

ferent approach to predicting the distance (d) over which weed seeds would

disperse, assuming a steady wind and no turbulence:

where H is the release height, U is the wind speed and V sis the terminalvelocity of the propagule However, while the model describes in some detailthe mechanisms by which seed is spread, in the absence of a population com-ponent, it is difficult to see how it can be extended to study problems of weedinvasion on a field or regional scale

A model that does combine mechanistic modeling of seed dispersal withthe life-cycle dynamics of a weed population was developed by Ballaré et al.(1987) In their work, they simulated the population dynamics and spread of

Datura ferox in a soybean crop Apart from a series of simple mathematical

expressions describing the life cycle of the weed, the model also included aspecific weed-dispersal algorithm, in which the spatial dispersion of theweed over time was a function of both the dispersal characteristics of thespecies and the type and direction of the combine harvester The result is adispersion pattern in which the seed is principally spread in the direction ofthe combine moves

One weakness of these models of seed dispersal is that they describe thelikelihood of weed invasion solely in terms of proximity to an existing area ofinfestation While this may explain most of the observed spatial heterogene-ity in weed incidence in arable crops, for perennial crops, such as forages,past management practices and weather conditions may be just as important

in influencing the spatial configuration In other words, the likelihood ofinvasion may be as much a function of the susceptibility of the area to inva-sion as it is to the proximity of the weed source

The Dynamics of Weed Population Density

Given the presence of an infestation, using knowledge of the temporaldynamics of weed populations, it should be possible to predict how fast theweed population will grow in the absence of controls Because of the com-plexity of the problem and the long-term character of weeds, as early as 1980Mortimer et al (1980) were advocating the use of simple mathematical mod-els of the life cycle of weeds to predict population densities The current state

Mature flowering plants

Seed shed

Seed bank

Emergent seedlings Viable

seedlings

Predation Mortality

Seed rate

Germination rate

Survival rate Flowering

rate

Figure 4.1 Diagrammatic representation of a typical weed life-cycle model.

(Reprinted from Crop Protection, 10, Doyle, C.J., Mathematical Models

in Weed Management, 432 –446 Copyright 1991, with permission of Elsevier Science.)

of the attempts to model life-cycle processes has been described in Doyle(1991), Cousens and Mortimer (1995), and Kropff et al (1996) In general,comprehensive models based on physiological principles are only availablefor parts of the life-cycle, such as plant growth, competition (Kropff and VanLaar, 1993), germination, and emergence (Vleeshouwers and Bouwmeester,1993) Instead, most models encompassing the whole life cycle have repre-sented it in terms of a series of growth stages, as diagrammatically repre-sented in Figure 4.1 The complex processes involved in the transition fromone stage to the next are then “blended into a few lumped parameters like agermination rate, a reproduction rate and a mortality rate” (Kropff et al.,

1996, p 7) Good examples of such models are Cousens et al (1986), Doyle et

al (1986), and Van der Weide and Van Groenendael (1990)

However, the detail in which the life-cycle processes in weeds are ied is only one issue More critically, there are various ways to extract thepopulation dynamics from the life-cycle processes, and these different waysmay lead to different results (Durrett and Levin, 1994; Kropff et al., 1996) Inparticular, three different approaches to modeling the integration of indi-vidual weed plants into a population have been adopted Kropff et al (1996)stylized these as (1) the density-based models, (2) the density-based modelsincorporating spatial processes, and (3) the individual-based modelsaccounting for spatial processes

stud-Of these, the most frequent modeling approach has been to assume thatthe key determinant of rates of population growth is the density of the weeds

