1Simulation and analytical models were developed for gorse Ulex europaeus. The simulation model incorporated spatially local density−dependent competition, disturbance, asymmetric competition between seedlings and established plants, a seed bank, local seed dispersal, an age structured established plant population, and temporal variation in the probability of disturbance. The analytical models were simple approximations of the simulation.
2The models extended our previously published model for Scotch broom Cytisus scoparius to include large−scale disturbances and possible management options, such as the use of fire, herbicides and oversowing with perennial grasses. Fire was assumed to influence established plant mortality, seed survival in the seed bank, and the probability of germination.
3We reviewed published data on the demography of gorse in New Zealand, the current management techniques, and the ongoing biological control programme.
4Over a wide range of biologically reasonable parameter values, the analytical models accurately predicted the outcome of the simulations. The analytical models worked well, providing gorse occupied a high proportion of the available sites and large−scale disturbances did not occur too frequently.
5The potential impact of seed−feeding biological control agents on gorse abundance was assessed, using the models, for several environmental and management scenarios. In particular, we explored how large−scale disturbance, such as fire and herbicide application, influences the outcome of biological control.
6The success of a biological control programme was found to depend critically on the frequency and intensity of disturbance, whether disturbed sites became suitable for recruitment, and the effects of disturbance on germination and seed mortality.
7The models highlight the need to manage recruitment opportunities carefully in order to maximize the effect of biological control agents. The models also indicate that details of plant population biology can have a profound effect on the success of any management strategy.
Gorse Ulex europaeus L. Fabaceae is native to Europe but is most common on the western European seaboard from northern France to Portugal (Tutin et al. 1968). Gorse is a spiny shrub that is characteristically associated with heathland vegetation in Europe, but commonly invades neglected land and forests. It has become naturalized in many temperate countries around the world, and is regarded as a serious weed in New Zealand, Chile, Hawaii, North America and Australia (Richardson & Hill 1998). Gorse was recognized as an important weed in New Zealand as early as 1859 (Thomson 1922) and is now present on at least 3·5% of New Zealand's land area (Thomson 1922).
Gorse readily invades disturbed ground and can form dense impenetrable thickets. It can suppress plantation forests, exclude grazing animals from pastures, and increase the risk of fire in native habitats and urban areas. If left undisturbed for 20–30 years, gorse can be replaced by longer−lived plant species (Wilson 1994) but fire or other major disturbance often rejuvenates gorse populations within this period. Because it is such an important weed (Hill & Sandrey 1986), there has been considerable research in New Zealand into the improvement of gorse control using herbicides, grazing management and fire, both separately and in combination (Gaynor & MacCarter 1981). Much of the ecological information summarized in this paper has been derived from these studies.
First, we briefly describe the biological control programme for gorse and the current management methods. We then introduce the basic population biology of gorse and develop a series of models. We use the models to explore the factors influencing the proportion of sites occupied by gorse. The models are extensions of our previously published models for Scotch broom (Rees & Paynter 1997). The previous models assumed that disturbances were essentially plant sized, whereas many types of disturbances, for example fire and herbicide application, act over much larger areas, and so we have extended the models to allow for this. We achieved this by assuming the probability a site becomes disturbed varies from year to year. In years when there is a large−scale disturbance, sites have a high probability of becoming disturbed. However, in years with no large−scale disturbance the probability of disturbance is low. Simple analytical approximations are developed to allow the results of the simulation studies to be interpreted. These approximations allow us to understand the main demographic processes determining the proportion of sites occupied by gorse, and hence the conditions under which gorse might become a serious environmental weed. The potential impact of seed feeders on the proportion of sites occupied by gorse is then calculated under a range of different environmental and management scenarios. The implications of these results for the management of gorse populations are discussed.
Overview of the biological control programme
Attempts to control gorse biologically are continuing. Exapion ulicis Forst. was the first control agent released in New Zealand, in 1931. This univoltine weevil commonly destroys over 90% of seeds formed in spring, but because gorse also sets seed in autumn the annual seed crop is probably reduced by only 35–50% (Cowley 1983) (Table 1). The bivoltine tortricid moth Cydia succedana (Denis & Schiffermüller) was released in 1992 to augment seed predation (Harman et al. 1996), and has established widely. The impact of this insect has been assessed at only one site, but at that site the two seed predators reduced the annual seed crop by up to 90% (T.P. Partridge, R.L. Hill & A.H. Gourlay, unpublished data).
