a model of the effects of tillage on emergence of weed ... mohler, c...february 1993 effects of...

A Model of the Effects of Tillage on Emergence of Weed SeedlingsAuthor(s): Charles L. MohlerSource: Ecological Applications, Vol. 3, No. 1 (Feb., 1993), pp. 53-73Published by: Ecological Society of AmericaStable URL: http://www.jstor.org/stable/1941792 .Accessed: 04/03/2011 11:11

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Ecological Applications, 3(1), 1993, pp. 53-73 C) 1993 by the Ecological Society of America

A MODEL OF THE EFFECTS OF TILLAGE ON EMERGENCE OF WEED SEEDLINGS'

CHARLES L. MOHLER Section of Ecology and Systematics, Corson Hall, Cornell University,

Ithaca, New York 14853 USA

Abstract. A simple model is developed in which the density of weed seedlings emerging in a field is related to (1) the ability of seedlings to emerge from various depths in the soil, (2) the survival of seeds at different depths, and (3) the depth of seed burial in no tillage, rotary tillage, and plow tillage. Other tillage regimes are considered by analogy. Literature is reviewed to determine biologically reasonable functions describing seedling emergence, seed survival, and distribution of seeds with depth, and parameters of these equations are estimated from data in the literature. Problems related to the mathematical description of these phenomena are discussed, and it is noted that some commonly held beliefs regarding survival of seeds in the soil are mutually incompatible. Although many studies have investigated the persistence of seeds as a function of depth in the soil, few have distinguished death from the production of seedlings. The model indicates that in the first year following input of seeds to the soil, no tillage will have more seedlings than tillage, but in later years no tillage will likely have fewer seedlings unless innate or induced dormancy is high or seed survival near the soil surface is unusually good. If seed return is allowed, no tillage or minimum tillage will have more seedlings perennially. Recovery of good weed control following a year with substantial seed input may be easiest if the soil is plowed deeply to bury the seeds, and then shallow or no tillage is used in subsequent years to avoid returning seeds to the surface. Much of the literature on the effects of tillage on weed density is difficult to interpret because little indication is given of the vertical distribution of seeds in the soil at the beginning of the experiment.

Key words: emergence; plowing; seed distribution; seeds; survival; tillage; weeds.

INTRODUCTION

Reduced tillage cropping systems have been advo- cated as a means of preventing erosion and maintaining desirable soil properties (Jones et al. 1968, Shear and Moschler 1969, Edwards 1975, Gebhardt et al. 1985, Shear 1985). Since tillage has traditionally been an important component of weed control (Gebhardt et al. 1985), the growing use of reduced tillage systems, and in particular no tillage (sometimes referred to as direct drilling), has prompted a substantial number of studies of weed response to soil disturbance. Although most authors have agreed that the reduction or absence of tillage allows the increase of perennial species via veg- etative growth (Triplett and Lytle 1972, Cussans 1975, Pollard and Cussans 1976, Koskinen and McWhorter 1986), the effects of tillage on the density of weed seedlings are far less clear. For example, some studies have found more seedlings in tilled plots (Roberts and Feast 1972), whereas others have found more without tillage (Moss 1985, Cardina et al. 1991, Mohler and Callaway 1992). Moreover, many studies have found the effects of tillage to vary among species (Bibbey 1935, Chan- cellor 1964a, Pollard and Cussans 1976, Froud-Wil- liams et al. 1983b, Buhler and Daniel 1988, Buhler and Opplinger 1990), or sites (Wilson and Cussans 1972,

Buhler and Mester 1991), or between years of an experiment (Wilson 198 1, 1985). The extensive and often confusing literature on the effects of primary tillage on weed populations has been previously reviewed by Cussans (1975, 1976), Froud-Williams et al. (1981), and Froud-Williams (1987).

An analytical model is here developed to clarify some of the population processes whereby tillage influences weed seedling density. The principal intent of the model is to provide a framework within which the large and often conflicting literature on weed response to tillage can be understood (cf. Cousens et al. 1987). In addition, it shows the approximate conditions under which weed densities are expected to be higher with one tillage regime than with another. Finally, the model is useful in identifying gaps in current understanding of processes affecting seeds in the soil and their emergence as seedlings. Although the model does not ex- plicitly include all of the processes whereby tillage af- fects weed seedling density, additional factors are explored as qualitative extensions to the model.

The present model is not designed to be predictive of the population dynamics of a particular species, and in this respect it differs from many recent weed population models (Cussans and Moss 1982, Cousens et al. 1986, Doyle et al. 1986, Lapham 1987, Maxwell et al. 1988, Mortimer et al. 1989). The present model seeks to describe and explain ways in which the dy-

' Manuscript received 22 December 1991; revised 19 March 1992; accepted 19 April 1992.

54 CHARLES L. MOHLER Ecological Applications Vol. 3, No. I

namics of the seed bank affect plant populations, and in this respect it is similar to work of Cohen (1966), MacDonald and Watkinson (1981), Mortimer et al. (1989), and Cousens and Moss (1990).

THE MODEL

The model explores the relationship among three processes: (1) the vertical distribution of seeds in the soil column, (2) the rate of emergence of seedlings from the soil as a function of depth of seed burial, and (3) the survival of seeds, also as a function of their depth of burial. Tillage operations are assumed to change the vertical distribution of seeds in the soil but not to affect the relation between seed depth and emergence or survival. The model further assumes that emergence occurs shortly after tillage, and that all seed mortality occurs after emergence but before the next tillage event. These assumptions and others introduced below are discussed after presentation of the model. Three tillage regimes are compared: no tillage, rotary tillage, and tillage with a moldboard plow. The seed distribution functions chosen to represent these regimes are those likely to obtain if the tillage regime were applied to a soil that had many seeds fall on the surface in the recent past.

The basic approach of the model is to (1) state the general structure of the relation between the three processes for each tillage regime, (2) adopt particular func- tional forms describing each process based on data from the literature and an understanding of the processes, (3) combine 1 and 2 to produce an equation that, when integrated over depth, gives the total seedling emergence for each regime, and (4) explore graph- ically the parameter conditions under which total emergence is the same for no tillage and each of the two tillage regimes. This process is followed to explore seedling emergence after 0, 1, 2, and 4 yr of emergence and survival, under the further assumption that no new seed input occurs.

No tillage Let fl(D, t) equal the number of seeds at depth D at

the beginning of year t in a no tillage field. The function f,(D, t) and other functions in the model are continuous with respect to depth but discrete with respect to time, since emergence of weeds tends to be a seasonal phe- nomenon. The distribution of seeds the following year will be

fn(D, t + 1) = s(D)[f,(D, t) - h,(D, t)],

where h,(D, t) equals the number of seeds at depth D that emerged in year t, and s(D) is the rate of survival of the seeds at depth D that did not turn into seedlings. Seeds that germinate but fail to emerge are considered to have died, and this source of mortality is not distinguished from others. Emergence from a particular depth h,(D, t) is a product of the number of seeds present at a depth and the proportion of seeds at that depth that produce seedlings, m(D),

h,(D, t) = m(D)fg(D, t)

Note that both s(D) and m(D) are assumed to remain constant through time. Then,

fn(D, t + 1) = s(D)fA(D, t)[l - m(D)].

By iteration,

fn(D, t) = fn(D, O)s(D)[ 1 - m(D)]!

and,

h,(D, t) = m(D)f,(D, O)s(D)'[l - m(D)]'. (1)

Finally, the total emergence, Tj(t), from all depths is

T =(t) h, (D, t) dD. (2)

To solve Eq. 2, it is necessary to provide functions for m(D), s(D), andf,(D, 0). Rate of emergence, m(D), commonly decreases rapidly with increasing depth for small-seeded weed species (Chancellor 1964a). For some weed species emergence is best when seeds are buried 1-5 cm, but very few species have maximum emergence from greater depths (Table 1). For many species, the emergence response, m(D), appears to be approximated by a negative exponential (Table 1). The proportion emerging at any depth D can then be expressed as

m(D) = moeD > 0, Om 1 (3)

where E is a parameter describing the decline in emergence with increasing depth (Fig. 1), and mo is the proportion of seeds emerging at depth 0. The parameter mO is essentially the proportion of seeds that are not dormant when exposed to surface conditions.

Many authors have noted that seed persistence tends to be poorest near the soil surface and increases with depth (Tables 2 and 3, and other references discussed

1.0

0.8 C) CD C) 0.6-

o 0.4 -

-~0.2 -=.

o2= a. 0.0. 0 2 4 6 8 1 0 1 2

Depth (cm)

FIG. 1. Emergence as a function of depth D, as described by Eq. 3 [m(D) = moe-1D], for three values of the parameter E. In all cases, the parameter governing dormancy, mi, equals 1.