From the current density, the rate of population growth is derived to give thenew density value From the middle 1970s, researchers such as Hassell (1975),Bellows (1981), and Law and Watkinson (1987) were modeling the dynamics

of single species over generations using nonlinear difference equations of thefollowing type:

where N t is the population size in period t, R is the asymptotic per capita increase in a population of uncrowded individuals, and a and b parameters describe the form and intensity of self-regulation At high densities b reflects

the extent to which a population compensates for a change in density Such amodel has been found to apply readily to plants with discrete generationsand no persistent seed bank However, such models can be expanded toincorporate a seed bank or to model species behaviour in mixtures (Mortimer

et al., 1989) Thus, the effect of introducing a second species into a ture is presumed to be a reduction in yield per unit area and the per capitarate of growth of the first species For a multispecies assemblage, comprising

monocul-three species, N 0 , N 1 , and N 2 , Equation 4.7 specifically becomes

where

density of plants is low However, an implicit assumption in this approach isthat each weed experiences a similar environment, so that it is impossible toincorporate the spatial dispersal of weeds (Kropff et al., 1996)

A rather obvious way of including the dispersal of weeds is to includespace in the model and allow for spatial gradients in density This has led tothe so-called reaction-diffusion models Versions of this type of model havebeen used to simulate the spread of weeds (Auld and Coote, 1980; Ballaré etal., 1987; Maxwell and Ghersa, 1992) The key variable still remains weeddensity, but it is now possible to look at spatial processes Thus, a recentmodel developed by González-Andujar and Perry (1995) has enabled theexamination of weed dynamics within patches over time, as well as permit-ting the testing of hypotheses about patch persistence and the extent of seeddispersal However, as Kropff et al (1996) have pointed out, over time thespatial gradients in these models either move or flatten out As a result, forany particular site, this approach to modelling weed density and dispersalrapidly reduces over time to modelling density alone

One step further is to abandon weed density as the basic variable in themodel and proceed with the configuration of weeds over space This is themodelling approach adopted by Antonovics and Levin (1980), Weiner (1982),Goldberg and Werner (1983), Barkham and Hance (1982), Pacala and Silander(1985), Silvertown et al (1992), and Wallinga (1995) Although a distinction

RN 0,t

0,t N 1,t 2,t)]

can be made between the individual-based models (e.g., Pacala and Silander,1985) and cellular automaton models (e.g., Silvertown et al., 1992), the under-lying principles can be understood by examining the work of Pacala andSilander (1985, 1987) The basic idea is that the performance of an individualplant or cell can be determined from the number, distance, and type of neigh-bors For each individual species, the population, dynamics is described interms of a series of sequential steps, comprising seed dispersal, germination,seedling survival, and seed production The novel aspect is that theseprocesses are formulated for single individuals, which germinate, grow, andyield seed that is dispersed into a defined area from which new individualsare established Essentially, the objective is to estimate a neighborhood areawithin which there is interference from neighbors on the target plant and out-side which the effects are negligible This estimation is achieved by deter-mining statistically the relationship between various biological processes,such as seed production, and the number of neighbors within a definedradius from the target plant By varying the radius, the appropriate neigh-bourhood size can be determined Knowing the radii together with the den-sity of species, estimates can be made of the number of neighbors and theconsequent impact on a given biological process, such as seed production perindividual plant, assuming the species are randomly distributed Allowingfor seed dispersal and germination, the level of infestation for the next yearcan be projected.

However, even though these models can readily accommodate multiplespecies, the application of models based on individuals and including spatialaspects is likely to be restricted As both van Groenendael (1988) and Kropff

et al (1996) have observed, they are very difficult to parameterize and putationally slow For this reason, there has been a resurgence of interest inthe simple density-based models Recently Mortimer et al (1996) extendedthe basic model given in Equation 4.8 to include spatial heterogeneity Thisinvolves treating weed populations as sets of sub-populations in a frag-mented landscape interconnected by dispersing propagules Accordingly,they added to the basic growth function a probability distribution functionthat describes the spread of propagules from each plant Assuming a field

com-comprising n patches, each with a certain level and composition of weeds, then the density of the weed population in patch x at time t is given by

