Ambrosia artemisiifolia originates from central USA and has invaded a wide range of habitat types on most other continents (Essl et al. 2015). It has severe adverse effects on agriculture (Bassett and Crompton 1975; Domonkos et al. 2017) and human health (Smith et al. 2013) due to its vast production of seeds and allergenic pollen, respectively. The monoecious annual typically develops pollen-producing flowers from mid-summer onwards, followed by female flowers in late summer, both aggregated in flowering heads. Each female flower can develop into a single seed, falling straight to the ground after maturation in autumn. Plants normally die before winter while shed seeds may accumulate in a long-lasting soil seed bank if not recruited in the next spring (Bassett and Crompton 1975; Toole and Brown 1946) (Fig. 1).

Figure 1.

Life cycle of the annual plant Ambrosia artemisiifolia. Months indicated are representative for populations in Europe where most new plants have established in June, have developed into seed-producing plants in September and then die while the seeds shed overwinter on or in the soil. The small loop represents (dormant) seeds that do not recruit but stay in the soil until the next year. The vital rates and corresponding parameters in the demographic model are listed for each period. The x represents new plant size in June, y the plant size in September, m the effect of mowing.

Overview of data and approach

In order to parameterise all vital rates and integrate the effects of mowing (Fig. 1), we combined four different data sets: data from i) a roadside mowing experiment, ii) a post-harvest seed quality experiment, iii) a demographic survey and iv) seed burial experiments. The mowing experiment comprised a five-year application of four mowing regimes to roadsides in Austria, varying in the timing and frequency of cutting and an untreated control (main experimental results of the first three years can be found in Milakovic et al. 2014b). These data allowed quantifying the effect of the tested mowing regimes on individual plant height in September y, flowering fl, fecundity fec and seed ripening sr and how effect sizes of the reproductive rates depend on adult plant height y (one of the size variables in our population model) and vary from year to year (for stochastic population models). Since mowing can also affect seed quality (Bohren et al. 2008; Sölter et al. 2016), we obtained the effects of cutting on seed viability sv from a separate post-harvest seed quality experiment (Karrer 2016c). Neither of these experiments was designed for demographic modelling and, together, they provided insufficient data to parameterise all vital rates. We therefore chose to parameterise our models with demographic data from other populations of A. artemisiifolia, which were not mown. We chose four unmanaged populations elsewhere in Europe with similar vegetation and bioclimatic conditions. We conducted a demographic survey in two years providing data on all vital rates except seed ripening sr, seed viability sv and seed survival σ in the soil seed bank. The species has a long-lasting seed bank (Bassett and Crompton 1975) and such age-structured seed banks may play an important role in the population dynamics of an annual, for instance determining the time to extinction (Kalisz and McPeek 1992, 1993). We therefore complemented these demographic data with survival rates in the soil seed bank σ from long-term burial experiments (Karrer 2016a; Karrer et al. 2016) and used these to parameterise reference models representing untreated controls. We then integrated the experimental mowing effects m into these reference models to obtain models of mowing treatments. All analyses and models were performed using R (version 3.3.3, R Core Team 2017).

Roadside mowing experiment

A 5-year mowing experiment was set up along roadsides at six locations in 2009 and in a seventh location in 2010 in Austria. All locations were already infested with A. artemisiifolia for an unknown period and managed by a regular mowing regime for road maintenance, comprising a cut around June (during vegetative growth of A. artemisiifolia) and in September (just before seed ripening of A. artemisiifolia). In summary, each location was divided into five blocks of 20 m length each and, at each location, each of five treatments was randomly assigned to one block. Apart from the untreated control, experimental treatments were yearly applied by road service maintenance teams and included the prevailing mowing regime in eastern Austria and three alternative mowing regimes varying in the timing and frequency of cutting (upper half of Table 1). For ease, we named the mowing regimes according to the months in which cuts were performed (see corresponding phenological stages in Table 1). Details on the experimental design, data collection and results of the first three years are given in Milakovic et al. (2014b). For our demographic model we used data of all five years collected in September before the last cut, when adult plants were bearing seeds. Data were available from a random 20 individual ragweed plants per treatment per location per year or fewer, if fewer were present (see Suppl. material 1, fig. S1 for sample sizes and missing data). Measurements included maximum plant height, female flowering (female reproductive structures absent or present), the total number of individual seeds on the plant (irrespective of their developmental stage) and the most advanced developmental stage of these seeds per plant (classified as still flower, developing seed or ripe seed). We analysed interactive effects of mowing treatment, year and plant size where possible and applicable on all of these response variables by generalised mixed effect models. Plant size was included because mowing effects may vary with plant size, which can be incorporated into a population model. Best statistical models were revealed by comparing values of corrected Akaike information criterion and used to obtain estimates of coefficients of vital rates for their integration into the demographic models. Suppl. material 1 provides details on the statistical analyses, including an overview of the factors in the statistical models (Suppl. material 1, Table S1).