Table 1. Estimated impact of Exapion on seed production at six sites in New Zealand (South Island) (R.L. Hill, unpublished data)
Proportion damaged by Exapion
Seeds per pod
Seed rain m−2 1996
Potential seed rain excluding Exapion 1996
Seed rain m−2 1995
Hoon Hay Valley
Five control agents that attack gorse foliage were introduced between 1989 and 1996 (Harman et al. 1996). It is too early to judge the fate of Agonopterix ulicetella (Stainton) (Oecophoridae), Scythris grandipennis (Haworth) (Scythrididae) and Pempelia genistella (Duponchel) (Pyralidae), but the gorse spider mite Tetranychus lintearius Dufour, Tetranychidae, and gorse thrips Sericothrips staphylinus Haliday, Thripidae, are now widely established in New Zealand. A coccinellid predator appears to regulate mite populations (R.L. Hill, L.M. Hayes & A.H. Gourlay, unpublished data) but large colonies remain common and can cause severe damage to gorse plants (Partridge, in press). Thrips produce large populations in culture, and commonly kill potted plants. Pot trials have demonstrated impacts on seedling growth even at low density (P. McGregor & P. Peterson, unpublished data) but the long−term impact of thrips on gorse plants in the field is not yet known. Neither control agent has caused noticeable mortality of mature gorse plants in the field. However, the classic insecticide–exclusion experiment conducted by Waloff & Richards (1977) suggests that insect herbivores caused a 50% increase in mortality in Cytisus scoparius over a 10−year period. Such effects of foliage−feeding insects may reduce the maximum age of gorse plants, seed production and probability of recruitment, in addition to influencing the probability of gaps appearing in the canopy.
The management of gorse populations
Until recently, fire was the most important method used to remove gorse and reduce the number of seeds in the seed bank. The effects of fire were enhanced by desiccation with herbicides or crushing to reduce stem moisture content. Burning leaves stumps that can resprout, but carefully managed fires can result in almost complete mortality (Chater 1931). In plantation forestry, the standard method for land preparation is to spray with herbicide, burn, and then spray the regenerating gorse after 1–2 years (Balneaves & Zabkiewicz 1981). Conducted well, this regime can destroy over 60% of seeds in the soil (Rolston & Talbot 1980) and reduce gorse densities to a point where there is no significant competition with tree seedlings.
Gorse seedlings compete poorly with perennial pasture plants such as Lolium perenne and Trifolium repens (Thompson 1974; Ivens 1983) and so, rather than spraying a second time, gorse control in pasture, after burning, is achieved by oversowing with perennial pasture plants and fertilizer, to promote competition with the emerging gorse seedlings. Gorse establishment can be reduced further by grazing the sward once it is well established, using sheep (West & Dean 1990). Ivens (1979) measured 70–100% reduction in the number of gorse seedlings because of competition, grazing and trampling.
Biology of gorse
Seed production, dispersal and survival
Ulex europaeus is a polycarpic perennial shrub that can flower 2–3 years after germination. Reproductive buds form in late summer, and flowering can occur from autumn to spring, depending on climate. The relative amount of seed set in autumn and spring varies from site to site and from year to year (Hill et al. 1991). Most seeds fall in spring, often in two peaks reflecting the time of seed set. Estimating seed production by measuring how much seed falls to the ground is confounded by the ubiquitous but variable impact of gorse seed weevil (Exapion ulicis). Most estimates in the literature do not account for this. In one study, seed rain was measured at 1392 seeds m−2, but corrected for losses to the weevil, annual seed production was estimated to be 23 205 m−2. Corrected estimates for annual seed production range from 442 m−2 to more than 36 741 m−2 (R.L. Hill, unpublished data) (Table 1). A few seeds can be dispersed 5 m from the parent plant (Moss 1959), but Hill et al. (1996) found that 39% of seeds fell within the plant canopy and 56% fell within 1 m of the centre of bushes. A small proportion of seeds probably disperses over longer distances by water, wind, on grazing animals and on machinery (Moss 1959). Ants disperse seeds in Europe (Chater 1931).
