SEARCH

SEARCH BY CITATION

Keywords:

  • Calathea ovandensis ;
  • criocerine beetles;
  • stage-class;
  • demographic rates;
  • temporal variation;
  • tropical Mexico

Summary

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. Supplementary material
  10. References

1 The effects of natural variation in herbivory, local competition, plant size, and fruit production on next year’s growth, survival and inflorescence production of individuals in natural populations of Calathea ovandensis were estimated during 5 years.

2 For each year, we estimated path coefficients (by standardized multiple regression analysis) for the direct effects of predictor variables on demographic rates. Separate analyses were performed for each life-history stage: seedlings, juveniles, pre-reproductives and reproductives, for a total of 55 analyses. Emergent patterns for stages were evaluated (Fisher’s combined probability test) by combining years. To determine significance of effects in single years, we calculated table-wide probabilities for each stage across multiple years (Bonferroni sequential test). Emergent patterns for years were also evaluated (Fisher’s combined probability test) by combining stages.

3 Survival of seedlings was positively affected by plant size and negatively affected by local competition. Survival of juveniles was positively affected by plant size, but not by other factors. Survival of large stages was not generally affected by any of the factors.

4 Relative growth rates of all stages were negatively affected by plant size; larger plants grew more slowly than smaller plants. Additionally, growth rate of juveniles was negatively affected by local competition, whereas growth rate of reproductives was positively affected by reproduction.

5 Next year’s inflorescence production was positively affected by plant size for both pre-reproductive and reproductive stages. For reproductives, it was additionally positively affected by current fruit production.

6 Analysis of differences among years showed that herbivory negatively affected both survival and growth in 1985, but not in other years, whereas local competition negatively affected survival in 1983 and growth in 1984.

7 Effects of biotic interactions varied among stages and through time. The large effects of competition on seedlings and juveniles was as expected, but the small effect of herbivory on small plants was surprising as was the striking temporal variation in its effect and its impact on large plants.


Introduction

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. Supplementary material
  10. References

Both herbivory and intraspecific competition are thought to influence plant population dynamics, and their relative importance is relevant to the general issue of top-down vs. bottom-up control of populations. A first step towards understanding effects on population dynamics is quantifying effects on particular demographic vital rates, e.g. survival or growth of given stages. Many field experiments (Rausher & Feeny 1980; Parker & Salzman 1985; Cottam et al. 1986; Bonser & Reader 1995; Edwards et al. 2000; Parmesan 2000; Van der Wal et al. 2000) and models (Louda et al. 1990; Maron & Gardner 2000) have investigated herbivory and competition together (for a meta-analysis of factorial experiments see Gurevitch et al. 2000). Although experimental studies have suggested that competition may increase the negative effects of herbivory and that herbivory may alter the outcome of competition, the effects of natural variation in levels of competition and herbivory have rarely been studied together. Nor has variation among life history stages in effects of herbivory and competition generally been emphasized (except Van der Wal et al. 2000), even though stages are likely to vary in their responses. For example, seedlings may experience stronger negative effects of both competition (because of their small size, Thomas & Weiner 1989; Pacala & Weiner 1991) and herbivory (because they have fewer stored reserves, Hendrix 1988; Crawley 1989). Surprisingly, there is a relative paucity of data on the effects of herbivory and competition on tropical plants (discussed in Marquis 1992b and in Gurevitch et al. 2000), even though biotic interactions are thought to be especially important for understanding population and community ecology of tropical plants (Janzen 1970, 1971).

The extent to which herbivores may affect plant demography has been discussed in several reviews (Verkaar 1987; Hendrix 1988; Crawley 1989) and investigated in field experiments (Marquis 1984, 1992a; Gange 1990; Louda & Potvin 1995; Maron 1998), as well as in simulation models (Maron & Gardner 2000). Herbivory may be variable (Marquis 1992b) and most often weak (Crawley 1989; Marquis 1992b), and its demographic effects may not be predicted by its magnitude (Crawley 1989; Marquis 1992a).

There is much evidence for the importance of localized competition in plant populations (Harper 1977; Mack & Harper 1977). Both empirical (Weiner 1984, 1988; Thomas & Weiner 1989; Ellison et al. 1994) and theoretical (Weiner 1982; Pacala & Silander 1985; Pacala & Weiner 1991) studies of the effects of competition on plant demography have focused on neighbourhoods of individual plants rather than overall density in populations. Competition may be strongest with conspecifics (Goldberg 1987).

Local competition and herbivory, together with current fruit production, may characterize the biotic ‘environment’ of a plant. It is unconventional to think of fruit production as a measure of the environment, but in some plants (including our study species) it represents the outcome of interactions with pollinators (Schemske & Horvitz 1988) and with consumers and defenders of reproductive tissues (Horvitz & Schemske 1984, 1988a). It is therefore a parameter that synthesizes the effects of biotic interactions on reproductive tissues into a common currency. We know of no studies that have examined the relative contributions of natural variation of all these biotic interactions to demographic fates in a natural plant population and few have addressed differences in such effects among life history stages.

Here we report the results of a long-term field study designed to estimate the effects of leaf herbivory, intraspecific competition, plant size and fruit production on next year’s growth, survival and inflorescence production in the tropical understorey herb Calathea ovandensis Matuda (Marantaceae). Other biotic interactions of this species have been studied previously, including pollination (Schemske & Horvitz 1984, 1988, 1989; Horvitz & Schemske 1988a), herbivory and ant-defence of reproductive tissues (Horvitz & Schemske 1984; Schemske & Horvitz 1988), seed predation (Horvitz & Schemske 1986b, 1994) and seed dispersal by ants (Horvitz & Schemske 1986a,b, 1994). Additionally, spatio-temporal variation in population dynamics has been extensively analysed (Horvitz & Schemske 1986c, 1995; Horvitz et al. 1997).

We measured natural variation among individuals in gross leaf area, leaf area damaged by herbivores, total neighbourhood leaf area and current fruit production in four study plots during 5 years. We also determined the demographic rates or fates (survival, relative growth rate and inflorescence production) of the same individuals and asked how they were influenced by herbivory, competition and fruit production, analysing the effects for each of four stages, seedlings, juveniles, pre-reproductives and reproductives, for each year. We investigated (i) which factors influenced each of the fates and if different factors were important for each fate; (ii) differences among stages and among years in the effects of these factors on demographic fates; and (iii) the variability and magnitudes of fates and factors within years for each stage. We expected small plants to be more susceptible to both herbivory and competition than large plants. We had no a priori expectation about the relative importance of these two biotic interactions.