Post-harvest seed quality experiment

The effects of cutting on seed viability were obtained from a post-harvest seed quality experiment (Karrer 2016c). Plants cultivated in a common garden in Vienna, Austria, bearing female reproductive structures were harvested by cutting them at different dates, corresponding to different developmental stages of the flowers and seeds. The harvested plants were left on the ground until the end of the growing season, when the developmental stage of the seeds was scored and their viability tested. We used the resulting percentage of ripe, viable seeds for each developmental stage harvested as seed viability. If plants were cut when female structures were still in the flowering stage (stages 1 and 2 in Karrer 2016b), these produce only 0.1% of viable seeds. Of plants cut while bearing unripe seeds, 27% of the seeds in early developmental stages (stage 3 in Karrer 2016b) and 43% of those in late developmental stages (stage 4 in Karrer 2016b) developed into ripe viable seeds. As the mowing experiment did not distinguish the age of unripe seeds, we used the average of these values (35%) for all unripe seeds. Of the seeds that were ripe when the plant was harvested (stage 5 in Karrer 2016b), 87% turned out to be viable.

Demographic survey

To serve as “reference” populations for the current mowing effect study, we selected A. artemisiifolia populations located in the same bioclimatic region as the Austrian sites of the mowing experiment (Continental or Pannonian), with the most similar habitat type possible (grasslands, since no unmanaged roadsides were available) and with plant heights covering the range of plant heights observed in the untreated controls of the mowing experiment. This yielded four populations located in Austria (AT), Hungary (HU), Italy (IT) and Poland (PL) (details in Suppl. material 2, Table S2). For the survey, we used specific standardised protocols developed for a coordinated European-wide demographic study of unmanaged populations of A. artemisiifolia across Europe started in 2014 (full demographic survey protocol available on https://www.protocols.io/, https://doi.org/10.17504/protocols.io.mmyc47w, see also Suppl. material 2). In summary, over a hundred individually labelled plants per population were monitored from June, when they were young vegetative plants, to seed set in September. This provided estimates of new plant size, survival, growth and flowering. Another set of 21 mature plants was harvested at seed set for estimates of fecundity (i.e. coinciding with the time in the year that plants in the mowing experiment were assessed before the cut in September). Numbers of new plants in quadrats and estimates of the associated soil seed bank size from soil samples provided estimates of recruitment rates. We monitored all four populations in 2014 and 2015, but no plants in the populations in Austria and Hungary survived until the end of the growing season of 2015 due to harsh competition by grasses. We therefore had six suitable reference data sets (AT14, HU14, IT14, IT15, PL14 and PL15) available for the analysis.

Seed burial experiments

To obtain values of seed survival rates, we used three of the largest available data sets for burial experiments with yearly measurements on our study species to date (Karrer 2016a; Karrer et al. 2016) (see overview in Suppl. material 3). Replicated bags with 50 seeds from plants from locations in Austria and Hungary had been buried at two different locations in Austria (details in Suppl. material 3, Table S3). Yearly sampling of subsets and subsequent viability tests provided three time series over 5 years, which we used to fit an exponentially declining model assuming age-independent mortality (Suppl. material 3, fig. S5). This provided three estimates of yearly seed survival rates in the soil seed bank (scenario “H” with seeds from Hagenbrunn, Austria: 0.792; scenario “K” with seeds from Kaposvar, Hungary: 0.963; scenario “U” with seeds from Unterpurkla, Austria: 0.921).