Gorse seeds are hard−coated and substantial seed banks can accumulate under parent plants. When interpreting the data given below it is important to remember that Exapion destroys between 35% and 50% of seed production, and so seed bank density should be increased by a factor of c. 1·5. The distribution of seeds in the soil has been measured many times, and approximately 75% of all seeds are found in the litter and the top 5 cm (Moss 1959; Ivens 1978; Zabkiewicz & Gaskin 1978). The size and behaviour of seed banks varies greatly. Chater (1931) recorded 44 seeds m−2 in close−turf plots, through which seeds could not penetrate, but 11 100 seeds m−2 in plots where there was a litter layer. Other instantaneous measures of seed bank density include 2070 seeds m−2 (Ivens 1978) and 133–20 742 seeds m−2 (mean = 5446; Zabkiewicz & Gaskin 1978). Partridge et al. (in press) showed that the seed bank under a 6−year−old patch of gorse declined by 45% (17 600 to 9600 m−2) during autumn and winter in one year, but recovered to 1·4 times the original level after the next seed fall. Ogle−Mannering (1995) recorded 56–21 730 seeds m−2 in sites of different age and vegetation cover. Moss (1959) estimated the survival of gorse seed in the seed bank by measuring the number of seeds present in pastures that had been free of gorse for different periods. Seed density in the top 5 cm ranged from 3322 m−2 in the field that had been free of gorse for 1 year, to 21 m−2 in a field that had been free of gorse for 26 years. No seed was recovered from the site where gorse had been absent for 28 years. R.L. Hill, A.H. Gourlay & R.J. Barker (unpublished data) measured the decline of the seed bank directly at three sites in New Zealand by recovering bags of buried seed and assessing survival over 10 years. At two sites, the seed bank was predicted to decline to 1% of its original level within 20 years (similar to the estimate provided by Moss 1959). However, at the third site seeds were predicted to remain viable for many decades.
Seeds are lost from the seed bank by germination or death, and it is difficult to isolate the relative influence of these processes (Rees & Long 1993). R.L. Hill, A.H. Gourlay & R.J. Barker (unpublished data) found that stored gorse seed and intact seed recovered from the soil both remained viable for at least 10 years, implying that losses were largely due to germination rather than seed death. Seed bank losses suggested by R.L. Hill, A.H. Gourlay & R.J. Barker (unpublished data) and by Moss (1959) imply a loss of approximately 20% of seeds from the seed bank annually. Popay & Adams (1990) found that emergence of seedlings ceased after 7, 7·5 and 9 years in cultivated, sprayed and vegetated sites, respectively, implying annual losses approaching 50%. Seeds can become buried as deep as 15 cm, but cannot germinate successfully from deeper than 5 cm (R.L. Hill & A.H. Gourlay, unpublished data) without major soil disturbance. Ivens (1982) measured emergence of seedlings in a cleared plot, and found that 25% of all seeds germinated or disappeared from the seed bank within 20 months, leaving a large, deeply buried, reserve capable of germinating later.
Studies consistently show that gorse seedlings survive poorly in competition with pasture grasses (Thompson 1974; Ivens 1979; Ivens & Mlowe 1980). Ivens (1978) found that 350 seedlings m−2 emerged over 16 months in plots initially cleared of vegetation, but mortality over that period was 41% and this increased as competing vegetation invaded the site. In undisturbed gorse plots, 170 seedlings m−2 were recorded and mortality was 70%. Seedlings surviving in the shade of bushes were etiolated, and were only 1% of the biomass of those in the open (Ivens 1978). Partridge et al. (in press) removed gorse plants from three sites with minimum disturbance to the litter and soil surface. Gorse germinated well at all sites, but the yearly survival varied; in two sites survival was 0–2% and 0–0·5%. Competition from grasses was thought to be the major mortality factor. At the third site, grasses were uncommon, and seedlings survived well until self−thinning became evident after 12 months. The role of interspecific competition was examined in a field experiment where 295–593 seedlings m−2 survived in plots that were burnt, cleared of litter or weeded, compared with 2 m−2 in control plots where competing vegetation flourished (Partridge et al., in press). Seedlings are also susceptible to drought. Chater (1931) found that 45% of marked seedlings survived to 10 months, and that 48% of the mortality was attributable to desiccation.
Grazing generally increases gorse seedling mortality. Rolston & Seneiro−Garcia (1974) found that grazing of gorse seedlings did not necessarily cause death, but Chater (1931) observed that herbivory resulted in the death of seedlings when in competition with grasses. Hartley & Thai (1979) found that seedling survival over winter fell from 15% to 0·85% if plots were grazed. Rather than creating microsites for further germination, trampling by grazing stock can result in additional seedling mortality (Hartley et al. 1980; Ivens & Mlowe 1980). Ivens (1982) found the maximum density of gorse seedling (618 m−2) occurred in plots that were burnt, sown with grasses and grazed, but after 20 months only 6% of these seedlings remained. In plots bared by root raking, then oversown with grasses but not grazed, 17% of the initial seedlings survived 20 months.