THE STUDY SITE AND SPECIES

Our research was conducted in a secondary forest at Laguna Encantada, near San Andrés Tuxtla, Veracruz, Mexico. This patch of tropical evergreen rain forest, covering an area of about 0.75 km2, is located at the periphery of a volcanic-crater lake. The terrain is rugged, with narrow canyons and extensive areas of sharp, volcanic rock jutting from the forest floor. Pastures dominate the surrounding vegetation, laced with numerous ‘living fences’ of Bursera simaruba Sarg. (Burseraceae), but patches of forest are common along the rivers and steep slopes. The rainfall is seasonal (80% of annual rainfall received from June to October) with a mean annual precipitation of 1996 mm and a peak (498 mm) in September (Soto 1976). During the rainy season, the understorey of the forest is dominated by our study species, which forms nearly monospecific stands.

Calathea ovandensis is an understorey, perennial monocotyledon of lowland secondary forests and successional patches within primary forests. Its growth and reproduction are seasonal. Plants shed all above-ground parts during the dry season, persisting as dormant rhizomes with energy stored in small, round (about 2.5 × 1 cm), starchy tubers. They reinitiate leaf production at the onset of the rainy season (June). Shoots, each comprised of a whorl of leaves, are produced sequentially throughout the growing season from the underground rhizome. There is no vegetative propagation. Individual plants (genets, sensuHarper 1977) are readily distinguished. Flowering peaks in August and fruit maturation coincides with peak rainfall in September. New seeds are dormant until at least the subsequent rainy season. Peak seedling emergence occurs in July. Some seeds remain dormant, resulting in a soil seed bank.

Demographic rates defined as transition probabilities are stage-dependent and are influenced by plant size and by variability in the environment, and inflorescence production depends upon plant size (Horvitz & Schemske 1995). Seed production per inflorescence is not usually pollen limited (Horvitz & Schemske 1988a), but is influenced positively by ants, negatively by a specialist ant-tended herbivore of reproductive tissues (Horvitz & Schemske 1984, 1988a), and, in some years, positively by some taxa of pollinators (Schemske & Horvitz 1988). Seeds are dispersed by ponerine ants (Horvitz & Schemske 1986b). Seeds in the soil experience a low rate of predation and may remain dormant for several years (Horvitz & Schemske 1994). Seedling recruitment is episodic in most populations, corresponding to 10-fold more seedlings in el Niño years compared to other years (Horvitz & Schemske 1995).

Population structure and dynamics differed among four plots and among four years (Horvitz & Schemske 1995; Horvitz et al. 1997). Population growth rate was highest in an el Niño year (1982–83 transition) (Horvitz & Schemske 1995). Analysis of contributions of variation in demographic transitions to variation in population growth rate indicated a larger effect of inter-year variation than of inter-plot variation (Horvitz et al. 1997), although plot-by-year interactions also made large contributions.

Methods

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. Supplementary material
  10. References

CENSUSES

To study demography and plant–animal interactions, we established four plots in 1982, located from 80 to 250 m apart. The plots were chosen to span the natural range of environmental variation, so that taken together they are representative of the range of habitats occupied by C. ovandensis in this forest. Plots differed in substrate, density and population structure. A detailed description of study plots is given in Horvitz & Schemske (1995). In August–September 1982, we marked all individuals within each plot with a numbered tag attached to a small stake inserted into the ground at the base of each plant. We censused these plots again in October 1982 and during the next 5 years (1983, 1984, 1985, 1986 and 1987) to obtain estimates of survival, growth and reproduction in these populations, marking and mapping new seedlings as they appeared. Each year we conducted one complete census in early August, when vegetative development was nearly complete for a season, measuring the size and counting the reproduction of all individuals (all years) followed by censuses of reproduction every 2 weeks until the end of October (all years except 1987). In 1983 and all subsequent years, each individual was mapped to the nearest cm, using an x–y co-ordinate system for each plot.

Although the calendar date of the 1987 census was comparable to other years, we later discovered that the phenological status of the population at that census was retarded, perhaps because of the extended dry season associated with that year’s el Niño. Vegetative shoots were not fully developed and neither plant size nor reproduction estimates were comparable to other years. We dropped the 1987 data entirely from our previous analyses of population growth (Horvitz & Schemske 1995). However, here we include some of the 1987 data, particularly the parameters that were not affected by the phenological issue. The number of new seedlings as counted in 1987 is included in analyses of recruitment. The effects of parameters measured in 1986 on survival and relative growth (but not reproduction) of plants in 1987 are also considered here.

PLANT SIZES AND STAGE CLASSES

Within a shoot, leaves are produced one at a time from a central meristem, as in other monocotyledons. Leaf sizes increase sequentially both within a shoot and between shoots on a single plant. To estimate the sizes (total leaf area) of plants non-destructively, we measured the lengths of all the leaves of each individual. A study of leaf tracings showed that leaf length is an excellent predictor of leaf area (Horvitz & Schemske 1988b, 1995). Using the regression relationship obtained from that study, we calculated the leaf area of each leaf and then summed these for the total (gross) leaf area of each plant each year at the annual census.

For this paper we have modified the stage classification that we previously used to characterize the population structure. The original classification, designed for use in a projection matrix model of population dynamics, was based on total leaf area, size of the largest leaf and reproductive status, and included eight stages: seeds, seedlings, juveniles, pre-reproductives and four different sizes of reproductives (Horvitz & Schemske 1995). To increase within-stage sample size and reduce the number of analyses to consider, we have now pooled all reproductives (analyses that we performed based on separate reproductive stages gave similar trends to those reported here), and the seed stage was also excluded.