N x,ty 1n P x,y f [N y,t1] (4.9)

where f [N y,t ] is the population growth function at patch y and P x,yis the

prob-ability that seed will disperse from patch y to patch x Although Mortimer et

al (1996) confined their analysis to a linear, single dimension habitat, it is atively easy to generalize to a two-dimensional habitat

rel-To parameterize this model, it is necessary to decide two key issues The

first is the form of the probability distribution function, P x,y Except where

seed dispersal is affected by cultivation (Ballaré et al., 1987), it is probably not

unrealistic to assume a weed plant disperses propagules symmetricallyaround each individual on a normal (Gaussian) distribution Where wind orcultivation leads to a skewed distribution, it can be represented by the use of

a generalized (or skewed normal) distribution The second issue concerns thechoice of growth function One possible functional form is Equation 4.8Streibig et al (1993) contended that this growth function was adequate forpredicting compositional change Certainly, using this function, Mortimer et

al (1996) were able to describe the spatial and temporal stability of weedpopulations

OPTIMUM WEED MANAGEMENT Extrinsic Factors Affecting Weed Populations

So far, attention has focused on the dynamics of weed populations under

a constant environment, where population changes are driven solely byintrinsic processes, such as intraspecific competition However, the environ-ment of a weed population is rarely constant, with factors such as manage-ment, weather conditions and interactions with other organisms varyingboth within and between generations As Cousens and Mortimer (1995) haveobserved, the relative importance of the different factors will vary with year,geographic location, and habitat However, insofar as weather and diseasefactors are unpredictable and uncontrollable, most attention has focused onhow crop management can affect weed populations By using this knowl-edge, hopefully better weed control strategies can be developed In particu-lar, an understanding of the effects of management practices on thecomposition and density of weed populations offers not only the prospect ofbeing able to predict the consequences of a particular management change,but also the ability to determine the most effective and economic method ofcontrolling a particular weed The development of management systemswith reduced dependency on herbicides has only shifted the emphasis stillfurther towards the management of weed populations through husbandrypractices (Kropff et al., 1996; Swanton and Murphy, 1996)

To achieve effective control of weeds requires the ability to answer threequestions:

1 What level of weed infestation justifies intervention?

2 At what stages during the weed life-cycle should interventionoccur?

3 How should the weeds be controlled?

As Doyle (1991; 1997) and Cousens and Mortimer (1995) have underlined, themost powerful technique at our disposal for answering such questions ismathematical modelling, coupled with experimental verification

Accordingly, this section reviews how far it has been possible to incorporateour knowledge of interactions between weeds and crop management intomodels so as to provide quantitative insights into effective and environmen-tally sustainable control techniques.

Weed Control Decision Thresholds

The prophylactic use of herbicides has come under increasing opposition

in the last decade and ways of reducing both the frequency and applicationrates of chemicals have been investigated (Jordan and Hutcheon, 1993;Turner, 1993; Elmore, 1996; Swanton and Murphy, 1996) Specifically, atten-tion has focused on the question of what level of weed infestation justifiesintervention, which has been widely approached using economic thresholdmodeling In itself, the concept is easily understood and can be summarized

as follows: as the weed population per unit area increases, the gain in cropyield from chemical control becomes greater than the cost of the control

measures The threshold density is where the cost of the control is equal to the

net benefit from control Provided that appropriate means for estimatingweed densities are available, then the theory is that the practical application

of the threshold concept will merely involve the farmer in judging whetherthe actual level of infestation exceeds the critical threshold density Examples

of such threshold models include Marra and Carlson (1983), Doyle et al.(1984), Cousens et al (1985), Cousens et al (1986), Auld and Tisdell (1987),Cousens (1987), Dent et al (1989), Moore et al (1989), Streibig (1989),Mortensen et al (1993), Swinton and King (1994), González-Andujar andPerry (1995), Buhler et al (1997), and Baziramahenga and Leroux (1998).However, threshold models have come under attack in recent years onfour counts (Doyle, 1997) First, they are dependent on experimental evi-dence regarding weed-crop competition In many instances, the experimentsare conducted at weed densities that are of limited relevance to the determi-nation of economic thresholds (Dent et al., 1989) Second, the vast majority ofthreshold models developed have assumed that the weeds are uniformly dis-tributed across the field However, many weed species exhibit a marked ten-dency to cluster, leaving large areas of a field relatively free of infestation.Compared with a field in which the weeds are uniformly distributed, theimpact on crop yield will be less and the consequent threshold density willtend to be higher (Dent et al., 1989; Brain and Cousens, 1990; Wiles et al., 1992;Johnson et al., 1995; Mortensen et al., 1995; Wallinga, 1995; Lindquist et al.,1998) To simulate the effect of patchy distributions of weeds, Brain andCousens (1990) developed a model incorporating a non-random distribution