Senescence, mortality and regeneration
Gorse is known to follow the −3/2 law of self−thinning (Wilson & Lee 1988). A study of stand structure in gorse thickets of different ages showed that stem density declined from 32 to 6 stems m−2 over 15 years, when the stand was considered to be mature (Lee, Allen & Johnson 1986). Beyond 20 years, stem density fell to about 2 stems m−2. Gorse can grow to 7 m tall in New Zealand, but is more commonly 2–4 m tall. Gorse tends to grow in even−aged cohorts, and recruitment under mature plants is not common. Lee, Allen & Johnson (1986) found some gorse seedlings under gorse of all ages, but the density peaked, at a mean of 20 seedlings m−2, in the 26–30 years class. Seedling density was lowest in the 6–10 years age class. Ivens (1982) found only 130 seedlings m−2 under undisturbed gorse where the seed bank exceeded 10 000 seeds m−2. Poor seedling germination under gorse plants has been attributed to shading and interception of rain by overhanging gorse plants (Ivens 1982). Recruitment is more common once gaps appear within the gorse thicket, through the senescence of individual gorse plants or large−scale disturbance, such as fire.
Little is known about how long gorse plants survive. Chater (1931) counted the growth rings in dead and dying gorse in England, and found that the plants were up to 30 years old. Similarly, Lee, Allen & Johnson (1986) estimated that the maximum age of plants in Otago (New Zealand) was 29 years. Druce (1957) found no gorse in vegetation plots that had been undisturbed for more than 34 years, and although Kelly (1965) found one plant aged 39 years, he considered that 25–30 years was a more typical estimate. Egunjobi (1969) found that gorse made up only a small fraction of the living biomass on a site that had been undisturbed for 33 years. In the north of New Zealand, gorse can grow 0·5–1 m annually, and the maximum age of plants in warmer regions may be lower than those estimated in cooler climates.
Baseline population parameters
Using these data we derived a baseline parameter set that is representative of gorse populations in New Zealand. This was used in population models to explore the key parameters controlling the proportion of sites occupied by gorse and to assess the potential impact of biological control agents and their possible interaction with various management strategies. Each site in the model was assumed to be 1·5 × 1·5 m in area, approximately the size of a mature plant. A description of the model is given in the next section. We set the maximum plant age, Amax, to 30 years and the minimum age for reproduction, Amin, to 2 years as suggested by the data. The per site fecundity was set at 20 000 seeds year−1. This estimate was based on the average seed production per m2 observed by R.L. Hill (c. 10 000; Table 1), multiplied by the area of a site (2·25 m2). Approximately 60% of seeds produced fall within 1 m of the centre of a bush, and so the proportion of seeds retained within the parental site, fh, was set at 0·6. The remaining 40% of seeds were equally distributed between the eight surrounding sites. The probability a seed was lost from the seed bank, d, was set at 0·2, in agreement with the studies of R.L. Hill, A.H. Gourlay & R.J. Barker (unpublished data) and Moss (1959). The probability of a seed becoming a seedling, g, was difficult to estimate from the published data as few studies quantified the viable soil seed population and the proportion of these that become seedlings. Therefore, in line with the data presented in Ivens (1982) and studies of similar leguminous shrubs (Rees & Paynter 1997), we set the probability of a seed becoming a seedling at 0·03. The probability a site became suitable for gorse colonization after senescence, pso, was set at zero. We did this for three reasons: (i) in undisturbed habitats gorse is often excluded after 30 years (Druce 1957; Lee, Allen & Johnson 1986; Wilson 1994); (ii) few seedlings are recorded under gorse canopies (Ivens 1982; Lee, Allen & Johnson 1986); and (iii) gorse seedlings have low survival when in competition with pasture grasses (Thompson 1974; Ivens 1979; Ivens & Mlowe 1980). The probability a seedling survives to the end of the first year is highly variable and so two values were used, s = 0·5 and s = 0·01. In the models that follow these parameter estimates were used. However, extensive simulation studies (not reported) indicated that all the main results were robust to biologically reasonable changes in the model parameters; see Rees & Paynter (1997) where an extensive sensitivity analysis of a similar model was presented.