LEAF HERBIVORY

We used a clear plastic sheet marked with a grid (about 0.64 cm) to estimate amount of leaf area damaged by herbivores on each leaf at the annual census. We observed three different kinds of damage. Criocerine beetles (Coleoptera, Chrysomelidae, Lema bipistulata Jacoby and L. plumbea Chevrolat) produced small linear leaf scraping damage between the veins, very similar to damage by rolled-leaf hispine beetles (Cephaloleia, Chelobasis, and Imatidium) (Strong 1977 and personal observation by C. C. Horvitz) that feed on other Zingiberales. Lepidopteran larvae (most often Saliana, a skipper, and occasionally Podalia) consumed larger portions of leaves. Orthopterans made holes through several layers of leaf tissue simultaneously, feeding inside rolled immature leaves and producing a row of perforations perpendicular to the mid-vein that occasionally resulted in loss of all tissue above the perforations (‘tear-on-dotted-line’ phenomenon). We summed all herbivore damage on all leaves per plant and calculated the percent of leaf area damaged by herbivores of each plant at each annual census.

LOCAL COMPETITION

We used the map co-ordinates and the length of the largest leaf of each plant to determine which plants were its neighbours. In this species, as in other Marantaceae, the above-ground space occupied by a plant changes diurnally as the leaves fold up and down (Kennedy 1983). Plants occupy maximum space when their leaves are extended outward. The underground parts occupy an area smaller than the above-ground area as defined by the extended leaves. The length of the largest leaf was taken to define the radius of a circle representing the above-ground area occupied and thus the likely area of the competitive influence of each plant. Any plants whose circles overlapped with that of a focal plant were counted as its neighbours. We calculated the sum of the leaf areas of all these neighbours which, since all C. ovandensis in these nearly monospecific stands were measured, estimates the neighbourhood competition experienced by each focal plant. Neighbours were identified and leaf areas summed by a FORTRAN program called dense (unpublished program, John Heywood).

Our measure of competition assumes that competitive influence is proportional to plant size (Weiner 1984; Goldberg 1987) and implies that small plants contribute less to competition with a focal plant than do large plants in the same neighbourhood. The potential competitive effect of each neighbour was not weighted by an index of asymmetry as it is in explicit models of asymmetry (Thomas & Weiner 1989; Pacala & Weiner 1991), since we had no a priori criterion for choosing an index of asymmetry for our species.

FRUIT PRODUCTION VS. INFLORESCENCE PRODUCTION

We used the number of inflorescences produced by a plant as an estimate of resources available for reproduction as ‘perceived’ by a plant, but number of fruits as an estimate of resources actually ‘spent’ in reproduction in any given year (Horvitz & Schemske 1988a,b). Fruit production per inflorescence is limited by plant–animal interactions including herbivores of reproductive tissues (Schemske & Horvitz 1988), whereas inflorescence production is closely related to plant size (Horvitz & Schemske 1995).

RELATIVE GROWTH VS. ABSOLUTE GROWTH

Because a plant’s ability to add new leaf area depends upon the amount of photosynthetic surface currently present, we chose to consider relative growth rate, proportional change in leaf area, rather than absolute growth rate as our index of growth. Relative growth rate decreases with initial plant size if leaf area increases by the same absolute amount for all initial sizes.

ANALYSIS

For this paper, we focused on 5 year-to-year transitions, 1982–83, 1983–84, 1984–85, 1985–86, and 1986–87. We used year-to-year transitions rather than cumulative effects over multiple years, because, in this species, plant size at the beginning of a growing season primarily reflects the amount of energy stored by the plant at the end the previous season. Two lines of evidence support this assertion. First, a field experiment to test the effects of reproductive effort on future fate showed significant within-season effects, but no second-year effects (Horvitz & Schemske 1988b). Second, an analysis of the effects of state 2 years previous to a given season on fate during a given season showed no significant effect, in contrast to an analysis of the effects of state 1 year previous to a given season (Horvitz & Schemske 1995). We pooled the data from all plots to increase sample sizes for regression analyses and to focus our investigation on differences among stage classes within each transition year. Separate regression analyses were performed for each stage class in each transition year.

The causal model underlying our analyses is that all the predictor variables could have direct effects on fates. There may also have been indirect effects through unresolved correlation, but we did not analyse these for this paper. In this context, we performed multiple regression analyses to obtain path coefficients for the direct effects (standardized regression coefficients) of predictor variables on fates (SAS 1996; proc reg, using the stb option in the model statement). Standardized regression coefficients express ‘the average change in standard deviation units of the dependent variable for one standard deviation unit of each independent variable’ (Sokal & Rohlf 1981; p. 623). In our analyses, they permit quantitative comparison of the direct effects of herbivory, neighbourhood competition, current size and current reproduction on three demographic fates: survival, relative growth and future inflorescence production. We considered 5 years × 2 fate variables (survival and growth) × 4 stages (all stages) plus 5 years × 1 fate variable (future reproduction) × 3 stages (only stages that became reproductive after a year) for a total of 55 regression analyses (Appendix 1). Prior to analysis, variables were transformed to improve normality as follows: (i) herbivory, percent of leaf area damaged, was transformed as arcsin√X; (ii) neighbourhood competition, sum of leaf areas of neighbours, was transformed as ln(X + 1); (iii) plant size, gross leaf area, was transformed as ln(X); (iv) relative growth (plant sizet+1)/(plant sizet), was transformed as ln(Xt + 1) – ln(Xt); and (v) current and future reproduction, number of fruits and number of inflorescences, respectively, were transformed as √(X + 1). Non-reproductive vs. reproductive stage classes and first year vs. other years required distinct statistical models. In particular, current reproduction was uniformly zero for seedlings, juveniles and pre-reproductives, and thus was not included as an effect in the models of their fates. Neighbourhood competition could not be included as an effect for the first year of the study, because plants were not mapped until the second year.

The statistics of the regression models were employed in summarizing and testing patterns as follows. We summarized differences among stages and differences among years by combining probabilities over years and over stages, respectively. As a second kind of test, we also examined the significance of single year effects by using a table-wide probability adjusting by the number of years tested. To examine emergent stage patterns, for each stage and predictor variable, we combined probabilities (of regression parameters) over years using Fisher’s combined probability test statistic (–2 ∑ ln P), which is χ2 distributed with d.f. = 2k, where k is the number of tests (Sokal & Rohlf 1981). We used the combined probabilities only when regression coefficients of large magnitude were of the same sign. To determine significance of effects on particular stages in single years, we calculated table-wide adjusted probabilities for multiple years by the Bonferroni sequential test (Rice 1989). The Bonferroni test is known to be overly conservative, but we feel it is useful for analyses of each stage in distinguishing strong effects in certain years. To examine emergent temporal patterns, for each year and predictor variable, we combined the probabilities (for regression parameters) over stages (Fisher’s combined probability test).