of weeds Essentially, it assumed that a field could be divided into a grid of

1 m2subplots While within each plot the weeds were considered to be domly spread, the number of weeds per subplot were described by a negative

ran-binomial distribution, which has been found to fit most weed seedling countdata (Johnson et al., 1995) The proportion of subplots containing weeds was

then a function of the mean weed density over the entire field (D) and the degree of clumping (k) Assuming that for each subplot the effect of weed

density on crop yields could be represented by a hyperbolic function, then the

proportionate crop yield loss (Y L) is represented by

Y L1 0

Dz1/ k  D k(1 z)k 1

where α and β are estimated parameters, and z is a variable lying between 0 and 1 Lindquist et al (1998) showed that where the mean weed density (D) and the clumping factor (k) were known, an accurate estimate of field-scale

crop yield losses could be obtained

The third criticism of threshold models is linked to the existence ofuncertainty (Auld and Tisdell, 1987) In weed control, there are three prin-cipal sources of uncertainty that may modify the perceived optimal thresh-old density for spraying: (1) the potential weed density; (2) the form of croploss function; and (3) the form of the herbicide dose-response function Amajor factor in deciding whether to use a herbicide is the size of the weedpopulation Where a pre-emergent herbicide is to be used, then there must beuncertainty about this Second, although the general form of the croploss function may be known, its precise shape varies with location and agro-nomic factors (Reader, 1985; Cousens et al., 1988) Thus, the economic thresh-old for spraying will vary accordingly Finally, the efficacy of a givenherbicide in controlling a weed infestation is sensitive to site and manage-ment practices (Zimdahl, 1993) Not only do these factors mean that the eco-nomic threshold density for a weed is subject to uncertainties, but the veryexistence of uncertainty is known to modify grower behavior (Doyle, 1987;Auld and Tisdell, 1987; Pannell, 1990) If farmers are risk averse, then they aremore likely to use herbicides in a prophylactic way and to apply them annu-ally as a security against weed invasion (Cousens and Mortimer, 1995) Theconsequence of all this is that specific weed threshold densities become lessrelevant

The final major conceptual problem with threshold models is that, inpractice, treating the damaging external effects of herbicides as a cost is notreally workable Apart from the problem of whether environmental damage,such as loss of plant and species diversity, can be measured in economicterms, the resultant threshold densities may be unacceptable Basically, theeffect of increasing the overall costs of applying chemical control is toincrease the threshold weed density at which significant crop losses occurand which the grower would not be prepared to tolerate Thus, in the absence

of alternative means of controlling weeds, the credibility of the predictedthresholds is subject to attack

Timing of Control

More recently, interest in the threshold level at which weed control is tified has been replaced by consideration of when to apply the control meas-ures during the life cycle of the weed Although this has become integrallybound up with moves towards non-chemical methods of control, the interestpredates the current focus on integrated weed management In particular,attention has focused on the relative efficacy of killing weed seeds rather thancontrolling weed plants once they have emerged In the early 1980s, Cussansand Moss (1982) used an exponential multi-stage model of the annual grass

jus-Alopecurus myosuroides to investigate the benefits of different cultivation

tech-niques to influence seed germination The model was subsequently extended

to include density-dependent plant mortality and seed production (Cousensand Moss, 1990) Medd and Ridings (1989) similarly investigated the relativemerits of seed versus plant kill using a three-cohort model of the life cycle of