Population models of unmanaged references

Our discrete-time population model describes a time step of a year, from October (after seeds have been shed and plants have died) to October. As, in our model, individuals only exist as seeds in October, our model could be seen as unstructured. However, most vital rates in the model describe individual performance of plants from June to October and are functions of the continuous size variables x (plant height in June) or y (plant height in September). Our model is hence similar to a periodic Integral Projection Model with size as a continuous state variable (Ellner and Rees 2006) and consists of the three periods indicated in the large loop in Fig. 1. For the unmanaged reference populations, the number of seeds in seed bank SB in October after seed dispersal is described by equation 1:

The first part of the equation describes the seeds that survived the entire year in the soil seed bank (small life cycle loop in Fig. 1) with survival σ, assuming that mortality occurs in winter (M. Leitsch-Vitalos, unpublished results). The second part describes the number of newly produced seeds in October at t+1 per seed at t and follows the large life cycle loop in Fig. 1 with integrals describing the transitions from June till September and from September till October, respectively. We use log-transformed plant height as a continuous variable describing individual size, because size classes are hard to distinguish in A. artemisiifolia and because this variable was the only common measure of size occurring in all data sets, while log-transformation yielded best fits of vital rate models. After seeds have survived the winter with probability σ, they recruit with probability ρ, resulting in nx new plants with distribution φ of size x in June. If they survive, ​s​(​​x​)​​​, they grow, g​(y, x)​, into ny plants of size y in September. If they flower, ​fl​(​​y​)​​​, they produce fec (y) new seeds. The total number of new viable seeds incorporated into the soil seed bank in October ​​(​​t + 1​)​​​ depends on the distribution sr​(y)​ of seeds over the ripening stages (flower, unripe seed, ripe seed) and the associated viability ​sv​(​​sr​)​​​ of each ripening stage. We did not include density-dependence in the model to conserve the ability to analyse intrinsic population growth rates analytically and because excluding density-dependence may be inappropriate when models are parameterised with realised levels of interspecific and intraspecific competition (Crone et al. 2013), which is the case in our demographic survey.

Using equation 1, we parameterised population models for all combinations of the six reference data sets and the three seed survival rates (i.e. a total of 18 reference scenarios, representing unmanaged controls). For details of the parameterisation, we refer to Suppl. material 4, which includes estimates of vital rates for each reference data set (Suppl. material 4, Table S4 and fig. S6–10). Integrations were applied to an extended range of plant sizes observed across all reference populations, from min (0.8 * the minimum height of new plants in June) to max (1.2 * the maximum plant height in September). We dealt with potential eviction (Williams et al. 2012) by adding all projected size values exceeding the size range to the corresponding most extreme size class.

Population models of experimental mowing treatments

To project the effects of the experimental mowing treatments, equation 1 was extended by including dependence on mowing treatment m into all the relevant vital rate functions, resulting in equation 2 (modifications to equation 1 are indicated in bold):

Details of the parameterisation are elaborated in Suppl. material 5. Mowing effects on growth g, flowering fl, fecundity fec and seed ripening sr were derived from the mowing experiment, mowing effects on seed viability sv from the post-harvest seed quality experiment. Other parameters remained unchanged. We hence parameterised a set of 360 population models with equation 2, integrating the effects of each of the four experimental mowing treatments into each of the five mowing years into each of the 18 unmanaged reference scenarios. In order to understand the mechanisms by which treatments affect population growth, we quantified the relative contribution of each of the affected vital rates to changes in population growth (Δr). For that, we integrated mowing effects of single vital rates one by one in equation 2 for each of the 360 population models.

Simulating new theoretical mowing treatments with population models

Our approach allowed assessing the effect of new, experimentally untested combinations of cutting dates. Since the cut in September only affects population growth by modifying seed quality (through reduced seed ripening and corresponding lower seed viability) and no other vital rates, we were able to theoretically simulate removal or addition of this cut from the experimentally tested mowing regimes (Table 1, lower half). Thus, by removing the effect of the September cut from the four experimental mowing treatments 69, 89, 679 and 689, we simulated four new theoretical mowing treatments (6, 8, 67 and 68, respectively. To assess their effects for each reference model in each year, we created a second set of 360 population models equivalent to the 360 described above, maintaining mowing effects on growth, flowering and fecundity, but removing effects on seed ripening and viability. We also simulated a new theoretical mowing treatment 9 constituting mowing only in September by integrating the effect of mowing in September into the 18 reference scenarios (untreated controls, treatment 0), resulting in a second set of 18 alternative population models. Specifically, we integrated the effect of mowing in September on seed viability for each seed developing stage.