Results

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. Supplementary material
  10. References

REGRESSION ANALYSES

Survival

Survival of small plants was significantly affected by predictor variables more often than survival of large plants. Regression models accounted for significant variation in survival of seedlings and of juveniles in each year of the study, but of reproductives in only 2 years, and not of pre-reproductives in any year (Appendix 1).

The effects of predictors on survival of each stage are summarized in Fig. 1. Combining probabilities over years for each stage showed that survival of seedlings was positively affected by plant size and negatively affected by local competition. Juveniles were positively affected by plant size, but not influenced by other factors and larger stages were not consistently affected by any of the factors.

image

Figure 1. Survival in Calathea ovandensis. Values of path (or standardized regression) coefficients are on the y-axis. Coefficients are from the multiple regression analyses for the effects of plant size, herbivory, neighbourhood competition, and, for reproductives, of fruit production (all at time t) on survival (at time t+ 1) for each stage class (Appendix 1). Fisher’s combined probability statistic (–2 ∑ln P, combined across years within each panel) is given in the upper corner of each. Significance of this test is given only for those panels in which large effects did not differ in sign among years (d.f. = 2 × the number of bars in each panel; NS means P > 0.05; *P≤ 0.05; **P < 0.01; ***P < 0.001; ****P < 0.0001; ± means large effects differed in sign). Probability levels on each bar are Bonferroni corrected with respect to multiple tests within each panel. Time t on x-axis represents years 1982–86.

Download figure to PowerPoint

Examination of effects in single years (Bonferroni-adjusted probabilities) showed that the positive effect of size on seedling survival was similar in magnitude to the negative effect of competition, except in 1985, when competition had no significant effect. For juveniles, survival was more affected by size than any other factor, whereas large plants showed only one significant effect (negative response of reproductives to herbivory in 1985).

Relative growth

Regression models accounted for significant variation in growth of reproductives in all years, of both seedlings and juveniles in 4 of 5 years, and of pre-reproductives in only 2 years (Appendix 1).

The effects of predictors on growth for each stage are summarized in Fig. 2. Relative growth rate of all stages was very significantly negatively affected by plant size, i.e. larger plants within a life stage grew more slowly than smaller plants (combined probability analyses). Juveniles were also negatively affected by local competition, whereas reproductives were positively affected by reproduction. Although growth of all stages was affected primarily by plant size, the magnitude of the effect was more consistent across years for seedlings and reproductives than for juveniles and pre-reproductives.

image

Figure 2. Relative growth rate in Calathea ovandensis. Conventions as in Fig. 1.

Download figure to PowerPoint

Bonferroni-adjusted analyses of growth of each stage in single years, showed that, for seedlings, plant size was the only significant predictor and it affected all years. For juveniles, plant size affected growth only in 1982 and 1983, but local competition reduced growth by a similar magnitude in 1984. Pre-reproductives showed only one significant effect in one year (size in 1983), but reproductives were affected by size in all years as well as by reproduction in 1982 (Fig. 2).

Inflorescence production

Regression models accounted for significant variation in next year’s inflorescence production of reproductives in all 5 years and of pre-reproductives in 3 of 5 years (Appendix 1).

The effects of predictors on next year’s inflorescence production for each stage are summarized in Fig. 3. Plant size had a positive effect for both pre-reproductive and reproductive stages and current fruit production also had a positive effect on next year’s inflorescence production (combined probability analyses). The primary effect was that larger plants made more inflorescences next year. The consistency and magnitude of the effect varied by stage class.

image

Figure 3. Inflorescence production in Calathea ovandensis. Conventions as in Fig. 1.

Download figure to PowerPoint

In single-year analyses (Bonferroni-corrected analyses), future inflorescence production by juveniles was not significantly affected by any predictor variable, and pre-reproductives were affected only by size (and only in 1982 and 1984). Reproductives were affected positively by plant size (consistently) and also, in some years (1982 and 1986) by current fruit production, and negatively by competition in 1983 (Fig. 3).

Summary of temporal patterns

Analysis of emergent patterns combined over stages for given years (Fisher’s combined probability test) showed that plant size had a significant effect in all years on all fates. The effect of 1986 sizes on 1987 inflorescence production is not considered, as it was not estimated comparably to other years (see Methods). There were 14 significant tests in this set of analyses, and the combined probability statistic (–2 ∑ ln P) ranged from 16.9 with d.f. = 6, to 71.5 with d.f. = 8; 13 of the tests had P < 0.0001 and one had P < 0.01. More interestingly, herbivory also had an effect, albeit only in 1985, when it negatively affected both survival and growth (–2 ∑ ln P= 24.4, 15.4, respectively; d.f. = 8, for both, and P < 0.01, 0.05, respectively). Local competition negatively affected survival in 1983 (–2 ∑ ln P= 27.6, d.f. = 8, P < 0.001) and growth in 1984 (–2 ∑ ln P = 17.7, d.f. = 8, P < 0.05).

Summary of effects of predictor variables

Gross leaf area frequently had a significant effect on fate. All significant effects of plant size on survival (Fig. 1) and on reproduction (Fig. 3) were positive, but all significant effects on growth rate were negative (Fig. 2). Survival of both seedlings and juveniles was better for larger plants. In older classes, larger individuals of the pre-reproductive stage class made significantly more inflorescences next year than smaller individuals of the same stage (in 2 and 4 of 5 years, for pre-reproductives and reproductives, respectively). The significant negative effect of plant size on growth rate was seen in many stages and years.

Apart from a negative effect on both growth and survival in 1985 (see above analysis of temporal patterns), damage by herbivores to leaves rarely had a significant effect on fate.

Local competition, measured as the leaf area of neighbours, had a significant effect on fate more often than herbivory, impacting seedling survival in 3 of 4 years, juvenile growth in 1984 and next year’s inflorescence production for reproductive plants in 1983.

Current fruit production had a significant effect (positive in each case) on fate in 3 of 15 regression analyses (future reproduction in 1982 and 1986 and growth in 1982).

VARIABILITY: DEMOGRAPHIC FATES

All three fate parameters differed much more among stages than among years and their variability among plants within a stage (CV = SD/mean × 100) decreased with increasing stage (Table 1).