wild oats Avena fatua They were able to show that if relatively small

improve-ments in seed kill could be achieved, in conjunction with herbicides, cant improvements in the rate of decline of weed populations could beobtained Finally, Pandey and Medd (1990) combined the technique of

signifi-dynamic programming with a population model of Avena species to examine

the efficacy of controlling weed seeds

The conclusions about the importance of weed seed kill reflect more eral evidence from plant competition studies that the period between cropand weed emergence is a critical factor which contributes to reductions incrop yields Accurate information on dates of weed emergence has been espe-cially important in determining potential crop yield losses However, thepractical difficulty is obtaining the daily information required (Kropff, 1988)for models able to predict weed seedling emergence to be of practical benefit(Forcella, 1993) Specifically, González-Andujar and Fernandez-Quintanilla

gen-(1991) developed a population model of Avena sterilis, in which there were

two quite distinct periods of seedling emergence Using the model, they wereable to show that two of the most critical factors influencing weed populationlevels were the dispersal and mortality of seeds during the summer and thefecundity of the first cohort of seedlings to emerge Thus, they were able to

pinpoint the critical stages in the life cycle of A sterilis as far as achieving

effective control was concerned Elsewhere Grundy et al (1996) and Prostko

et al (1997) have focused on the influence of the distribution of weed seedswithin the soil profile on seedling emergence While Prostko et al (1997) usedFermi-Dirac distribution functions to model weed emergence as influenced

by depth of weed seed burial, Grundy et al (1996) used a simulation modelwith several soil layers The significance of these “seed burial” models is that,

by combining them with models that determine the effects of cultivation onseed distribution, it should be possible to improve the predictions of seedlingemergence from the seed bank

Optimal Weed Management

Integrated Weed Management

A logical extension of the investigations into the most critical and tive stages in the life cycle of weeds for controlling them is the optimalmethod of control Thus, many of the studies concerned with examining therelative efficacy of weed seed and plant killing investigated the merits ofchemical and non-chemical methods of control In a review covering 1984 to

effec-1996, Colbach and Debaeke (1998) found no less than twenty-six weeddemography models, which incorporated some cropping system effects Themajority considered soil tillage and herbicide applications, but under 20%considered other cultivation techniques, such as crop cultivar, sowing date,sowing density, harvesting, or stubble burning Few, if any, explicitly inte-grated the effects of crop management Thus, in most models, a constantseedling mortality rate is associated with a set of weed control methods Forchemical methods of control, the rate is typically determined by dosage andactive ingredients, and for mechanical control it is determined by timing oftillage operations However, as Debaeke and Sebillote (1988) observed, inter-action between cultivation methods and weather conditions is frequentlycritical in determining mortality rates Likewise, the process of weed seeddispersal is never considered, yet wind-borne seed from outside the field canplay a significant role in determining levels of weed infestation Finally,although some demographic models of weeds include consideration of thepatchy distribution of weed species, none of the models considering theeffects of cultivation practices, researched by Colbach and Debaeke (1998),assumed anything but a uniform distribution of weeds

The significance of this is that public concern about the environmentalcosts of continued reliance on chemical methods of weed control has led tothe search for more sustainable practices that rely on a reduced use of allinputs as a means of safeguarding natural resources and minimizing the neg-ative impacts on the environment This research has given birth to the con-

cept of integrated weed management, in which attention is focused on how

changes in crop management practices, such as tillage methods, planting terns, and the use of cover crops, can minimize the need for herbicides (Burn,1987; Elmore, 1996; Swanton and Murphy, 1996) Certainly, through the use

pat-of mathematical models, (Cussans and Moss, 1982; Wilson et al., 1984; Meddand Ridings, 1989; Cousens and Moss, 1990; Pandey and Medd, 1996), it hasbeen shown that combining weed seed kill through cultivation practices with

a reduced herbicide application can be more cost effective than relying solely

on killing weed plants by chemical means However, as the review byColbach and Debaeke (1998) revealed, weed population models must beimproved in three key areas if they are to make a tangible contribution to theevaluation and management of cropping systems: (1) incorporation of