Introduction to the models
The model uses a coupled map lattice formulation that allows a simple representation of a spatially explicit population (Crawley & May 1987; Hassell, Comins & May 1991; Durrett & Levin 1994) and is described in detail in Rees & Paynter (1997). Specifically, we assume there are a large number of identical sites; each is 1·5 × 1·5 m, the approximate size of an adult gorse plant (R.L. Hill, personal observation). The sites are arranged in a square lattice with wrap−around margins. This means that seeds dispersed from one edge of the plot land on the opposite side; in this way all sites within the lattice are equivalent. In all numerical simulations, a grid of 75 × 75 sites is used. Numerical quantities estimated from the simulation model are, unless otherwise stated, arithmetic means of the last 200 years of a 500−year simulation. Each site can be in one of three states, occupied by gorse, unsuitable for colonization by gorse, or open and so suitable for colonization by gorse. Sites that are unsuitable for gorse colonization are assumed to contain native vegetation. In each year events occur in the following order (steps).
1Sites, irrespective of their state, become disturbed with probability pdist.
2Gorse seeds germinate at each site, resulting in a Poisson distribution of recruits at time t in site i, j with mean:
where g is the probability a seed becomes a seedling, s is the probability a seedling survives to the end of the first year, and Sti,j is the number of viable seeds in the site. We use a Poisson distribution here to model effects of demographic stochasticity (May 1974).
3The number of seeds in each site is reduced according to the decay probability, d, so:
The parameter d subsumes all sources of loss from the seed bank and so d is always greater than or equal to g.
4If a site is disturbed and the number of recruits is greater than zero, then gorse successfully recruits at that site. By setting the site dimensions so that it can accommodate a single adult gorse plant, we assume the law of constant yield (Harper 1977) holds over all densities, and so avoid having to track the number of recruits at each site. All gorse recruits that occur in undisturbed sites (i.e. those already occupied by gorse or unsuitable) are assumed to die in their first year.
5Disturbed sites, which have not been colonized by gorse, become unsuitable for colonization as the ground cover recovers from the disturbance.
6Sites containing plants older than the minimum age for reproduction, Amin, produce F seeds and these are dispersed locally. Some fraction, fh, of seeds produced is retained in the parental site, and the rest are dispersed equally to the eight neighbouring sites.
7Plants older than Amax senesce and these sites become open, and so suitable for gorse recruitment with probability pso, otherwise the site becomes unsuitable.
8Plants grow older.
For a discussion of these assumptions and extensions to the model, see Rees & Paynter (1997). The computer simulation is spatially explicit, and incorporates spatially local competition, asymmetric competition between seedlings and established plants, local seed dispersal, a seed bank and an age structured established plant population, and so is a realistic description of the known population biology of gorse.
The age structure of the gorse population follows a truncated geometric distribution (Rees & Paynter 1997); specifically, let zx be the fraction of gorse plants aged x, then:
For examples of the use of this probability distribution see Rees & Long (1992, 1993). Two summary statistics of this distribution are required in the models; these are the fraction of gorse plants aged Amax, denoted zmax, and the fraction that are reproductive, denoted fr, which is given by.
An approximate analytical model
In order to determine the main factors influencing gorse abundance, we extended the approximation methods developed in Rees & Paynter (1997). Here we briefly describe the non−saturation approximation, developed in Rees & Paynter (1997), for the proportion of sites occupied by gorse, and then extend this approach to incorporate the effects of large−scale disturbances. Equations describing the simulation assume that the system is censused after the senescence of plants (i.e. step 7 in the simulation model). We describe the system using four variables: the fraction of sites occupied by gorse at time t, Gt; the fraction of sites that are unsuitable for gorse establishment, Ut; the fraction of open sites, Ot; and the average number of seeds per site, St. In order to construct the model we need to calculate the probability an open site gets colonized, assuming (i) it previously contained a reproductive gorse plant, pgc, and (ii) it did not contain a reproductive gorse plant, pngc. Details of these calculations are given in Rees & Paynter (1997).
We can then derive a set of equations that ignores details of the spatial arrangement of gorse plants and, instead, uses the fraction of sites occupied. This is known as a mean field approximation, hence:
where pdist is the probability of disturbance, zmax the fraction of gorse plants in the maximum age class, pso the probability that a site which contained a senescent plant (i.e. one of maximum age) becomes suitable for recruitment following senescence, and fr the proportion of gorse plants of reproductive age. Details of the derivation of these equations are given in Rees & Paynter (1997).