Table 1.  Demographic fates (survival, relative growth and inflorescence production) in Calathea ovandensis (X, mean; CV, SD/mean × 100; n, number of plants) in the subsequent year for a given year’s stages; non-reproductive stages may become reproductive
FatesStage19821983198419851986
CVnCVnCVnCVnCVn
  1. The 1987 census was ‘biologically’ earlier than others because of an extended dry season, and reproduction was only censused once that year, making the growth and reproduction from 1986 to 1987 underestimates in comparison with other years. Sample sizes for survival are slightly higher than in Table 2, because there were always a few plants missed at each annual leaf-size census, but then they were picked up again later. Sample sizes for growth and reproduction are smaller than for survival, as these parameters are only defined for survivors.

Survival (no. livet+1/no. livet)Seedlings0.09314.41950.04469.214260.07370.97810.06381.84040.02702.7654
Juveniles0.58  85.31360.45111.1  1670.47106.81150.66  72.01060.57  88.2  76
 Pre-reproductives0.89  35.3  820.96  20.7    740.88  38.1  720.95  22.1  870.83  45.0  78
 Reproductives0.92  29.22040.96  21.1  2120.97  18.82070.99  10.81730.98  14.8187
Relative growth (sizet+1/sizet)Seedlings4.87105.3  164.44  94.5    615.36126.2  503.50117.4  262.27  76.8  13
Juveniles2.74102.7  782.60  96.4    731.94103.2  501.95106.4  631.57  74.8  43
 Pre-reproductives1.43  69.1  691.34  55.3    691.14  54.7  611.35  58.0  831.19  65.6  64
 Reproductives1.27  62.11830.86  51.2  1970.86  52.61951.04  45.71690.92  51.0182
Reproduction (inflorescencest+1)Seedlings0.0  170.0    610.0  500.0  260.0  13
Juveniles0.15351.0  790.05424.1    750.04499.9  510.12348.0  690.0  43
 Pre-reproductives0.71120.4  730.56104.2    700.48140.4  630.47121.4  830.03565.6  65
 Reproductives2.26  73.81871.77  71.1  1991.34  94.22001.52  92.41700.28193.2183
Survival

Survival increased with increasing stage (mean proportion surviving 0.06, 0.55, 0.90 and 0.96, respectively, for seedlings, juveniles, pre-reproductives and reproductives). Survival was highest in 1985 (1.1 × mean over all years).

Growth

Relative growth rate decreased markedly with increasing stage (mean 4.1, 2.2, 1.3, and 0.99, respectively, for seedlings, juveniles, pre-reproductives and reproductives). The high growth rate observed for seedlings is influenced however, by the fact that only those seedlings that survived to the subsequent year are included. High values of (plant sizet+1)/(plant sizet) mean that those seedlings that survived grew quite rapidly, but do not necessarily reflect growth rates within a growing season. Large plants grew less rapidly than small ones; in fact, the largest plants often shrank rather than increased (Table 1). Growth was highest in 1982 and lowest in 1986.

Inflorescence production

Future inflorescence production increased markedly with increasing stage (mean 0.1, 0.6, and 1.7, respectively, for juveniles, pre-reproductives and reproductives). (Seedlings never became reproductive by the next year, Table 1). 1982 was the year of highest future inflorescence production.

VARIABILITY: HYPOTHESIZED PREDICTORS

Results are given in Table 2.

Table 2.  Predictors of demographic fates (size, herbivory, competition, and fruit production) in Calathea ovandensis (X, mean; CV, SD/mean × 100; n, number of plants), values in a given year as predictors of fates in the subsequent year
PredictorStage19821983198419851986
CVnCVnCVnCVnCVn
Size (leaf area, cm2)Seedlings    18.9  60.8195    15.7  52.11426    13.6  49.3781    13.6  49.7404    11.7  48.7654
Juveniles  116.7  76.7135    87.2  76.7  165  105.0  60.4114  110.6  63.2100  105.0  59.5  76
 Pre-reproductives  636.1  39.4  78  584.0  38.4    74  492.2  43.3  70  496.7  36.6  87  482.4  38.7  77
 Reproductives1519  46.82011778  65.2  2101397  53.02031210  50.31721185  49.5186
Herbivory (% leaf area)Seedlings    15.3143.8195      4.4279.61426      2.4393.2781      3.8268.9404      3.8238.7654
Juveniles      6.4202.8135      2.2196.4  165      1.9518.6114      4.6266.8100      4.6208.4  76
 Pre-reproductives      2.0198.8  78      2.4331.9    74      1.7520.3  70      3.5191.0  87      4.3320.1  77
 Reproductives      3.2212.4201      2.2305.9  210      0.6320.6203      2.7198.2172      1.0136.7186
Competition (neighbourhood leaf area, cm2)Seedlings2229121.214251368  92.67811205115.54041355107.0654
Juveniles1758124.4  1651603100.11141021117.81001349105.1  76
Pre-reproductives1980102.1    741904101.4  701668  79.9  871501  94.7  77
 Reproductives5310101.9  2103344  68.32032365  73.71722848  64.6186
Reproduction (no. fruits)Reproductives    21.7  62.8203    32.8  71.8  211    20.4  62.5205    17.5  84.0173    32.0  78.7186
Size

Plant size varied among stages, by definition. Among-plant variability in size within stage class was low (the mean CV = 53%, N= 20 stage-years).

Herbivory

Percentage of leaf area damaged by herbivores tended to be low (mean = 3.6%, N = 20 stage-years) and decreased with increasing stage from a mean of 5.9% for seedlings to 1.9% for reproductives, with highest values recorded in 1982 (mean over stages was nearly twice and the seedling stage was nearly four times that of next highest year). Within a stage class, among-plant variability in herbivory was about fivefold greater than in plant size.

Local competition

Local competition varied among years and stages as well as within stages, and was highest in 1983 (1.4 × mean over 4 years) and for reproductive plants (1.7 × mean over 4 stages). Leaf area of neighbours was similar for all other stages. Variability was about twice as great as in plant size.