February 1993 EFFECTS OF TILLAGE ON WEEDS 55

below). For purposes of model construction, the following form is assumed for the survival function,

s(D) = f3(l - e-D), a >O 0, 0 <3 < 1 (4)

where s(D) is the probability that a seed at depth D that did not turn into a seedling will survive until the following year, and a and : are constants. By Eq. 4, no seeds survive from one year to the next at the surface, and the proportion surviving approaches f asymptotically as depth increases. The rate at which the proportion surviving increases with increasing depth is given by a. As a increases, the asymptotic survival rate is approached at shallower depth, and the effect of additional mortality experienced by seeds near the surface is reduced (Fig. 2). Values of a greater than ;20 are effectively equivalent to a constant survival with respect to depth.

The infiltration of seeds into the soil column in untilled conditions has been little studied. It is reasonable to suppose, however, that the proportion reaching some depth D + AD would be a constant fraction of the proportion reaching a depth D. In that case the proportional distribution of seeds with respect to depth may be approximated by a negative exponential

N,(D) = QoePD, p > 0 (5)

where N,(D) is the density of seeds at depth D, QO is the density at the soil surface, and p is a constant. This equation fits most data on the vertical distribution of seeds following a single surface sowing without subsequent soil disturbance, and data on presumably equilibrium vertical distributions of seeds in untilled soils (Table 4). When standardized to express the relative distribution of seeds, the equation becomes

f,(D, 0) = pe-PD, p > 0. (6)

Incorporating all of these assumptions, Eq. 1 becomes

h,(D, t) = mOpe-E+P)Dt[ 1 - aD]f

[1 - moe-D]I. (7)

For large a and E, Eq. 7 may be approximated by

h,(D, t) mopole-(,P)D[1 - te-D][1 - tmoe-D],

but over much of the interesting range of these parameters the approximation is invalid and the polynomials must be expanded before integration. This limits solutions to small values of t. Fortunately, most of the interesting dynamics are exhibited in the first few years. For years 0 and 1, total emergence is

T(O) = mop(E + P)' T(l) = mopf[(E + p)- mo(2f + p)'

- (a + e + p)-' + mo(a + 2E + p)-']. (8)

Eq. 8 is complicated but can be explained as follows.

The first term within the brackets expresses the effect of emergence during the current year. The second term in the brackets represents the depletion of the seed pool by emergence in previous years, the third term the depletion of the seed pool by mortality near the soil surface, and the fourth term the interaction of these two effects. Finally, total emergence is scaled by the asymptotic survivorship, f, and by p. That emergence is proportional to p may seem counter-intuitive, since for a given value of QO, larger p implies fewer seeds near the soil surface. However, standardization of the seed pool to unity to facilitate comparison of tillage regimes causes the proportion of the seed pool that is near the surface to increase with p (Fig. 3). Equations for later years have analogous form, with additional between-year interaction terms.

Rotary tillage

The model for rotary tillage is similar to that for no tillage except that (1) all seeds are assumed to lie above the depth of rotary tillage, Dr, (2) the equation describing the initial distribution of seeds in the soil following rotary tillage is assumed to be uniform over the interval O < D < Dr (Fig. 3), and (3) the uniform distribution is re-established at the beginning of each season by tillage.

The latter two assumptions have the consequence that the vertical distribution of seeds in year t, r(t), is a constant with respect to depth. Then

r(t + 1) = r(t)F,

where F is the fraction of seeds persisting in the soil from year t to t + 1. Since F is the fraction that do not emerge but that survive,

rDr

f s(D) r(t)[1 - m(D)]dD

F=f ) rDr

Ir(t) dD

0.8 a= 0.5

. 0.6

CD 0.4 c 0

o 0.2 0-

0~ 0.0 ,

0 10 20 30 40 50 Depth (cm)

FIG. 2. Seed survival as a function of depth D, as described by Eq. 4 [s(D) = f3(1 - e-,D)], for three values of the parameter a. In all cases, the asymptotic survivorship, f, equals 0.6.

56 CHARLES L. MOHLER Ecological Applications Vol. 3, No. 1

where s(D) and m(D) are again the survival and emergence rates. F can be reduced to

rD,

F= D,-I s(D)[f - m(D)]dD,

which demonstrates that F is a constant independent of year t. Therefore,

r(t) = r(O)F'.

Analogous to the no tillage regime, emergence as a function of depth, hr(D, t), is

hr(D, t) = m(D)r(t),

and total emergence Tr(t) is

rDI

Tr(D, t) = f hr(D, t) dD.

The uniform vertical distribution of seeds in the soil profile following the initial rotary tillage can be expressed as

Nr(D) = Qr, when 0 < D < Dr

0, when D > Dr

where Nr(D) is the density of seeds at depth D, and Qr is the density in the tilled horizon. Standardizing to express the relative density of seeds gives

r(O)=DDr', whenO <D <Dr

0, when D > Dr (9)

Assuming that the rate of emergence as a function of depth again follows Eq. 3, and survival as a function of depth is expressed by Eq. 4, then

F D=,D' f[Dr - a-(l - etl),-) '(1 -e-)

+ mo(a + c)-'(l -e-(t+oD- A (10)

For typical rotary tillage depths of 10-20 cm and values of a and e greater than about 0. 1, which are commonly found (Tables 1 and 2), Eq. 10 simplifies to

Ftz Dr-' 3[D,. -a-' - moE- + mj(a + E)--] (11)

Finally,

Tr(t) = mo(EDr)I'(I - e-,Dr)Fp t >- 0. (12) Regardless of whether Eq. 10 or 11 is used, the sec-

ond term in the brackets represents the depletion of the seed pool by emergence in previous years, the third term the depletion of the seed pool by mortality near the soil surface, and the fourth term the interaction of these two effects. The annual depletion of the seed pool is also scaled by the asymptotic survivorship, f. Com- putations for the graphical analysis of the model were made using Eq. 10.

Tillage by moldboard plow The model for tillage by moldboard plow is similar

to that for no tillage except that a different function is required to describe the initial distribution of seeds in the soil. This modification does not change the form of Eq. 1. Most measurements of the vertical placement of seeds following a single plowing have found skewed, bell-shaped distributions, but the direction of skewing has been inconsistent among studies (see discussion below). For purposes of model development, the distribution is here approximated by a symmetrical tri- angle with no seeds at the surface or at the depth of

0.6 A. No tillage

a) 0.4-

CD \ p =0.5 (/) C, 0.2

CD \

. a) -

~~p =o0.1 0.0

0 10 20 30

0.10 B. Rotary tillage

a)

CD 0.05 a)

0.00_ Dr

0 5 10 15 20

0.15 C. Plow tillage

C= a) 0.10

a)/ \

a) a) 0.05 /\

Er ~~~~~~DP 0.00

0 10 20 30 Depth (cm)

FIG. 3. Distribution of seed density with respect to depth as described by (A) Eq. 6 for no tillage, (B) Eq. 9 for rotary tillage, and (C) Eq. 13 for plow tillage. In A, the distribution is shown for two values of the parameter p, which describes the rate of decline of seed density with depth in no tillage. In B and C, the distributions are shown for depth of rotary tillage, D,., of 15 cm, and depth of plow tillage, Dp, of 20 cm respec- tively.


plowing, D,p, and a maximum density of seeds, Q,,,, at 0.5 D,} (Fig. 3).

The triangular distribution of seeds can be expressed as

Q,(0. 5D,D) 'D when 0 < D ' 0. SD, Np(D) = 2Q,, - Q,(j0.5DP)-'D when 0.5Dp < D ' Dp

0 when D > DP

which when standardized gives

4DP-2D when 0 < D ' 0.SDp fp(D, 0) = 4Dp-' -4DP-2D when 0.5Dp < D ' Dp

0 when D > D, (13)

Assuming rate of emergence follows Eq. 3, then total emergence in year 0 is

Tp(0) = 4mo(E Dp)-2( I -e-0.5(9p)2.

Solutions for later years would require information on the proportion of seeds at each depth i that move to each depth j following subsequent tillage events. Although some information is available on movement of seeds during successive plow tillage events (Cousens and Moss 1990), it is not sufficiently detailed to allow construction of an analytical model. However, since repeated plowing without the addition of new seeds creates an increasingly uniform vertical distribution of seeds, it seems likely that after a relatively few years, emergence for plow tillage might approximate that for rotary tillage (e.g., as expressed by Eq. 12).

ASSUMPTIONS AND PARAMETERIZATION OF THE MODEL

One benefit of creating a model is that it reveals the assumptions underlying an investigator's conception of a process. Models, the present one included, are simplifications of the real world, and many of the assumptions inherent in a model relate to the way in which the model simplifies reality. Each of the primary equations in the model represents an assumption regarding the operation of a relevant biological or agricultural process. Accordingly, each deserves to be examined for validity. In addition there are certain structural assumptions implicit in the way the primary equations are put together to construct the model.

One critical assumption is that new weed seeds are not shed onto the field. Complete control year after year is rare, and is usually unnecessary for good crop production (Aldrich 1984). However, focusing on just the fate of seeds already resident in the soil greatly simplifies the analysis of the seed pool and thereby aids in understanding relations among the phenomena affecting seeds. In a sense, the present model could be considered one component of a larger model of the effects of tillage on weed demography. Consequences of reseeding are considered qualitatively below.