Analyses of population models

We obtained the projected intrinsic population growth rate, r, for each population model parameterised and compared them to assess the effect of treatments and the contribution of single vital rates. Since the effect of seed ripening only exerts an effect on r through the corresponding reduction in seed viability, we calculated the contribution of seed ripening alone as the difference between the growth rate when seed viability only was integrated and the growth rate when integrating both seed ripening and viability. To acknowledge temporal variation in experimental mowing effects (Metcalf et al. 2015), we also estimated a stochastic intrinsic population growth rate (r_s) for each experimental mowing treatment in each reference scenario by iterating a population vector through a time series, sampling population model matrices of different mowing years with equal probability at every time step, using the R package IPMpack (version 2.1, Metcalf et al. 2013).

For plant height in September, the full model with the interaction of treatment and year fitted the data best. The pattern of treatment effects was nevertheless fairly consistent across the years without a clear pattern over time (Fig. 2A and Suppl. material 1, fig. S2). Experimental treatments with a previous cut in August (89 and 689) reduced final plant height in September most, the treatment with a previous cut in July (679) moderately, while the treatment with a previous cut in June (69) increased or reduced height slightly, depending on the year and location (Suppl. material 1, fig. S1). All vital rates related to reproduction were strongly affected by treatment and plant height. In the best model of flowering, treatment and plant height had independent effects (Suppl. material 1, fig. S3). All mowing treatments and especially treatment 89 reduced flowering probability compared to the control, but the effect decreased with plant height and became negligible for plants taller than 40 cm (Fig. 2B). The best model of fecundity had no treatment × year interactions (Suppl. material 1, fig. S4), so the relative treatment effect was similar for all years (Fig. 2C). All mowing treatments increased size-dependent seed production, but the magnitude of this compensation changed with plant height, increasing for treatments 69 and 679 (i.e. the larger the plant, the stronger compensation of seed production), but decreasing for treatments 89 and 689, which include a cut in August (Fig. 2C).

Figure 2.

Fitted effects of experimental mowing treatments on vital rates. Experimental mowing treatments are indicated by their code (69, 89, 679, 689, see Table 1) and figures present fitted effects on A) mean plant height in September per year, B) flowering probability, C) fecundity and D) the development of seeds (see details of statistical models in main text and Suppl. material 1). Suppl. material 1 Effects in A–C are relative to that of the control treatment (0) and for B–D across all years as a function of the back-transformed covariable plant height in September. Dotted ends of lines in C and of the horizontal line at the bottom of D indicate where models were extrapolated beyond the range of observed plant height values.

The best model for seed ripening contained the interaction between treatment and plant height. We found that mowing treatments generally delayed the development of seeds, especially for the transition from flowers to unripe seeds in smaller plants (Fig. 2D). Cutting in June resulted in relatively more ripe seeds if plants were not consecutively cut in July or August (Fig. 2D, treatment 69). Since the post-harvest experiment indicated that cutting reduces the viability of flowers and unripe seeds, this change in seed ripening has implications for the seed quality.

We projected stochastic intrinsic population growth, r_s, for all 360 integrations of experimental mowing treatments and reference models. Although different seed survival scenarios resulted in very different values of r (Suppl. material 6, fig. S11), they did not alter patterns of experimental treatment effects. Therefore, we here report results based on seed survival scenario H, which had the lowest survival rates and best matched observed population dynamics in the reference data sets (S.T.E. Lommen, unpublished data). Projected r_s varied a lot between reference data sets, but patterns of treatment effects were consistent (Fig. 3). Experimental treatments with cuts in August (89 and 689) always resulted in the lowest r_s and, in most cases, r_s was reduced until below replacement level (r = 0, where population size remains constant). The commonly applied treatment 69 performed worst by only decreasing r_s somewhat, whereas treatment 679 had intermediate effects. The deterministic growth rates, r, based on mowing effects in single years (Suppl. material 7, fig. S12), are in line with the pattern of r_s, except in reference IT14 where effects of mowing treatment 69 in 2012 project increased r compared to the control treatment.

Figure 3.

Effect of experimental mowing treatments on stochastic population growth rates r_s for seed scenario H. Panels represent different populations (AT, HU, IT, PL) in year 2014 or 2015 (14 and 15, respectively) as detailed in Suppl. material 2, Table S2. The dashed line indicates the population replacement level.