Fruit production

The number of fruits per reproductive plant varied nearly twofold across years. Fruit production depends upon two components: inflorescences produced per plant and fruits produced per inflorescence, whose relative importance differs between years (Schemske & Horvitz 1988; Horvitz & Schemske 1995). Fruit production in 1983 was high because plants made more inflorescences because of larger plant size and in 1986 because plants made more fruits per inflorescence because of favourable biotic interactions. Variability in fruit production within stage class was about 1.4 times that in plant size.

Discussion

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. Supplementary material
  10. References

PLANT SIZE

The evidence that plant size strongly impacted survival, relative growth and next year’s inflorescence production was of two kinds: firstly, the large effect of stage-class on each of these fate variables and secondly, the many instances of significant within-stage-class size effects. These results are not surprising for a long-lived perennial species with indeterminate growth. Previous research had already determined that demographic fates defined as transition probabilities were size-dependent (Horvitz & Schemske 1995). This result had motivated our use of a size-classified model in our previous analysis of population dynamics (Horvitz & Schemske 1995) as well as our inclusion of plant size as a predictor variable in the current analysis. Previous research had not addressed the variability of fates within size classes and had not analysed growth and reproduction in the same way that we do here.

In the current analysis, we found that the effect of plant size within a stage-class was important in different ways for different stages. Survival was consistently affected by plant size only for seedlings and juveniles. These small stages are probably most vulnerable to the annual loss of above-ground tissue during the dry season; if they are not big enough they simply cannot produce enough reserves to survive. Growth of seedlings and reproductives was consistently (and juveniles were often) affected by plant size. Perhaps the most surprising result here is that the size of pre-reproductives tended to affect their future inflorescence production more consistently than their growth. An association of large plant size with more reproduction and/or greater probability of becoming reproductive is a common pattern (Weiner 1982, 1988; Pacala & Silander 1985).

HERBIVORY

Damage by herbivores to leaves rarely had a significant effect on fate, impacting survival and growth only in 1985. Seedlings were least affected by herbivory, even though they had more damage than other stages. Patterns in the effects of herbivory thus contrasted with patterns in its magnitude. This factor was the only one whose effects differed more markedly among years than among stages, although the amount of damage varied more among stages than among years. The levels of herbivory were quite low for most years (higher in 1982) and stages, generally consistent with the idea that damage in natural populations is low, typically 5–15% of leaf area (Crawley 1989; Marquis 1992b). It has often been predicted that herbivory should have its biggest effects on seedlings (Hendrix 1988; Crawley 1989) and it is also expected that larger amounts of herbivory will result in a larger effect on plants (a threshold effect is often seen, e.g. Marquis 1984). Some have, however, challenged the idea that the magnitude of damage should be associated with effects on plant performance (Crawley 1989; Marquis 1992b) and our results support this. The surprising lack of effect of herbivory on seedlings here may be due to their higher relative growth rates, which may have compensated for tissue removal. Compensatory growth may lessen the effects of herbivores, both for individual plant performance and for population-level parameters (Louda et al. 1990).

LOCAL COMPETITION

Local competition (leaf area of neighbours) affected fates more often than herbivory. Significant effects were most often on survival (three cases) vs. one on relative growth and one on inflorescence production. Small plants were most affected by competition, including seedlings and juveniles. These patterns in the stage-related effects of competition contrasted with patterns in the magnitude of competition. Neighbourhood leaf area was highest for reproductives, the stage least impacted by it, with other stages having very similar values, but only the seedling stage being consistently significantly affected by it. This result is consistent with previous research that small plants are more likely to be impacted by competition than large plants (Thomas & Weiner 1989; Pacala & Weiner 1991). We therefore examined the ratio of the average size of neighbours to the size of focal plants and found that it varied by orders of magnitude among stages (73.2, 7.8, 1.1 and 0.5 for seedlings, juveniles, pre-reproductives and reproductives, respectively mean for 4 years, 1983–86). In 1983, the year of highest neighbourhood leaf area, there were more significant effects of competition than in the other years. Thus, unlike herbivory, temporal variation in the magnitude of neighbourhood leaf area was associated with temporal variation in its effects on plants.

HERBIVORY AND COMPETITION TOGETHER?

Factorial field experiments that have included high and low density treatments crossed with high and low herbivory treatments have often reported interaction effects on plant performance. Gurevitch et al. (2000) performed a meta-analysis of relative effects of competition and herbivory on survival and growth of five plant species. They found that plant growth was affected equally by competition and herbivory, and that there was no significant interaction. Plant survival, however, was more strongly affected by herbivory than by competition and there was significant interaction; in the presence of herbivores, competition had a stronger effect than it did in their absence. Rausher & Feeny (1980), not included by Gurevitch et al., found that herbivores had a large effect on mortality and growth of plants, and that plant density had a negative effect on growth in the presence of herbivores. Similarly, Parker & Salzman (1985), which was included in the meta-analysis, found that herbivores had a large effect on plant death rate and that competition only affected death rate in the presence of herbivores. In contrast, Cottam et al. (1986) (not included), found a large effect of competition and a small effect of herbivores on plant growth; only for the competing plants did herbivory have a significant effect. A subsequent study (Parmesan 2000) experimentally manipulated herbivory but used natural variation in density: use of an annual species enabled measurement of the effects on plant fitness, which was reduced by both increased density and increased herbivory. However, herbivory mattered most when density was lowest, a result that was contrary to expectations, but this may be an indirect effect of low density caused by low productivity.

Several recent experimental studies have examined the relative effects of herbivory and competition in the context of a productivity gradient, with conflicting results. Van der Wal et al. (2000) evaluated impacts on seedlings separately from impacts on larger plants; seedlings were less affected by herbivory than by competition. Overall, herbivory had its greatest effect in a low productivity site (perhaps similar to Parmesan 2000) and competition (for light) had its greatest effect in high productivity sites; herbivore exclusion increased competitive effects at all productivities. Bonser & Reader (1995), in contrast, found that the effects of both competitors and herbivores on plant growth were greatest at high productivity sites where they were both important, but at low productivity sites competition was more important than herbivory.

Our study was based on natural variation in both herbivory and competition and our results are not consistent with the patterns found in the meta-analysis of experimentally applied treatments. Rather than a greater effect of herbivory than competition on survival, we found that competition effects tended to be more frequent than herbivory effects. Nor did our data suggest interaction, as herbivory and competition effects rarely co-occurred. The impact of competition, but not of herbivory, was stage-dependent and the year of strongest herbivory effects (1985) differed from those of strong competitive effects (1983 and 1984). Our data do not address whether there are confounding productivity effects across plants or years that would cause variation in density, effects of competition and/or herbivore resistance.