Multiplication of the survival and emergence rate functions makes the structural assumption that emergence and survival can be treated as nonoverlapping events within an annual cropping cycle. The obser- vation that many weed species have a period of a few weeks during which the bulk of the annual emergence normally occurs (Roberts and Neilson 1980, 1981, Roberts and Boddrell 1983, Ogg and Dawson 1984, Chancellor 1986) supports this assumption. Other species have a prolonged period of emergence, or have two seasonal peaks of emergence (Roberts and Ricketts 1979, Froud-Williams et al. 1984). Modifications would be required to apply the model to such species. Froud- Williams et al. (1984) found that the flush of emergence was more prolonged with tillage, but that the timing of emergence was little affected. In any case, the model's validity does not depend on simultaneous emergence in tilled and untilled conditions.

The model also assumes that all effects of tillage on seedling emergence and survival are expressed via vertical position of seeds in the soil. Chancellor (1985) reviewed the effects of tillage on germination of annual weeds and concluded that the three principal germination stimuli influenced by tillage are light, soil at- mosphere, and amplitude of temperature fluctuations. Tillage exposes seeds to a light flash before reburial, allows greater diffusion of oxygen into and carbon di- oxide out of the soil, buries residue and promotes dry- ing of the soil, thereby increasing the amplitude of temperature fluctuations. All of these factors promote germination of at least some species (Wesson and Wareing 1969a, Thompson et al. 1977, Chancellor 1985; C. L. Mohler and J. R. Teasdale, unpublished manuscript; Teasdale and Mohler 1993). Several studies have noted increased emergence, increased seed mortality, or both, following frequent, repeated tillage (Brenchley and Warington 1933, Roberts and Dawkins 1967, Roberts and Feast 1972, 1973a, b, Ogg and Daw- son 1984, Warnes and Andersen 1984), but whether these effects are the result of changes in soil properties or the exposure of seeds to near-surface conditions is unclear. Only Banting (1966) has attempted to study the effect of tillage while controlling seed position. He placed caged seeds at 5, 10, 15, and 20 cm and then either cultivated to 3.8 cm once each summer or not. Seed persistence at 5 and 10 cm was slightly less in the cultivated than in uncultivated soil, but differences were small. The technical difficulties of creating similar depth distributions of seeds with and without soil disturbance at the actual level of the seed are daunting and may preclude resolution of the problem.

Emergence rate

Many students of weed biology have examined the effect of depth of seed burial on seedling emergence. Data from 20 of these studies are summarized in Table 1. All of the investigations in Table 1 involved counting seedlings produced from seeds buried at different


TABLE 1. References giving data on emergence as a function of depth of seed placement, and the nature of the emergence response curve based on visual inspection of the data. Where emergence was a monotonic, concave function of depth (m, cc)*, Eq. 3 was fitted to the data. For these cases, parameter values and degrees of freedom for deviations from the regression (df) are given, and approximate standard errors (:SE) are shown.

Optimum Curve depth

Reference Species Condition form* (cm)t Baird and Dickens (1991) Diodia virginiana L. n-m 2 Balyan and Bhan (1986) Trianthema portulacastrum L. n-m i Bell et al. (1962) Cyperus esculentus L. m, cc s Blackshaw (1990) Malva pusilla Sm. n-m i Eastin (1983) Melochia corchorifolia L. n-m 0.5-5 Hopen (1972) Portulaca oleracea L. m, cc 0 Ilnicki and Fertig (1962) Solanum carolinense L. n-m 1.3 Kollar (1968) Avenafatua L. m, cc 0

Convolvulus arvensis L. m, cc 0 Cirsium arvense (L.) Scop. m, cc 0

Lapham and Drennan (1990) Cyperus esculentus L. m, cc s Mester and Buhler (199 1) Setariafaberi Herrm. 1 0?C n-m 2

150C m, cc 0 200C m, cc 0

Abutilon theophrasti Medik. 10?C n-m 2 150C m, cc 0 200C m, cc 0

Peters and Dunn (1971) Digitaria sanguinalis (L.) Scop. m, cv 1.3 Digitaria ischaemum (Schreb.) Muhl. m, cv 1.3-3.8

Rahn et al. (1968) Echinochloa crusgalli (L.) field n-m 1.2 loam m, cc 0 sandy loam m, cc 0 compacted m, cc 0 loose m, cc 0

Raleigh et al. (1962) Agropyron repens (L.) Beauv. greenhouse m, cc s field m, cc s

Stoller and Wax (1973) Setaria lutescens (Weigel) Hubb. Planted in 1966 n-m 5.1 Ipomoea hederacea (L.) Jacq. " m, cc s Xanthium pensylvanicum Wallr. " m, cc s Datura stramonium L. " m, cc s Abutilon theophrasti Medic. " m, cc s Ambrosia trifida L. " m, cc s Setaria lutescens (Weigel) Hubb. Planted in 1968 n-m 2.5 Ipomoea hederacea (L.) Jacq. " m, cc s Polygonum pensylvanicum L. " n-m 2.5 Datura stramonium L. " n-m 5.1 Abutilon theophrasti Medic. " m, cv s Ambrosia trifida L. " m, cv 2.5 Ambrosia artemisiifolia L. " m, cc s

Sweet (1986) Galinsoga ciliata (Raf) Blake? m, cc 0 Sweet et al. (1978) Ambrosia artemisiifolia L. clay loam m, cc 0

silt loam m, cc 0 sand m, cc 0

Tayalla et al. (1988) Ischaemum afrum (J.F. Gmel.) Dandy without glumes m, cc s with glumes n-m 2.5

Vengris et al. (1972) Portulaca oleracea L. field m, cc 0 growth chamber m, cc 0

Watkinson (1978) Vulpiafasciculata (Forskal) Samp. m, cv 0-0.5 Weaver and Cavers (1979) Rumex crispus L. m, cc 0

Rumex obtusifolius L. m, cc 0 Wiese and Davis (1967) Schedanardus paniculatus (Nutt.) Trel. n-m 0.6-1.3t

Amaranthus retroflexus L. n-m 0.6-1.3t Echinochloa crus-galli (L.) Beauv. n-m 0.6-2.5t

* m, cc-monotonic, concave; m, cv-monotonic, convex; n-m-non-monotonic. t Depth at which emergence was maximum. "s" indicates that emergence was greatest at the shallowest depth tested. t Optimum depth depended on temperature. ? Author stated that results for G. parviflora Cav. were nearly identical to those for G. ciliata.

depths. Two basic patterns have been observed: (1) a monotonic decrease of emergence in response to increasing depth, and (2) a non-monotonic response in which shallow burial increased emergence but deep burial reduced emergence. About half the species in

these studies showed the monotonic emergence response assumed in the model. Further evidence on the differing response to burial among species comes from Williams (1978) who found that Agropyron repens (L.) Beauv. germinated slowly until stirred into the soil,


TABLE 1. Continued.

Depths MO e

tested (cm) X Z SE X SE df

0-8 0-11

0.6-3.8 0.66 0.17 1.0 0.2 2 0.5-10

0-10 0-2.5 0.28 0.05 2.2 0.5 3

0.6-5.1 0-15 0.06 0.02 0.03 0.03 5 0-15 0.070 0.012 0.26 0.04 5 0-15 0.16 0.02 0.70 0.09 5

0.1-2.0 0.26 0.02 1.1 0.1 3 0-6 0-6 0.91 0.02 0.061 0.005 2 0-6 0.88 0.03 0.071 0.009 2 0-6 0-6 0.53 0.06 0.14 0.03 2 0-6 0.48 0.01 0.098 0.008 2

1.3-10.2 1.3-10.2 0-17.8 0-17.8 0.75 0.08 0.33 0.05 3 0-17.8 0.52 0.05 0.34 0.04 3 0-17.8 0.76 0.07 0.30 0.04 3 0-17.8 0.52 0.15 0.39 0.13 3

1.3-15.2 0.87 0.18 0.31 0.05 7 1.3-15.2 4.0 1.1 1.3 0.2 2 2.5-15.1 2.5-15.1 0.57 0.30 0.40 0.15 1 2.5-15.1 0.32 0.09 0.17 0.04 2 2.5-15.1 0.52 0.22 0.28 0.09 2 2.5-15.1 1.2 0.4 0.32 0.07 2 2.5-15.1 0.91 0.20 0.12 0.03 2 1.3-10.2 1.3-10.2 0.60 0.10 0.74 0.09 2 1.3-10.2 1.3-10.2 1.3-10.2 1.3-10.2 1.3-10.2 0.63 0.16 0.36 0.09 2 0-1 1.1 0.3 3.6 1.3 1 0-8 0.66 0.10 0.58 0.10 4 0-8 0.65 0.08 0.46 0.06 4 0-8 0.78 0.24 0.56 0.19 4 1-10 0.60 0.06 0.52 0.05 2 1-10 0-8 0.62 0.11 1.5 0.3 4 0-8 0.60 0.10 1.1 0.3 4 0-10 0-5 1.1 0.3 0.87 0.32 2 0-5 1.0 0.1 0.49 0.09 2 0-10.2 0-10.2 0-10.2

whereas Agrostis gigantea Roth. germinated rapidly on the soil surface but more slowly after stirring. Another sort of information relevant to the emergence response has been obtained by carefully excavating seedlings in the field to determine the depth from which they emerged (Chancellor 1 964b, Holroyd 1964, Moss 1985, Dekker and Meggitt 1986). Such data only reflect the emergence response if the seed distribution was uni-

form down to the maximum depth of emergence. Only Moss (1985) provided information on seed distribution. The extensive survey by Chancellor (1964b) was interesting in that again about half of the cases showed a monotonic response. Chancellor (1 964b) and Froud- Williams et al. (1984) found that mean depth of emergence was inversely related to seed size, implying that the model as here developed is applicable primarily to small-seeded species.