We assessed the contribution of all vital rates and seed quality to changes in projected deterministic intrinsic population growth r, which were independent of seed survival. All treatments reduced r mainly through the decrease in growth (i.e. lower plant height in September) and seed viability counteracting the increased size-dependent seed production (Fig. 4). The importance of each of these vital rates, however, differed between treatments (Fig. 4) and reference models (Suppl. material 7, fig. S13). In the most successful treatments 89 and 689, changes in growth contributed most to reduction in r (medians of -77% and -82%, respectively), while seed viability was the second most important (-34% and -31% respectively). The cut in September thus contributed to reducing r, but did not have the strongest effect. In treatment 679, reduction in seed viability and growth were equally important (-71% and -67%, respectively), but only achieved an overall intermediate effect due to strong increased size-dependent fecundity (+49%). In the least effective treatment 69, the reduction in r was largely due to reduced seed viability (-136%) opposing the effect of increased fecundity (+30%), while the effect of growth was negligible (-5%). In this treatment, the cut in September is crucial to obtain reduction in r. Mowing effects on flowering probability were of negligible importance in all mowing regimes.

Figure 4.

The influence of single vital rates and the September cut on population growth. Figures show the relative contributions of each vital rate (g = growth, fl = flowering, fec = fecundity, sr = seed ripening, sv = seed viability, see Fig. 1) and the cut in September (Sept, i.e. combined effect of sr and sv) to the total change in the population growth r per treatment. The y-axis represents the percentage change in r compared to the untreated reference, relative to the total change due to the mowing treatment (red dashed line at -100%). Boxplots indicate variation across reference data sets (N = 6) and years (N = 5, if applicable).

We plotted r-cost relationships of all experimental and theoretical mowing treatments, assuming that each cutting intervention has the same costs. Therefore, the relative costs are represented by the number of cuts. Fig. 5 shows the r-cost relationships for the Austrian reference population in 2014 (AT14) and seed survival scenario H, but the main patterns are independent of the seed survival scenario (Suppl. material 8, fig. S14) and are similar in other reference data sets (Suppl. material 8, fig. S15). The figure reveals that the effectiveness of a given number of cuts is highly dependent on the timing of these cuts. With a budget for a single cut, cutting just before female flowering (here in August) is by far more cost-effective than cutting during vegetative growth (here in June) or before seed set (here in September). When a budget for two cuts is available, cutting just before female flowering and before seed set (here August and September) was most cost-effective and reduced ragweed growth rate more than the best 1-cut treatment. With a budget for three cuts, cutting during vegetative growth, just before female flowering and before seed set (here June, August and September) was the most cost-effective, but was hardly better in reducing ragweed growth rate than the best 2-cut regime. These three most cost-effective regimes thus all include a cut just before female flowering (here August). The graph also shows that some theoretical regimes are more effective than experimentally tested regimes with the same or a higher number of cuts (for instance, treatment 8 and 9 are more effective than 67 and 69 and treatment 68 is more effective than 679).

Figure 5.

Effect-cost relationships of mowing regimes for the Austrian reference population in 2014 (AT14) for seed survival scenario H. For each mowing regime (dots with labels indicating the months of cutting, see Table 1) and the untreated control (the dot at x = 0), the intrinsic growth rate r (as mean of the 5 years of experimental data) is plotted versus the relative costs of the regime (equalling the number of cuts). Mowing regimes theoretically simulated (by removing or adding the September cut to experimental treatments in the model, see Table 1) are indicated with an asterisk. Lines connect consecutive cuts, showing how extending mowing regimes with additional cuts at specific moments alters r.

Overall, our population modelling approach has proven to be a useful tool for comparing population-level effects of different mowing regimes for an annual plant with a long-lasting seed bank. Integration of mowing effects into reference models of four geographically distant populations in Europe in two different years showed that patterns of projected population effects were consistent across time and space (Suppl. material 4, figs S6–10), despite the variation in dynamics amongst the reference locations and years (Suppl. material 4, Table S4). The results of our study can thus inform management in a wide geographic area and are robust to temporal variation in population dynamics. This is likely partly due to the annual life cycle of this species and the drastic effects of mowing. By disentangling effects of cutting at specific moments, our method also proved capable in designing new mowing regimes (i.e. new combinations of cuts at specific moments) that were experimentally untested. Even more regimes could be theoretically tested in this way if future management experiments were designed to single out effects of cuts at specific moments and if the measurements were adapted to provide input for demographic models (Bourdôt et al. 2016). We have shown that the effect of a mowing regime on A. artemisiifolia population size is not simply a function of the total number of cuts, but highly depends on the timing of the subsequent cuts it comprises. Fewer well-timed cuts can therefore be more effective in reducing population sizes of A. artemisiifolia along roadsides than regimes with a higher number of cuts. Our work highlights the importance of a cut before female flowering (in our case in August), as this was part of all most cost-effective management options found in our study.