Although it is not possible to obtain an analytical expression for the equilibrium proportion of sites occupied by gorse, this can be calculated numerically. However, when all disturbed sites are colonized, we obtain:
Hence, the fraction of sites occupied by gorse when all open sites are colonized is set by the probability of disturbance, pdist, the probability a site becomes suitable for colonization after senescence, pso, and maximum plant longevity, Amax. As maximum longevity becomes larger so zmax becomes smaller and G* approaches unity. Note, even when all open sites can be colonized, the proportion of sites occupied at equilibrium is still less than one, providing plants have finite longevity. This equation provides a useful upper bound on the proportion of sites occupied by gorse. Once the equilibrium proportion of sites occupied by gorse, G*, has been calculated the equilibrium seed bank, S*, can be determined using:
Assuming pso = 0, we can simplify equation 5 to give:
With the baseline parameter set and setting pdist = 0·05 we obtain, using equation 7, G* = 0·79, and numerical solution of equation 4 gives G* = 0·79. Clearly, this approximation solution, equation 7, is extremely accurate. Numerical solution of the simulation model gives G* = 0·77; as shown by Rees & Paynter (1997), this approximation scheme is accurate providing seed production and the proportion of sites occupied by gorse is high.
Detailed validation of this model is not possible because of the simplistic way in which space, and within−site competition, is modelled. However, the biological assumptions used to construct the model are in agreement with the known population biology of gorse. In addition to this, using the baseline parameter set, assuming pdist = 0·05 leads to a predicted seed bank density of 30 000 m−2, in agreement with several studies that have found c. 20 000 seeds m−2 (correcting for Exapion gives 1·5 × 20 000 = 30 000 m−2; equation 6).
This simple model assumes that disturbances act at the level of the individual plant (i.e. each site in the model). For gorse in many habitats, this seems unlikely as fire and large−scale disturbances, such as herbicide application, occur. In order to understand how these influence gorse dynamics, we assumed that the probability of an individual site being disturbed, pdist, varied from year to year. Specifically, we assumed that in some years large−scale disturbances occur, independently at random, with probability pLdist. In these years, the probability of an individual site being disturbed is pdistL. However, when there is no large−scale disturbance then the probability of disturbance is pdistnL. By setting pdistL to some large value, say 0·95, and pdistnL to a low value, say 0·05, in years when large−scale disturbances occur 95% of all plants die, whereas in years with no large−scale disturbance only 5% die. The age structure of the gorse population, with large−scale disturbances, also follows a truncated geometric distribution, but with zx given by:
where for notational convenience φ = (1 – pLdist)(1 –pdistnL) + pLdist(1 – pdistL). We compared the simulation results with the solution of equation 4, by calculating the average value of pdist, which is:
The results of the simulation, using the baseline parameters, are shown in Fig. 1. When large−scale disturbances occur infrequently, the model converges to the model described above, and G* ≈ 0·8 as expected. As the probability of a large−scale disturbance increases, G* rapidly increases to near complete occupancy. Only with very frequent large−scale disturbances does the population become extinct. This leads to the prediction that gorse should occur with almost complete cover, or be absent; this is in agreement with field observations (R.L. Hill, personal observation). The approximation provides an accurate description of the simulation results providing the probability of a large−scale disturbance, pLdist, is not too large. This approximation ignores (i) the detailed spatial structure of the gorse population and (ii) the effects of non−equilibrium age structure. The assumption of an equilibrium age structure means that there are always reproductive gorse plants present in the population, whereas in the simulation model this may not be the case. Because of this, the analytical model overestimates the proportion of sites occupied. Thus, there will inevitably be discrepancies between the simulation and analytical results. However, it is encouraging that a good understanding of a complex spatial simulation model, incorporating temporal variation in one of the main demographic parameters, can be understood using simple approximations.
Assessing the potential impact of seed−feeding biological control agents
We assessed the potential impact of seed feeders on the abundance of gorse for two levels of seedling survival, 0·5 and 0·01, with 50%, 75% and 95% seed destruction over a range of disturbance regimes. The results of the simulation and analytical approximations are shown inFig. 2 and Fig. 3. In each case, the analytical approximation accurately describes the proportion of sites occupied by gorse providing pLdist is not large. With high seedling survival, s = 0·5, seed feeders have very little impact on gorse abundance (Fig. 2), but when seedling survival is low, s = 0·01, seed feeders can have a dramatic impact on the abundance of gorse (Fig. 3). As in the previous models for broom (Rees & Paynter 1997), we find there is an interaction between disturbance regime and the impact of biological control agents. At high levels of disturbance, the gorse population becomes dominated by young pre−reproductive plants, and so the population becomes seed limited as few plants produce any seed. Under these conditions seed feeders have their greatest effect.