Brain and Cousens (1989) introduced a dose-response equation that could be used to fit both monotonic and non-monotonic emergence responses, but the equation is too mathematically intractable for use in the analytical model developed here. It offers a more general alternative to Eq. 3, which could be useful in simulation models.

To obtain estimates of the parameter e, emergence data on species in Table 1 showing a monotonic response were fitted to a negative exponential (Eq. 3) using the Gauss-Newton method with stephalving (SAS Institute 1989). Squared deviations were weighted by the inverse of expected values to compensate for prob- able correlation between mean and standard deviation. The first depth showing no emergence was included in the regression, but observations of zero emergence from more deeply placed seeds were not. The fit was good for most cases, as indicated by visual inspection of graphs and low approximate standard errors for most e (Table 1). Estimates of e ranged from 0.03 to 3.6, with 69% in the interval between 0.1 and 1.0 (Table 1). Although it was not appropriate to fit Eq. 3 for species showing a non-monotonic emergence response, such a response is somewhat similar to a monotonic response with a small value of e.

Of the studies that provided information suitable for curve fitting, only a few (Stoller and Wax 1973, Weaver and Cavers 1979, Tayalla et al. 1988, Lapham and Drennan 1990) provided information on germinability of the seeds tested. Consequently, discussion of the mo values is pointless, except to note that only one ex- ceeded 1.0 by more than one standard error, as is required by biological reality.

Survival rate

Most investigators have noted that seeds persist longer when mixed into the soil by tillage or experimental procedures than when left at or near the soil surface (Thurston 1961, Roberts and Feast 1972, Wilson and Cussans 1972, Stoller and Wax 1974, Wilson 1981, 1985, Froud-Williams et al. 1984, Warnes and An- dersen 1984), although a few have observed the reverse trend (Gleichsner and Appleby 1989, Donald 1991). Seed persistence in the soil is the proportion of seeds remaining after emergence and mortality, and is here distinguished from the survival of seeds that do not produce seedlings. Table 2 summarizes the form of the persistence response for several studies potentially relevant to parameterization of the model. All reports in


TABLE 2. Effect of depth of seed burial on (A) survival of seeds that did not produce seedlings, and (B) persistence of all seeds.* Multiple data sets for a given species were analyzed separately; the nature of differences among data sets is given in braces after the reference.

Reference !nature of casest, Cases in which survival as a function of depth was Species Increasingt Constant Decreasing Variable Total

A) Survival data Dawson and Bruns (1975)

Echinochloa crus-galli L. 1 1 Setaria viridis (L.) Beauv. 1 1 Setaria lutescens (Weigel) Hubb. 1 1

Froud-Williams et al. (1983a) !sites and yearst Mixed species 2 3 5

Moss (1985) treatments, Alopecurus myosuroides Huds. 1 1 2

Stoller and Wax (1973) !years Setaria lutescens (Weigel) Hubb. 1 1 2 Ipomoea hederacea (L.) Jacq. 1 1 2 Abutilon theophrasti Medic. 1 1 2 Ambrosia trifida L. 1 1 2 Datura stramonium L. 1 1 2 Ambrosia artemisiifolia L. 1 1 Xanthium pensylvanicum Wallr. 1 1 Polygonum pensylvanicum L. 1 1

Total 7 2 7 7 23 B) Persistence data

Banting (1966)t !experiments, treatments, and years Avenafatua L. 4 (2) 1 7 12

Banting et al. (1973) {treatments and yearsS Setaria viridis (L.) Beauv. 3 2 5 10

Dawson and Bruns (1975) jyearst Echinochloa crus-galli L. 1 1 Setaria viridis (L.) Beauv. 2 1 3 Setaria lutescens (Weigel) Hubb. 1 1

Donald and Zimdahl (1987) {seed sources, sites, and yearst Aegilops cylindrica Host. 10 (1) 2 4 8 24

Froud-Williams et al. (1983a) !sites and yearsS Mixed species 2 3 5

Harradine (1986) Bromus diandrus Roth. 1 1

Kannangara and Field (1 985) 1 years Achillia millefolium L. 2 2

Lapham and Drennan (1990) {years} Cvperus esculentus L. 1 1 2

Leguizam6n (1986) {years and experimentst Sorghum halepense (L.) Pers. 1 1 2

Miller and Nalewaja (1990) !sites and yearsS Avenafatua L. 2 4 6

Moss (1985) !experiments, treatments, and yearst' Alopecurus myosuroides Huds. 1 1 4 6

Rampton and Ching (1966)? {years and soilst Lolium multiflorum Lam. 1 1 Agrostis tenuis Sibth. 2 2 Trifolium pratense L. 2 2 Trifolium incarnatum L. 2 2 Poa pratensis L. 1 1 Festuca arundinacea Schreb. 1 1 Fesetuca rubra var. commutata Gaud. 1 1


TABLE 2. Continued.

Reference !nature of cases Cases in which survival as a function of depth was

Species Increasingt Constant Decreasing Variable Total

Stoller and Wax (1973) jyears} Setaria lutescens (Weigel) Hubb. 1 1 2 Ipomoea hederacea (L.) Jacq. 2 2 Abutilon theophrasti Medic. 2 2 Ambrossia trifida L. 1 1 2 Datura stramonium L. 1 1 2 Ambrosia artemisiifolia L. 1 I Xanthium pensvlvanicum Wallr. 1 Polvgonum pensylvanicum L. 1 1

Taylorson (1970) 'dormancy condition of seeds} Amaranthus retroflexus L. 2 (1) 2 Barbarea vulgaris R. Br. 2 2 Echinochloa crusgalli (L.) Beauv. 2 (1) 2

Thomas et al. (1986) {experiments and yearst Setaria viridis (L.) Beauv. 6 6

Zorner et al. (1984) Idormancy condition of seeds Avenafatua L. 2 2

Total 50(5) 5 13 44 112 * In terms of the model, survival is s(D) and persistence is s(D)[1 - m(D)]. Nature of the response function was judged

based on visual inspection of the data, and only cases in which sufficient data were available to make a judgment were included. Only cases without soil disturbance, and those in which seed return was prevented, were included. Cases in which survival or persistence increased or was constant as depth increased were analyzed further (See Table 3 and text).

t For the cases shown in parentheses, the survivorship function (Eq. 4) could not be fitted to the data because persistence values were a concave monotonically increasing function of depth over the range of depths studied. t Data from the 20-25 cm layer of soil in Experiment 1 were not included because Banting (1966) indicated that the low

survival there could have been an artifact of the experimental procedure. ? See also Rampton and Ching (1970).

which seeds were buried at three or more depths and in which data could be assessed over approximately 1-yr intervals were included. Each case listed in Table 2 is based on observations on a species over a 1-yr period for a particular site or experimental condition. Data were reworked as necessary to find the proportion of viable seeds remaining after 1-yr intervals. Cases were ignored if the author indicated that significant seed input occurred during the year, or that the soil profile was disturbed. Cases classed as variable had seed persistence that increased and then decreased with increasing depth, or decreased and then increased. Most such cases were from later years when few seeds were left to observe, and probably reflected random varia- tion rather than a biological response. Although persistence of seeds during the tenure of the experiment by Froud-Williams et al. (1 983a) decreased with depth or was variable (Table 2), the authors stated that the greater density of moderately deep seeds at the first sampling date indicated faster decline near the surface.

Overall, Table 2 supports the view that persistence of seeds increases with depth, though the contrary ex- amples suggest that this effect is not universal. Most of the cases in which persistence decreased with depth involved annual grasses with relatively large, short- lived seeds (see also Gleichsner and Appleby 1989), but such species sometimes show the more usual response as well.

In most of the studies cited in Table 2, seeds were enclosed in mesh packets or tubes before burial (Ban- ting 1966, Rampton and Ching 1966, 1970, Zomer et al. 1984, Kannangara and Field 1985, Harradine 1986, Leguizam6n 1986, Thomas et al. 1986, Donald and Zimdahl 1987, Miller and Nalewaja 1990). This procedure kept seeds together at the desired depth in the soil profile, but it had the unfortunate consequence that seeds that could have produced seedlings were killed. Consequently, in terms of the model, the data estimate s(D)[ 1 - m(D)], which is to say, persistence of seeds in the soil, rather than s(D), the survival of seeds that do not produce seedlings.