FRUIT PRODUCTION

Current reproduction affected fate in only three cases (future inflorescence production twice, and growth rate once, all positively). Two of these effects were in 1982, which was not a year of high fruit production. These effects are not caused by plant size only. In 1982, plant size affected growth negatively and future inflorescence production positively; in contrast, current reproduction affected both growth and future inflorescence production positively. In 1986, plant size did not significantly affect future inflorescence production, but fruit production did. A previous experiment may shed some light on this result. Because of within-season costs of reproduction, plants with high reproduction grow less during a season than plants with low reproduction (Horvitz & Schemske 1988b) resulting in smaller plants at the end of the season and presumably at the beginning of the subsequent rainy season. If we couple this result with the result that small plants grow more rapidly than large plants within a season, we may have an explanation for why plants that made more fruits grew more rapidly in addition to making more fruits in the future. Perhaps these plants ‘escaped’ the general pattern that reproductive plants grew slowly.

1985 WAS THE WORST OF YEARS AND THE BEST OF YEARS

The year 1985 was unusual. First, it was the only year when competition did not affect seedling survival. Secondly, it was the only year in which herbivory did have significant effects. We don’t know why. It was the year of highest overall survival, but not by a large factor (1.1 × the mean). We note that 1985 was also distinct in some of our previous studies. It was the only year of significant directional selection on corolla tube lengths (Schemske & Horvitz 1989). It was the year that a rare but very efficient pollinator, Rhathymus, was most abundant and that a common pollinator, Euglossa, visited flowers 2.7 × more frequently than in other years. Thus, 1985 was the year that pollinator visitation had large effects on fruit production (Schemske & Horvitz 1988). In terms of population dynamics, the 1984–85 transition year contributed the most to overall variation in population growth rates (Horvitz et al. 1997). In three of four study plots, 1984–85 was the worst transition year for population growth rate, but in the fourth plot it was the best year (Horvitz & Schemske 1995).

Conclusions

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. Supplementary material
  10. References

In general, we found that the effects of biotic interactions varied among stages and through time. The large effect of competition on seedlings and juveniles was not surprising, but the small effect of herbivory on small plants was surprising. Temporal variation in the effect of herbivory was striking, as was its impact on large plants. More rapid growth by small plants was also striking. One of our five study years differed in several respects from the other years for an unknown reason. We conclude that natural variation in biotic interactions and their effects should be studied for several years and for all life stages of plant populations. Our future work will be concerned with analysis of these effects on plant population dynamics.

Acknowledgements

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. Supplementary material
  10. References

We thank especially Gonzalo Quino Xolo, Jorge Herrera and Randy Nutt for field assistance during several years, Lynn Pautler, Alejandro Villegas Gapi, Michelle Watters, Carol Yoon, Robert Raguso, André Chapp, Carol Berkower, Lori Scanlon, Juan Carranza and Ricardo Calvo for field assistance during single seasons, Luis Villa and Alicia Zapata Villa for permission to work on their land, Refugio Cedillo T. and Gonzalo Perez H. for assistance in conserving the field site, NSF grants DEB-8206993 and DEB-8415666 for providing research funds, John Heywood for writing the FORTRAN program to parameterize neighbourhood competition, and G.R. Burgess and C.L. Staines for determination of the beetles. We thank T.O.M. for facilitating and supporting analyses and writing and two anonymous referees for comments on a previous draft.

Supplementary material

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. Supplementary material
  10. References

Appendix 1 Multiple regression analyses of the effects of plant size, herbivory, neighbourhood competition and fruit production on survival, relative growth and inflorescence production the following year.