In this model, we have assumed that large−scale disturbances only affect the parameter pdist, which determines the probability of survival of gorse plants. However, fire also kills seeds in the soil and can result in over 60% seed mortality, providing the fire is well−managed (Rolston & Talbot 1980). To incorporate this effect we included an additional seed mortality, before seed germination in the model (i.e. step 2), in years when there was a large−scale disturbance (i.e. fire). The probability of fire−induced seed mortality was set at 0·4. This gives an overall probability of a seed being lost from the seed bank of c. 0·5 in years when there is a fire. We set the fire−induced seed mortality at 0·4 because, although higher rates of mortality have been reported in the literature (Moss 1959; Zabkiewicz & Gaskin 1978; Rolston & Talbot 1980), these only occur if the fire is well managed and in many situations this will not be the case.
The results of the simulation studies are shown in Fig. 4 and Fig. 5. As expected, the additional fire−induced seed mortality makes it more difficult for gorse to persist, particularly when fires occur frequently. The impact of biological control agents is negligible when seedling survival is high (s = 0·5; Fig. 4). However, when seedling mortality is high (s = 0·01; Fig. 5) seed−feeding biological control agents can have a dramatic impact on the abundance of gorse (compare a and d in Fig. 5).
The final effect of fire on gorse population dynamics incorporated into the model, was to allow for fire−induced germination. Several studies have shown that fire can enhance germination (Moss 1959; Rolston & Talbot 1980; Rees 1997) and theoretical studies have shown that this germination behaviour can promote persistence (Rees & Long 1992). We incorporated this effect by setting the probability that a seed becomes a seedling, g, to 0·2 in years when there was a fire. This means the probability a seed is lost from the seed bank, d, also needs to be adjusted. Assuming germination acts before seed mortality the parameter, d, may be written as:
where d′ is the probability of seed mortality. In the baseline parameter set we assumed g = 0·03; this gives d′ = 0·175. If we increase the germination probability, while keeping d′ fixed, then the probability a seed is lost from the seed bank can be calculated using equation 10. If g = 0·2 and d′ = 0·175, then, using equation 10, we obtain d= 0·34. The effects of fire−enhanced germination are twofold. First, increasing g reduces the proportion of seeds that die in the seed bank because the time spent in the seed bank is reduced. Secondly, because fire creates open sites suitable for colonization, increased germination after a fire increases the chance of a seed germinating in an open site, which increases the probability of successful recruitment (Rees & Long 1992). Both these effects tend to promote population persistence and so make biological control, using seed feeders, more difficult. These effects are seen in Fig. 6 and Fig. 7 where, as expected, fire−promoted germination increases the proportion of sites occupied by gorse. The effect, however, is relatively slight when seedling survival is high (Fig. 6) but becomes more pronounced at low seedling survival (Fig. 7). The impact of biological control in this scenario is also reduced (compare a and d in Fig. 7).
We explored the effects of herbicide application:
1assuming oversowing with perennial grasses resulted in either 90% or 50% of sites becoming unsuitable for gorse recruitment, where herbicide resulted in gorse mortality; and
2with and without grazing, which we mimicked by setting the probability a seedling survived the first year at either 0·5 or 0·01.
In addition, we assumed herbicide application resulted in 95% mortality and had no effect on germination or seed survival in the seed bank. The results of the simulation studies are shown in Fig. 8 and Fig. 9. As expected when the probability of a large−scale disturbance (i.e. herbicide application), pLdist, is small, the results of the simulations converge, with G* ≈ 0·8. When seedling survival is high, reductions in plant fecundity have little effect on gorse abundance (Fig. 8); however, under these circumstances herbicide application and oversowing can have a dramatic effect on gorse abundance. If herbicide application is combined with grazing, resulting in low seedling survival (s = 0·01), then seed feeders can have a substantial effect on gorse abundance (Fig. 9).
The models demonstrate how the qualitative behaviour of a complex simulation model can be understood by developing analytical approximations (see Figs 2 and 3). The approximations and simulation results demonstrate that in environments where gorse produces many thousands of seeds, the key parameters controlling gorse abundance are: (i) the average rate of disturbance (equation 9); (ii) maximum longevity; and (iii) the probability that a site becomes suitable for gorse colonization after senescence (equation 5). In environments where gorse produces few seeds, say as a result of seed−feeding biological control agents, then all factors influencing recruitment become important (i.e. seed bank decay, probability a seed becomes a seedling, and the probability of seedling survival). Under these conditions, the simulation model is required to evaluate the potential effects of biological control agents.