A few studies (Stoller and Wax 1973, Froud-Wil- liams et al. 1983a, Moss 1985) provided coordinated information on emergence and survival that was used to compute the response of seed survival to depth (Ta- bles 2A and 3). In addition, the persistence data of Dawson and Bruns (1975) were adjusted to estimate seed survival by assuming that the total emergence reported all occurred during the 1 st yr. Parameters were estimated by fitting Eq. 4 to data using nonlinear least squares regression without weighting. Of the 23 cases from these studies having sufficient information to compute survival, seven each had increasing, decreasing, and variable responses, and two showed no response of survival to depth (Tables 2A and 3). Several other studies, all on Avena fatua, have shown that sur-


vival of seeds that did not produce seedlings increased when seeds were buried (Banting 1966, Wilson 1972, Wilson and Cussans 1972, 1975). Overall, the available evidence does not support the generalization that survival of seeds remaining in the soil increases with depth. However, since Eq. 4 with a large a is appropriate for cases in which survival is unaffected by depth, the equation is reasonable for the majority of species.

Fitting Eq. 4 to the cases in Table 2A in which survival increased or was constant with depth shows that a is usually > .05 (Table 3), but the number of cases is small. If loss of seeds near the surface were mainly due to death rather than emergence, then survival would approximate persistence, and fitting Eq. 4 to the studies in Table 2B would be valid. Comparison of estimates of a for the Dawson and Bruns (1975) data with and without this approximation showed that the error it introduces can be large. However, since fitting persistence data in place of survival data should underesti-

mate a, the approximation can provide additional information on the lower limit of a in real systems. Fitting the 45 cases listed in Table 2B in which persistence increased asymptotically with depth and the 5 cases in which survival did not vary with depth showed that a was always > .01, and in 700% of the cases, was > .1.

All of the cases in Table 2A in which survival was an increasing or constant function of depth had values of f >0.1 (Table 3). Since emergence does not deplete the pool of deeply buried seeds, estimates of : are less affected by use of persistence data in place of data on survival. In 94% of the cases listed in Table 2B, f was >0. 1. Biological reality requires that : be < 1.0.

Eq. 4 implicitly assumes that no seeds survive at the surface. This assumption could be avoided by adding a constant to the right side of the equation, but this change would complicate the mathematics substantially and only marginally improve the fit for most of the cases discussed above. As with the alternative form of the emergence function, the modified survival function with nonzero intercept might prove useful in a detailed simulation model of a particular species.

Use of a survival-depth function that is independent of time implicitly assumes that the rate of seed survival at a given depth in the soil is constant from one year to the next. A few studies on seeds of weedy grasses have shown that survival rate is not always constant (Burnside et al. 1977, Donald and Zimdahl 1987), but a large body of work indicates that seeds in whole soil profiles usually experience constant rates of depletion (Roberts 1962, Roberts and Dawkins 1967, Roberts and Feast 1973a, b). Semilogarithmic plots of data from other studies (Forbes 1963, Thurston 1966) con- firm this general trend (data not shown). Several studies found that depletion occurred faster in cultivated than in undisturbed soil (Roberts and Dawkins 1967, Rob- erts and Feast 1973a, b), probably because frequent cultivation brought buried seeds to the surface where

TABLE 3. Estimates of parameters of the seed survivorship function (Eq. 4) and degrees of freedom for deviations from the regression (df). Data are for survival of seeds that did not produce seedlings.

a Range Reference (x of depths

Species X -SE X SE df tested (cm)

Dawson and Bruns (1975) Echinochloa crus-galli (1959-1960) 0.38 0.29 0.52 0.10 1 2.5-20 Setaria viridis (1959-1960) large* 0.72 0.05 1 2.5-20 Setaria lutescens (1959-1960) 0.07 0.12 0.61 0.56 1 2.5-20

Stoller and Wax (1973) Planted in 1966

Ipomoea hederacea large* 0.62 0.02 2 2.5-15.2 Planted in 1968

Setaria lutescens 0.88 0.68 0.15 0.03 2 1.3-10.2 Ipomoea hederacea 0.57 0.07 0.29 0.01 2 1.3-10.2 Abutilon theophrasti 0.76 0.24 0.64 0.05 2 1.3-10.2 Ambrosia trifida 0.29 0.25 0.11 0.04 2 1.3-10.2 Ambrosia artemisiifolia 0.055 0.004 l.Ot 3 1.3-10.2

* The value of a was very large and could not be estimated precisely. t ,B was originally estimated to be > 1, which is biologically impossible. Therefore a was re-estimated with d set equal to

1.0.

E- 100

,C 10 Dm=0.6931P

? 1\

D .1

E .01

.01 .1 1 1 0 p

FIG. 4. Relation between p, the rate at which seed density declines as a function of depth, and D,, the median depth of seed burial in no tillage.


TABLE 4. Estimates of the parameter p (Eq. 5), which describes the rate of decline in seed density with depth in untilled soil, based on published data. Intercept and degrees of freedom for deviations from the regression (df) are also shown. :5SE = approximate standard errors of the parameters.

Intercept Range Reference Time (QO)___of depths

Condition period* X aSE A' SE df tested (cm)t Cardina et al. (1991) {mixed seed pool}

No-till, Wooster soil 25 yr 2.5 1.6 0.42 0.18 1 2.5-12.5 No-till, Crosby soil 25 yr 3.0 1.4 0.48 0.14 1 2.5-12.5 No-till, Hoytville soil 25 yr 0.98 0.09 0.18 0.02 1 2.5-12.5 Sod, Wooster soil 25 yr 1.1 0.2 0.21 0.03 1 2.5-12.5 Sod, Crosby soil 25 yr 1.4 0.5 0.25 0.07 1 2.5-12.5 Sod, Hoytville soil 25 yr 1.5 0.2 0.27 0.03 1 2.5-12.5

Chippindale and Milton (1934)t Llety-Ifan-hen

Calluna vulgaris Salisb. oo 1.4 0.5 0.50 0.13 3 1.3-11.4 Ponterwyd, Nardus association

Potentilla erecta Hampi. oo 0.92 0.36 0.34 0.11 2 1.3-8.9 Galium saxatile L. oo 1.2 0.2 0.43 0.05 3 1.3-11.4 Erica cinerea L. cc 1.2 0.5 0.43 0.13 3 1.3-11.4 Calluna vulgaris Salisb. cc 1.6 0.4 0.57 0.10 5 1.3-16.5 Agrostis spp. cc 1.4 0.4 0.50 0.11 2 1.3-8.9

Frong6ch Ranunculusflammula L. oo 1.0 0.2 0.39 0.05 5 1.3-16.5 Campanula hederacea L. cc 0.83 0.16 0.31 0.05 3 1.3-11.4 Luzula campestris Br. cc 0.85 0.14 0.32 0.04 3 1.3-11.4 Juncus communis Mey. cc 0.56 0.06 0.22 0.02 8 1.3-24.1 Juncus articulatus L. cc 0.49 0.09 0.19 0.03 6 1.3-19.0 Carex spp. cc 0.33 0.07 0.13 0.02 10 1.3-29.2 Agrostis spp. cc 1.0 1.1 0.40 0.28 10 1.3-29.2 Poa trivialis L. cc 0.81 0.75 0.31 0.20 10 1.3-29.2

Moore and Wein (1977) {mixed seed pool} Betula-Fagus forest 40+ yr 1.6 0.4 0.71 0.14 1 1-5 Acer-Fagus forest 40+ yr 0.71 0.03 0.29 0.01 1 1-5 Acer-Abies forest 40+ yr 0.64 0.36 0.30 0.15 3 1-9 Picea-Pinus forest 40+ yr 1.0 0.4 0.47 0.18 1 1-5 Picea forest 40+ yr 1.7 0.4 0.77 0.12 3 1-9

Moss (1985) Avena fatua L. Experiment 2 9 mo 2.3 0.6 0.26 0.05 1 3.8-18.8 Experiment 2 21 mo 2.3 1.2 0.26 0.09 1 3.8-18.8 Experiment 3 10 mo 1.5 1.0 0.42 0.25 2 1.2-20 Experiment 3 22 mo 1.4 0.5 0.39 0.14 2 1.2-20 Experiment 3 34 mo 0.85 0.33 0.20 0.07 2 1.2-20

Robinson and Kust (1962) Striga asiatica (L.) Kuntze cc 0.28 0.10 0.017 0.006 8 7.6-145

Van Esso et al. (1986) Area A, initial census Sorghum halepense (L.) Pers. z7 mo 1.0 0.3 0.25 0.06 3 2-18

Weaver and Cavers (1979) Rumex crispus L. 8 mo 2.0 0.2 0.64 0.04 1 1.2-11.2

18 mo 0.88 0.23 0.23 0.06 1 1.2-11.2 Rumex obtusifolius L. 8 mo 2.2 0.1 0.68 0.03 1 1.2-11.2