References

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Conclusions
  8. Acknowledgements
  9. Supplementary material
  10. References
  • Bonser, S.P. & Reader, R.J. (1995) Plant competition and herbivory in relation to vegetation biomass. Ecology, 90, 21762183.
  • Cottam, D.A., Whittaker, J.B. & Malloch, A.J.C. (1986) The effects of chrysomelid beetle grazing and plant competition on the growth of Rumex obtusifolius. Oecologia, 70, 452456.
  • Crawley, M.J. (1989) Insect herbivores and plant population dynamics. Annual Review of Entomology, 34, 531564.
  • Edwards, G.R., Bourdot, G.W. & Crawley, M.J. (2000) Influence of herbivory, competition and soil fertility on the abundance of Cirsium arvense in acid grassland. Journal of Applied Ecology, 37, 321324.
  • Ellison, A.M., Dixon, P.M. & Ngai, J. (1994) A null model for neighbourhood models of plant competitive interactions. Oikos, 71, 225238.
  • Gange, A.C. (1990) Effects of insect herbivory on herbaceous plants. Pests, Pathogens and Plant Communities (eds J. J.Burdon & S. R.Leather), pp. 4962. Blackwell Scientific Publications, Oxford.
  • Goldberg, D.E. (1987) Neighbourhood competition in an old-field community. Ecology, 68, 12111223.
  • Gurevitch, J., Morrison, J.A. & Hedges, L.V. (2000) The interaction between competition and predation: a meta-analysis of field experiments. American Naturalist, 155, 435453.
  • Harper, J.L. (1977) Population Biology of Plants. Academic Press, London, England.
  • Hendrix, S.D. (1988) Herbivory and its impact on plant reproduction. Plant Reproductive Ecology (eds J.Lovett Doust & L.Lovett Doust), pp. 246263. Oxford University Press, New York.
  • Horvitz, C.C. & Schemske, D.W. (1984) Effects of ants and an ant-tended herbivore on seed production of a neotropical herb. Ecology, 65, 13691378.
  • Horvitz, C.C. & Schemske, D.W. (1986a) Ant-nest soil and seedling growth in a neotropical ant-dispersed herb. Oecologia, 70, 318320.
  • Horvitz, C.C. & Schemske, D.W. (1986b) Seed dispersal of a neotropical myrmecochore: variation in removal rates and dispersal distance. Biotropica, 18, 319323.
  • Horvitz, C.C. & Schemske, D.W. (1986c) Seed dispersal and environmental heterogeneity in a neotropical herb: A model of population and patch dynamics. Symposium on Frugivores and Seed Dispersal (eds A.Estrada & T. H.Fleming), pp. 169186. Dr W. Junk Publishers, Dordrecht, Netherlands.
  • Horvitz, C.C. & Schemske, D.W. (1988a) A test of the pollinator limitation hypothesis for a neotropical herb. Ecology, 69, 200206.
  • Horvitz, C.C. & Schemske, D.W. (1988b) Demographic cost of reproduction in a neotropical herb: an experimental field study. Ecology, 69, 11281137.
  • Horvitz, C.C. & Schemske, D.W. (1994) Effects of dispersers, gaps, and predators on dormancy and seedling emergence in a tropical herb. Ecology, 75, 19491958.
  • Horvitz, C.C. & Schemske, D.W. (1995) Spatiotemporal variation in demographic transitions for a tropical understory herb: projection matrix analysis. Ecological Monographs., 65, 155192.
  • Horvitz, C.C., Schemske, D.W. & Caswell, H. (1997) The relative <<importance>> of life-history stages to population growth: prospective and retrospective analyses. Structured Population Models in Marine, Terrestrial and Freshwater Systems (eds S.Tuljapurkar & H.Caswell), pp. 247271. Chapman & Hall, New York.
  • Janzen, D.H. (1970) Herbivores and the number of tree species in tropical forests. American Naturalist, 104, 501208.
  • Janzen, D.H. (1971) Seed predation by animals. Annual Review of Ecology and Systematics, 2, 465492.
  • Kennedy, H. (1983) Plants: species accounts: Calathea insignis (Marantaceae). Costa Rican Natural History (ed. D. H.Janzen), pp. 204206. University of Chicago Press, Chicago, IL.
  • Louda, S.M. & Potvin. M.A. (1995) Effect of inflorescence-feeding insects on the demography and lifetime fitness of a native plant. Ecology, 76, 229245.
  • Louda, S.M., Keeler, K.H. & Holt, R.D. (1990) Herbivore influences on plant performance and competitive interactions. Perspectives on Plant Competition (eds J. B.Grace & D.Tilman), pp. 413444. Academic Press, San Diego, CA.
  • Mack, R.N. & Harper, J.L. (1977) Interference in annuals: spatial pattern and neighbourhood effects. Journal of Ecology, 65, 345363.
  • Maron, J.L. (1998) Insect herbivory above- and below ground: individual and joint effects on plant fitness. Ecology, 79, 12811293.
  • Maron, J.L. & Gardner, S.N. (2000) Consumer pressure, seed versus safe-site limitation and plant population dynamics. Oecologia, 124, 260269.
  • Marquis, R.J. (1984) Leaf herbivores decrease fitness of a tropical plant. Science, 226, 537539.
  • Marquis, R.J. (1992a) A bite is a bite is a bite? Constraints on response to folivory in Piper arieianum (Piperaceae). Ecology, 73, 143152.
  • Marquis, R.J. (1992b) Selective impact on herbivores. Plant Resistance to Herbivores and Pathogens: Ecology, Evolution and Genetics (eds R. S.Fritz & E. L.Simms), pp. 301325. University of Chicago Press, Chicago.
  • Pacala, S.W. & Silander, J.A. (1985) Neighbourhood models of plant population dynamics. 1. Single species models of annuals. American Naturalist, 125, 385411.
  • Pacala, S.W. & Weiner, J. (1991) Effects of competitive asymmetry on a local density model of plant interference. Journal of Theoretical Biology, 149, 165179.
  • Parker, M.A. & Salzman, A.G. (1985) Herbivore exclosure and competitor removal: effects on juvenile survivorship and growth in the shrub Gutierrezia microcephala. Journal of Ecology, 73, 903913.
  • Parmesan, C. (2000) Unexpected density-dependent effects of herbivory in a wild population of the annual Collinsia torreya. Journal of Ecology, 88, 392400.
  • Rausher, M.D. & Feeny, P. (1980) Herbivory, plant density, and plant reproductive success: the effect of Battus philenor on Aristolochia reticulata. Ecology, 61, 905917.
  • Rice, W.R. (1989) Analyzing tables of statistical significance. Evolution, 43, 223225.
  • SAS (1996) SAS, Version 6.12. SAS Institute Inc, Cary, NC.
  • Schemske, D.W. & Horvitz, C.C. (1984) Variation among floral visitors in pollination ability: a precondition for mutualism specialization. Science, 255, 519521.
  • Schemske, D.W. & Horvitz, C.C. (1988) Plant–animal interactions and fruit production in a neotropical herb: a path analysis. Ecology, 69, 11281137.
  • Schemske, D.W. & Horvitz, C.C. (1989) Temporal variation in selection on a floral character. Evolution, 43, 461465.
  • Sokal, R.R. & Rohlf, F.J. (1981) Biometry. W.H. Freeman, New York.
  • Soto, M. (1976) Algunos aspectos climáticos de la regíon de Los Tuxtlas. Vestigaciones Sobre la Regeneración de Selvas Altas En Veracruz, México (eds A.Gómez-Pompa et al.), pp. 70110. Compañia Editorial Continental, S.A., Consejo Nacional para la Enseñanza de Biología, Instituto de Investigaciones sobre Recursos Bioticas, México, D.F.
  • Strong, D.R. (1977) Rolled-leaf hispine beetles (Chrysomelidae) and their Zingiberales host plants in Middle America. Biotropica, 9, 156169.
  • Thomas, S.C. & Weiner, J. (1989) Including competitive asymmetry in measures of local interference in plant populations. Oecologia, 80, 349355.
  • Van der Wal, R., Egas, M., Van der Veen, A. & Bakker, J. (2000) Effects of competition and herbivory on plant performance along a natural productivity gradient. Journal of Ecology, 88, 317330.
  • Verkaar, H.J. (1987) Population dynamics: the influence of herbivory. New Phytologist, 106 (2), 4960.
  • Weiner, J. (1982) A neighbourhood model of annual-plant interference. Ecology, 63, 12371241.
  • Weiner, J. (1984) Neighbourhood interference amongst Pinus rigida individuals. Journal of Ecology, 72, 183195.
  • Weiner, J. (1988) The influence of competition on plant reproduction. Plant Reproductive Ecology (eds J.Lovett Doust & L.Lovett Doust), pp. 228245. Oxford University Press, New York.