This study and our previous work on broom (Rees & Paynter 1997) clearly illustrates the importance of modelling disturbance regimes when trying to understand the management of weed populations. Disturbance affects many critical aspects of plant population biology and the way it is modelled can have a profound effect on the conclusions drawn. For example, if disturbance acts to both kill plants and create suitable conditions for establishment, then low rates of disturbance result in small population sizes, as establishment is rare. At high rates of disturbance, the population is driven to extinction as few individuals survive to reproductive age (Rees & Paynter 1997). In contrast, if disturbances only create suitable conditions for establishment then population size increases with the rate of disturbance (Rees & Paynter 1997). There are also important interactions between disturbance and other aspects of demography, such as seed survival in the seed bank and germination.
In the models presented, we have assumed that disturbance acts on one of two scales: the individual plant or entire habitat. In years when a large−scale disturbance does not occur, we assumed that each site in the habitat has some small probability of being disturbed. When large−scale disturbances occur, all sites within the model have an increased probability of disturbance. These large−scale disturbances could be the result of fire or herbicide application. Clearly there are other ways in which disturbance could be modelled. For example, we could have disturbances of different spatial extents, say affecting several contiguous sites. However, experience with the model suggests that when gorse occupies a high proportion of the sites then spatial effects become unimportant and average levels of occupancy provide a good description of the system. When gorse is rare then spatial effects can become important, as areas within large disturbances cannot be colonized, so making persistence more difficult.
The modelling results presented suggest that seed feeders can play a useful role in the management of gorse populations. However, in order to obtain the greatest impact, biological control must be used as part of an integrated control programme, with implementation of management practices that kill plants, prevent or substantially reduce subsequent recruitment and reduce seedling survival. Using fire to kill gorse stands will often increase gorse abundance, as it creates ideal conditions for recruitment (Fig. 2). It seems unlikely that fire alone will allow efficient management of gorse populations because it takes several years for stands to develop enough litter and dry stems to allow a fire to burn. However, if fire is used in conjunction with management practices that reduce seedling survival, then burning sites on average every 5 years can have a dramatic effect on gorse abundance (Fig. 7).
The use of fire in conjunction with biological control is complicated because fires kill seeds in the soil and increases seed germination, in addition to killing plants and biological control agents. Obviously increasing seed mortality makes it more difficult for gorse populations to persist and favours biological control with seed feeders. Increased germination has the opposite effect as it results in reduced losses from seed mortality and increased recruitment success (Rees & Long 1992). Both these effects make population persistence easier.
The models assume the biological control agent destroys a constant fraction of seed production. Clearly, after a fire the population of the control agent will be reduced, leading to lower levels of attack (for an example from the biological control of Hypericum perforatum, see Briese 1996). In these circumstances, the results presented should be considered as upper estimates of the impact of the control agent. However, the situation is more complicated as fires can result in the release of nutrients, which promote the build up of the control agent's population (Briese 1996). As suggested by Briese (1996), this means that the use of fire and biological control should not be considered as incompatible management strategies.
The importance of combining herbicide application with oversowing, to prevent gorse establishment, is clearly illustrated in Figs 8 and 9. Simply applying herbicides that kill gorse plants and other vegetation, so creating suitable germination microsites for gorse, leads to an increase in the area covered unless herbicides are applied frequently. In contrast, combining herbicide application with oversowing results in a decrease in the area occupied by gorse even if herbicides are applied infrequently (say less than once every 10 years; Fig. 8). As in the other management scenarios, if seedlings have a high probability of survival (s = 0·5) then seed−feeding biological control agents have little impact on gorse dynamics (compare Fig. 8a and 8d). However, if seedling survival is low, as a result of grazing, then seed−feeding biological control agents can have a dramatic impact on gorse abundance (compare Fig. 9a and 9d). However, this final conclusion depends on the assumption that grazing does not create suitable conditions for gorse establishment. In practice, this means that the pasture created after application of herbicide and oversowing will have to be managed carefully to prevent overgrazing.
The main results echo those of our previous study of the biological control of broom (Rees & Paynter 1997) and other studies on ragwort Senecio jacobaea (McEvoy & Coombs 1999) and thistles Carduus nutans (Shea & Kelly 1998). All these studies highlight the importance of carefully managing recruitment opportunities. It appears, therefore, that recruitment might be the Achilles heel of these species, and increased efforts to understand the factors controlling successful recruitment might reap rich rewards. The correct management of recruitment is particularly important in long−lived weeds, such as gorse, where a single fire can allow the establishment of a stand that can persist for 30 years and the development of a substantial seed bank that could persist for even longer.
We should like to thank Quentin Paynter and Mark Lonsdale for helpful comments on the manuscript. Part of this work was undertaken while the senior author was a recipient of a McMasters fellowship.
Received 1 October 1999; revision received 29 August 2000