18 mo 1.1 0.1 0.31 0.03 1 1.2-11.2 * Time since last soil disturbance. For Chippindale and Milton (1934), Robinson and Kust (1962), Moore and Wein (1977),

and Cardina et al. (1991) seed input was continuous over the time period. For Weaver and Cavers (1979), Moss (1985), and Van Esso et al. (1986) seed input occurred at the beginning of the period.

t Range of midpoints of soil layers. t The cases listed include all species that were represented in the aboveground vegetation of the site, occurred in at least

three of the 2.5-cm soil strata examined, had densities of at least 20 seeds per 2090-cm2 area sampled, and showed a monotonic decrease in density with depth. They were taken from data on four pastures that had never been cultivated. In addition these sites had 60 species with <20 seeds, of which 39 occurred only in the top 5 cm, 6 species with >20 seeds which occurred only in the top 5 cm, and 11 species that occurred in three or more strata and which had >20 seeds but which showed a non-monotonic relation between density and depth. Of the latter, 6 species did not occur on the sites at the time of sampling.


conditions promoted germination. However, depletion rate was constant in both situations. Constant depletion rate and increasing persistence with depth of burial seem mutually exclusive phenomena, since total seed pool should decline faster early on when the surface pool is being rapidly depleted. In a cultivated soil seeds are regularly brought near the surface, and thus a constant depletion rate is understandable, but the resolution of the apparent contradiction for undisturbed soils is obscure.

Vertical distribution of seeds in the soil Studies of seed distribution in untilled soils have

consistently found a rapid decline in seed density with depth (Chippindale and Milton 1934, Russell and Mehta 1938, Robinson and Kust 1962, Roberts 1963a,

Moore and Wein 1977, Weaver and Cavers 1979, Moss 1985, Van Esso et al. 1986, Cardina et al. 1991). Chip- pindale and Milton (1934) found that a few species in undisturbed British pastures departed from this pat- tern, but these were few among the many species they studied, generally were species that stored well in the soil, and probably reflected a period of high seed input some time well before the sampling date. Eq. 5 was fitted to data from all studies in which either (1) seeds were placed on soil that had previously been free of that species, or (2) seed input had been continuous for a long time and therefore the seed distribution could be expected to have reached equilibrium (Table 4). Procedures were the same as those used to fit emergence data. For both pulsed and continuous seed input, the fit was generally good, as indicated by visual inspection of graphs and low approximate standard errors of most p (Table 4). The initial seed distribution assumed for untilled soil, Eq. 5, thus appears to be valid for a variety of cases. It would probably not be appropriate if, say, a large population of seeds was buried by plowing 2 yr prior to initiation of the no-till regime, and then input of seeds was prevented during the intervening year. Judgment must be used in ap- plying any model.

For the data sets examined p was mostly in the range 0.2 to 0.8 (Table 4). Since D,>, = - (ln 0.5)/p, where D,r is the median depth of seed burial, this range of p corresponds to median depths of burial between 0.9 and 3.5 cm (Fig. 4).

Several authors have found seed distributions following tillage by tine implements that were similar to those for no tillage (Wicks and Somerhalder 1971, Fay and Olson 1978, Moss 1985). Ball and Miller (1989, 1990) found much higher weed seed densities in the top 15 cm following chisel plowing than following moldboard plowing. Moss (1985), the only study making a direct comparison of seed distribution in no-till and tine tillage, found that seeds were somewhat more deeply distributed following tine tillage but still mostly near the surface. With respect to the model, tine tillage and no tillage appear to differ primarily in the value of p. Although Dunham et al. (1958) found that seed distributions after 9 yr of disking or plowing plus disking were similar, in general most seeds probably stay close to the surface when disking is the primary tillage.

Distributions of seeds and seed-sized plastic beads following moldboard plowing and seedbed preparation have been well studied. The majority of studies have found skewed bell-shaped distributions of seed density, with the peak density somewhat below half the depth of tillage, but well above the bottom of the plow layer (Russell and Mehta 1938, Roberts 1963a, Rottele and Koch 1981, Van Esso et al. 1986, and Knab and Hurle 1986, cited in Cousens and Moss 1990). A few studies have found peak densities close to the depth of plowing (Soriano et al. 1968, Pareja et al. 1985, Cousens and Moss 1990), some have found bell-shaped density dis-

A

100 - _ _ _ _

10 Dr = 20 Dr 10 NT

.1- RT

.01 .01 .1 1 10 100

B

100

10 - NT

? 1

.1 Dp =15

PT Dp =25 .01 I

.01 .1 1 10 100

p

FIG. 5. (A) Regions of the parameter space defined by p and E in which either no tillage or rotary tillage produces more seedlings in year 0. p is the rate at which seed density declines as a function of depth in no tillage and E is the rate at which emergence declines as a function of seed depth. The break between the two regimes is shown for two values of the depth of rotary tillage, Dr. (B) Regions of the parameter space in which either no tillage or plow tillage produces more seedlings in a year 0. The break between the regimes is shown for two values of the depth of plow tillage, Dp. The small window in the center of each figure shows the range of parameters en- countered in data taken from the literature (Tables 1 and 4).


tributions with the peak nearer the surface (Roberts 1963a, Pawlowski and Malicki 1968), and two have found roughly uniform densities through the upper 75% of the plow layer (Wicks and Somerhalder 1971, Fay and Olson 1978). Repeated plowing with negligible seed input quickly creates an approximately uniform distribution of seeds in the plowed horizon (Van Esso et al. 1986, Cousens and Moss 1990).

Probably no one function could precisely represent all of the possible seed distributions created by conventional tillage. The triangular distribution (Eq. 13) adopted for this model tends to underestimate differences between plow tillage and no tillage since it places the bulk of the seeds somewhat higher in the soil profile than has usually been observed after a single plowing of a surface seed pool.

Russell and Mehta (1938) found a slight decline in seed density with depth following rotary tillage. After 9 yr of rotary tillage, Roberts and Stokes (1965) found a strongly decreasing density of seeds with depth. Eq. 9 is probably a reasonable approximation only if the working of the tilled layer is very thorough. Depth of rotary tillage, Dr, is usually between 10 and 20 cm. For most of the computations below, Dr was set at 15 cm.

RESULTS AND DISCUSSION

In the initial year of comparison (t = 0), the model predicts that both rotary and plow tillage will produce fewer seedlings than no tillage over a wide range of parameter values (Fig. 5). Only if the median depth of burial of seeds in no-till is exceptionally deep (p small), or tillage exceptionally shallow (D, or DI, small) will no-till have fewer seedlings than either of the tillage treatments. Because the behavior of the system is heavily dominated by the near-surface portion of the seed pool, depth of tillage has only a small effect on the parameter values at which tillage and no tillage are equivalent (Fig. 5). This result assumes that most seeds are near the surface before tillage. If most of the seeds were deeply buried at the outset, then emergence following tillage would probably exceed emergence without tillage.

The latter conclusion is supported by results of the model from later years. Assuming that no new seeds are added to the system, the surface seed pool in no- till becomes severely depleted by emergence and mortality. In contrast, with rotary tillage a portion of the seed pool is returned to the surface each year, and consequently the parameter conditions under which no

m= 1.0

100- t =1,a=0.2 t =2,a=0.2 t =4,a=0.2

10 RT RT RT 1 < | 1 n ~~~~~~RT nl

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~. s. .. ............... ..\. ...........................~~~~~~... ....... ................. ... ......................................... .01

.0 Z

t=1, a= 0.5 t =2, a= 0.5 t =4, a= 0.5 10 RT RT

? 1- RT ~ ~ ~~~R

.1 ~~~RT

\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.E ."'''"'... .. .

.01 NT .01 .15 1 10 .01 .1 1 10 2 .01 .1 1 t 10, 10

... ...... . ......... FIG. 6. Regions of the parametr_spacdefindbypandinhichetherntillaeorrtarytilage.poduces

in s , , ad 4, fr ss w t d y (' 1. p is te re a wh sd d y d s as a f o o" d

in~~~~~~ notlaeadi_ h aea hc emergence::::::::::::: declines: as a funtio of: seed depth. Reut ar hw_o heauso

, therae-twicsedurivlicrassaafuctonfeph..hesmll.inowin.he e of eh fI

r0a e r i dt tae fo t la (Table 1 and 4)

........ ..... . FIG 6 Reios o te praete sacedeine b p nde i wicheihernotilag orroarytilag poduesmor sedlng in ear 1,2,and4, or ees wthot drmncy(m( = ).p i th rte t wichsed dnsiy dclnesas fucton f dpt in o tllae nd isth rae a whchemegene eclnesasa fncton f eeddeph.Resltsareshwn or hre vlue o a, th rat at hichseedsurvval icreaes a a fnctin ofdept. Th. malwndwintecetr.fechfguesow.h range~~~~~~~~~.......... ofprmeesenonerdi.dt.aknfomtelieaur.Tbls1an.)


tillage has more seedlings than rotary tillage become increasingly restricted (Fig. 6). When near-surface survival is low (a = .2 in Fig. 6), rotary tillage has more seedlings by the 2nd yr (t = 1), but even when survival is nearly constant (a = 5 in Fig. 6), parameter conditions leading to more seedlings in no tillage are limited by the 5th yr (t = 4) to values of e that are at the high or low extremes of those observed (Table 1). Although the model could not be fully developed for the case of plow tillage, it seems likely that the deeper burial of seeds by plowing would make the lower emergence in no tillage appear even more quickly if that regime were contrasted with plowing. The asymptotic survivorship, /, has no effect on the parameter conditions under which tillage is more advantageous than no tillage. It does affect the relative amount of emergence when emergence is greater in one system, but that analysis is too complex for discussion here.

Seed dormancy that is not broken by near-surface conditions causes the initially greater emergence in no- till to persist somewhat longer than it would otherwise (Fig. 7). However, if near-surface mortality is even moderate, then no tillage produces fewer seedlings by year 2 (a = .5, t = 2 in Fig. 7). Note that the value of m0 of 0.4, which was used in the calculations, corresponds to 60% of the seeds remaining dormant when exposed to near-surface conditions. This is a higher dormancy rate than has usually been found in popu-

lations of buried seeds (Wesson and Wareing 1969b, Schafer and Chilcote 1970, Zorner et al. 1984), so the differences between Figs. 6 and 7 are probably extreme.

These results are only partially dependent on the form of the survival function. In year 0, seed survival is not a consideration, and after several years without tillage, the surface seed pool will be greatly reduced by emergence even if survival of nongerminating seeds is good. By analogy with the effect of changing from small to large a (Figs. 6 and 7), a shift from Eq. 4 to a function in which survival decreased with depth would probably broaden the range of e and p over which no-till produces more seedlings in years 1 and 2.

A commonly violated assumption of the model is that seedling emergence is best for seeds at the soil surface. Relaxing this assumption changes the results for year 0 substantially, since burial of seeds by tillage may then promote emergence, whereas the seeds remaining on the surface without tillage may stay dormant. This situation has occasionally been observed (Froud-Williams et al. 1984, Egley and Williams 1990). It should be most common when tillage is shallow, or seedlings are capable of emerging from great depth. Only a few large-seeded species such as Avena fatua and Echinochloa crus-galli commonly emerge in large numbers from the depth of peak seed density observed following tillage (Holroyd 1964, Rahn et al. 1968). For less robust species that still emerge better when buried,

MO =0.4

100 10 t =1, a =0.2 t =2,a=0.2 t =4,ca=0.2 10 -

1 - RT RT

iL1 - J _ - --::NT t = 1, a = 0 .5 T: .. R .. :Eji t = 2 , a = 0

.5

t = 4, a =0O. 5 . ..... ... .

~~~~~~~~~~~~~~~~~~~~~~~............ 1 0 -T 1 / 05.. /

: -"~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.'..'.-'-..,........ DT..

-,i,,,,, I RT RT

Cs 1

.1 -RT _ _

.01_ I

.0 1 .......................

1 RT RT a R:::T-'-

.01:::::>::::::::::::::::::::::-::- 1 1 10 .01 1 1 10 .01 .1

1 FG. of seed d t (in a 0.4

It - i

~~~~~~~~~~~~RT II

.01 - I_l

.01_ l l l _ l l l I~~~~~~~.......... .01 .1 1 10 .01 .1 1 10 .01 .1......1........

.... ... .... ... ... FIG.7 A.fo Fi. 6,bu fr 0%ofsedsdomat .= 4


the relative abundance of seedlings in tilled and untilled ground will depend on the balance between seed placement by the tillage implement and the emergence response, and is difficult to predict in a general way.

For species that require burial for establishment, seeds in no-till are likely to die before reaching a suitable depth for germination, unless seed survival near the surface and the natural rate of infiltration of seeds into the soil are both high. Consequently, in later years, no tillage is likely to be the less weedy regime for these species as well.

Minimum tillage with tine implements or disks produces seed distributions that are qualitatively similar to no tillage, but with greater median depth of burial (smaller p). Hence, for species with emergence response approximated by Eq. 3, the results presented in Figs. 5-7 should obtain if p is properly adjusted. In contrast, species whose emergence is improved by burial would be expected to have greater year 0 density in minimum tillage than in any other regime. With minimum tillage, most seeds will be buried deeply enough to establish, but few will be buried so deeply as to enter enforced dormancy. In later years, the seed pool is likely to be exhausted relative to both no-till and the more severe tillage regimes, and hence minimum tillage should have the lowest seedling densities of all.

If the shedding of substantial numbers of seeds into the field is allowed, then every year is like year 0, and

consequently no tillage will have more seedlings than tillage year after year. In this situation, deeper tillage regimes will tend to minimize emergence.

Comparison of model predictions (summarized in Table 5) with field studies requires careful attention to experimental procedures. For example, the distribution of seeds at the beginning of the experiment is critical, and the first observations on seedling emergence may or may not correspond to the time referred to here as year 0. Table 6 summarizes data taken from 15 studies in which (1) some information was given that indicated the initial distribution of seeds, (2) seed return to the soil was prevented, and (3) tillage occurred once per year. As indicated by the model, when seeds are mostly at the surface, deep tillage has been found to decrease emergence relative to shallow or no tillage in year 0 (Table 6A). When shallow tillage was compared with no tillage (Table 6A; Froud-Williams et al. 1984), the slight degree of burial appeared to increase seedling emergence, perhaps because the species had non-monotonic emergence responses. In year 1 the tillage regime having the highest seedling density varied greatly (Table 6). This result is also in accord with the model, which predicts that the regime with the most seedlings depends on the parameter values for the species. Again as expected, where seeds were buried or mixed throughout the soil at the beginning of the experiment, usually tilled treatments produced more

TABLE 5. Summary of consequences of tillage on relative density of weed seedlings.

Conditions Relative seedling density*

Seed return prevented Seeds do not require burial

Year 0 Seed pool mostly on surface before tillage NT, MT> RT > PT Seed pool mostly buried before tillage PT > RT > NT, MT

Year 1 Near-surface survival good and dormancy hight NT, MT > PT, RT Near-surface survival poor and dormancy lowt PT, RT > NT, MT

Later years Near-surface survival good

Dormancy high NT, MT> PT, RT Dormancy low PT, RT > NT, MT

Near-surface survival poor PT, RT > NT, MT Seeds require burial

Year 0 MT> RT > PT, NTt Later years PT, RT > NT, MT

Seed return allowed Year 0 (same as for seed return prevented)

Seeds do not require burial Seed pool mostly on surface before tillage NT, MT> RT > PT Seed pool mostly buried before tillage PT > RT > NT, MT

Seeds require burial MT> RT > PT, NTt Later years MT > NT > RT > PT * Tillage regimes: PT, plow tillage; RT, rotary tillage; MT, minimum tillage with tines or disks; NT, no tillage. Tillage

regimes separated by a comma may or may not differ in seedling density. t The outcome is affected by the combined action of near-surface survival and seed dormancy. The higher either of these

factors, the more likely it is that seedling emergence will be greater with no tillage than with tillage. t Outcome of the comparison between no tillage and plow tillage depends on position of seeds in each regime relative to

burial requirements for emergence.


TABLE 6. Comparison of seedling emergence in various tillage regimes* as reported in studies that did not allow seed input and that indicated initial position of seeds in the soil.t The experiment years considered to correspond to times t = 0, t = 1, and t - 2 are indicated.

Reference t = 0 t= 1 t - 2 Species Result Result Result

A) Seeds mostly on the soil surface Bibbey (1935) 1935

Avena fatua L. PT > NT Brassica arvensis Ktze. NT PT Thlaspi arvense L. NT> PT

Buhler and Daniel (1988) 1984, 1985 Setaria faberi Herrm. NT> TT> PT Abutilon theophrasti Medik. PT > TT > NT

Egley and Williams (1990)t: ? 1977 1978 1979, 1980, 1981 Sida spinosa L. DT z NT DT NT DT> NT Abutilon theophrasti Medik. NT> DT DT NT DT > NT Anoda cristata (L.) Schlecht. NT> DT DT NT DT> NT Ipomoea spp. NT> DT DT > NT DT NT Sesbania exalta (Raf) Rydb. ex A. W. Hill NT; DT NT DT DT NT Amaranthus spp. NT> DT DT> NT NT> DT grass DT > NT DT NT DT> NT

Froud-Williams (1983) 1980-1981 Bromus sterilis L. NT> TT> PT

Froud-Williams et al. (1984) 1977-1978 1978-1979 Alopecurus myosuroides Huds. SS NT SS> NT Agrostis gigantea Roth SS NT 0 Capsella bursa-pastoris (L.) Medic. SS NT [SS NT] Papaver rhoeas L. SS > NT [SS> NT] Plantago major L. SS NT 0 Polygonum aviculare L. SS NT SS > NT Stellaria media (L.) Vill. SS > NT SS > NT Tripleurospermum inodora L. NT SS [SS> NT] Veronica arvensis L. SS NT [SS > NT] Viola arvensis Murr. [SS > NT]

Lueschen and Andersen (1980)11 1975 1976 1977, 1978 Abutilon theophrasti Medik. NT> PT NT> PT NT> PT

Moss (1985) 1975 1976 Alopecurus myosuroides Huds.-expt. 2 NT TT> PT NT > TT PT

1977 1978 1979 - expt. 3 NT>TT>PT NT TT>PT NT>TT PT

Moss (1987) 1978-1979 1979-1980 Alopecurus myosuroides Huds. TT ; NT TT NT

Sweizer and Zimdahl (1984)? 1980-1981 Mostly Amaranthus retroflexus L. DT > PT

Wilson (1978) 1971-1972 1972-1973 1973-1974 Avena fatua L. TT PT PT TT TT ; PT

Wilson (1981)# 1975 1976 1977, 1978 Avena fatua L. NT> TT> PT PT> NT TT [PT TT NT]

Wilson and Cussans ( 1972) 1969-1970 A venafatua L.-Yarnton NT> PT

-Spelsbury PT > NT -Tackley PT > NT

Wilson and Cussans (1975) 1972-1973 Avenafatua L. TT P PT

B) Seeds buried or mixed into the soil Bibbey (1935) 1934

Avena fatua L. PT > NT Brassica arvensis Ktze. PT > NT

Chancellor (1964a) 1963 Anagallis arvensis L. PT - NT Viola arvensis Murr. PT > NT Trifolium repens L. PT z NT Senecio vulgaris L. NT ; PT Aphanes arvensis L. PT > NT


TABLE 6. Continued.

Reference t = 0 t = 1 t - 2 Species Result Result Result

Sonchus asper (L.) Hill PT NT Poa annua L. PT > NT Cerastium vulgatum L. PT> NT Raphanus raphanistrum L. PT > NT Taraxacum officinale Weber NT PT Sagina procumbens L. NT> PT Ranunculus repens L. PT > NT Polygonum persicaria L. PT> NT Juncus bufonius L. NT PT Gnaphalium uliginosum L. NT > PT Arabidopsis thaliana (L.) Heynh. PT NT

Egley and Williams (1990)? 1977 1978 1979, 1980, 1981 Sida spinosa L. NT DT DT ; NT DT > NT Abutilon theophrasti Medik. [NT > DT] [DT > NT] [DT > NT] Anoda cristata (L.) Schlecht. [NT > DT] NT> DT NT > DT Ipomoea spp. NT DT [NT : DT] DT > NT Sesbania exalta (Raf.) Rydb. ex A. W. Hill 0 [NT> DT] [DT > NT] Amaranthus spp. NT DT DT > NT [DT > NT] grass NT DT NTh DT DT > NT Trianthema portulacastrum L. DT > NT DT > NT [DT > NT] Euphorbia spp. DT : NT DT > NT DT NT Portulaca oleracea L. NT > DT NT> DT NT> DT

Froud-Williams et al. (1984) 1977-1978 1978-1979 Alopecurus myosuroides Huds. SS > NT SS > NT Agrostis gigantea Roth SS z NT SS > NT Capsella bursa-pastoris (L.) Medic. SS > NT SS> NT Papaver rhoeas L. [SS > NT] SS> NT Plantago major L. SS ; NT SS> NT Polygonum aviculare L. SS > NT NT> SS Stellaria media (L.) Vill. SS > NT NT SS Tripleurospermum inodora L. SS : NT SS> NT Veronica arvensis L. SS > NT SS NT Viola arvensis Murr. 0 SS > NT

Sweizer and Zimdahl (1984)** 1980-1981 Abutilon theophrasti Medik. PT > DT

Wilson (1985)tt "yr 0" "yr 1" "yr 2 and 3" Avenafatua L. TT > PT PT > TT PT > TT * Tillage regimes: PT-plow tillage, or its equivalent with a spade; NT-no tillage; TT-tillage with a tine implement or

chisel plow; DT-tillage with disks; SS-shallow hand-stirring of the soil. t Treatments were considered approximately equal if the difference was not statistically significant, or, in the absence of

statistics, if the weedier treatment had <50% more seedlings. Comparisons in brackets appeared to be based on a small number of seedlings. The treatment with the largest density of seedlings is always listed first. A zero indicates that no emergence was observed in either treatment, and ... indicates that no data were taken for that species during the year.

: Seeds plowed in and then additional seeds sown on the soil surface. ? Disked to 15 cm. II PT = one-plowing continuous fallow, NT = untilled chemical fallow. ? Annual plowing followed by unrestricted seed production occurred for three years, and then the tillage treatments were

applied. # Seeds mixed into the top 5 cm. ** Seed production was prevented for six years and the soil was plowed annually; then the tillage treatments were applied. tt Based on autumn censuses summed over three starting years of the experiment.

seedlings than untilled or shallowly tilled treatments during year 0 (Table 6B). Few studies examined emergence beyond year 1, but as expected, those that did generally found either no difference between tillage treatments, or more seedlings with deep tillage (Table 6).

Many important studies of tillage effects on weeds did not meet the criteria for inclusion in Table 6. For example, Chepil (1946) found average emergence over a 5-yr period to increase as tillage decreased. Zorner et al. (1984) calculated that emergence of Avenafatua

would increase with increasing depth of tillage due to high mortality near the soil surface, but they assumed that all germinating seeds produced seedlings. In studies where soil disturbance was repeated several times each year (Brenchley and Warington 1933, Roberts and Dawkins 1967, Roberts and Feast 1972, 1973a, b, Ogg and Dawson 1984, Warnes and Andersen 1984), seedling emergence usually increased, probably due to improved physical conditions and exposure of a larger proportion of seeds to the near-surface environment. This important finding neither supports nor refutes the


model, but is generally compatible with its assumptions and results.

As predicted in Table 5, most studies in which reseeding has been allowed have found higher weed densities in reduced tillage (Bond et al. 1971, Wrucke and Arnold 1985, Cardina et al. 1991, Teasdale et al. 1991, Mohler and Callaway 1992). Several studies found higher densities of grass weeds in reduced tillage, but more broadleaf weeds with plowing (Jones 1966, Pol- lard and Cussans 1976, 1981, Froud-Williams et al. 1983b). Since broadleaf weeds tend to survive better in the soil than grass weeds (Lewis 1973), they may be able to persist better than grasses when the soil is plowed.

Many studies have used measures of weed abundance other than density (Dunham et al. 1958, Roberts 1963b, Kapusta 1979, Wilson et al. 1986, Buhler and Oplinger 1990, Mohler 1991), or have compared mul- tifaceted reduced tillage systems with conventional plowing (Wallace and Bellinder 1989, 1990). Most of these studies have found more weeds in reduced tillage treatments, but some found no difference or variable results depending on the species (Dunham et al. 1958, Wallace and Bellinder 1989, Buhler and Oplinger 1990).

Results of the model as a whole (Table 5) indicate strategies for dealing with infestations of weed seeds. When a great abundance of seeds is thoroughly mixed with the soil, probably the best approach will be to use no, or minimum tillage, and attempt to deplete the surface fraction of the seed pool. If this approach is to be effective, then reseeding must be prevented, for example through use of herbicides or by shallow cultivation. Repeated superficial cultivation has the additional benefit of promoting germination and thereby speeding decline in the number of seeds close enough to the surface for emergence. In contrast, when con- fronted with a year of weed control failure in which many seeds are shed onto the surface of an otherwise clean soil, the best strategy will be to plow as deeply as possible, and then use minimal soil disturbance methods thereafter. The effectiveness of this approach has been demonstrated by Moss (1985).

Although some results of the model could have been predicted without resort to mathematics, the model has revealed some effects of tillage that would not be apparent otherwise. In particular, the complexities of the relation between depth of seed burial in no-till, emergence as a function of depth, and near-surface seed survival would have been difficult to unravel without the model, particularly for years 1 and 2 (Figs. 6 and 7). Similarly, the finding that the effect of minimum tillage on the seed pool is more like no-till than like plow or rotary tillage probably would not be predicted without consideration of the form of the seed distribution functions for the various regimes. Moreover, the rigor of relating published studies to the systematic structure provided by the model reveals similarities and differences among studies that would otherwise be obscure (Table 6). Finally, the model focuses attention

on the important role that knowledge of initial vertical distribution of seeds plays in studies of tillage effects on weed populations. Relatively few tillage studies have quantified or controlled for the vertical distribution of seeds, yet this may be the most important factor de- termining relative weediness of tilled and untilled plots in a field.

ACKNOWLEDGMENTS I thank M. Pacenza, M. Santos, and J. Chung for assistance

in preparing the manuscript, C. Castillo-Chavez for early ad- vice on the structure of the model, and P. Karieva, K. Ma- loney, M. Santos, and an anonymous reviewer for comments on the manuscript. This work was supported by Hatch funds (Regional Project NE-92, NY(C)- 183458 from the New York State Agricultural Experiment Station.

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