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Two versions of a stage-structured model of Cirsium vulgare population dynamics were developed. Both incorporated density dependence at one stage in the life cycle of the plant. In version 1 density dependence was assumed to operate during germination whilst in version 2 it was included at the seedling stage. Density-dependent parameter values for the model were estimated from annual census data in a factorial grazing experiment. Version 1 of the model produced significant estimates of density dependence under field conditions. The estimated values, when included in a simulation of the dynamics, produced two-point limit cycles under conditions of hard grazing. The limit cycles were most pronounced at the early rosette stage. Comparison of the effects of density dependence at the two different stages in the life cycle revealed a strong difference in predicted dynamics. This emphasizes the importance of determining where density dependence operates under field conditions and the potential problems of arbitrarily assigning it to particular life-history stages. Version 1 of the model produced a good prediction of observed mean plant density across the different grazing treatments (r2=0.81, P<0.001).

Recent studies have used transition matrix elasticity analysis to investigate the relative role of survival (L), growth (G) and fecundity (F) in determining the estimated rate of population increase for perennial plants. The relative importance of these three variables has then been used as a framework for comparing patterns of plant life history in a triangular parameter space. Here we analyse the ways in which the number of life-cycle stages chosen to describe a species (transition matrix dimensionality) might influence the interpretation of such comparisons. Because transition matrix elements describing survival (“stasis”) and growth are not independent, the number of stages used to describe a species influences their relative contribution to the population growth rate. Reduction in the number of stages increases the apparent importance of stasis relative to growth, since each becomes broader and fewer individuals make the transition to the next stage per unit time period. Analysis of a test matrix for a hypothetical tree species divided into 4–32 life-cycle stages confirms this. If the number of stages were defined in relation to species longevity so that mean residence time in each stage were approximately constant, then the elasticity of G would reflect the importance of relative growth rate to ?. An alternative, and simpler, approach to ensure comparability of results between species may be to use the same number of stages regardless of species longevity. Published studies for both herbaceous and woody species have tended to use relatively few stages to describe life cycles (herbs: n=45, $$\bar x = 6.16 \pm 4.63$$ ; woody plants: n=21, $$\bar x = 8.38 \pm 3.57$$ ) and so approximate this approach. By using the same number of stages regardless of longevities, the position of species along the G-L side of the triangular parameter space largely reflects differences in longevity. The extent of variation in elasticity for L, G and F within and between species may also be related to factors such as successional status and habitat. For example, the shade-tolerant woody species, Araucaria cunninghamii, shows greater importance for stasis (L), while the gap-phase congener species, Araucaria hunsteinii, shows higher values for G (although values are likely to vary with the stage of stand development).

Vertebrate and invertebrate herbivores are both important in mesotrophic grasslands and these two different classes of herbivore potentially interact in their effect upon plant populations. We used two field experiments to test for higher order interactions (HOIs) among sheep, slugs and seedlings, using the mechanistic definition that an HOI occurs when the presence of one species modifies the interaction between two others. In each experiment slug addition and slug-removal treatments were nested inside treatments that altered sheep grazing intensity and timing, and the emergence, of seedlings from experimentally sown seeds was monitored. In Experiment 1, seedling numbers of Cerastium fontanum were increased by intense summer grazing by sheep in both slug-addition and slugremoval treatment, but winter grazing by sheep only increased seedling emergence if slugs were removed. In Experiment 2, winter grazing by sheep significantly reduced total seedling emergence of four species sown (Lotus corniculatus, Plantago lanceolata, Leucanthemum vulgare, Achillea millefolium), but the effect was only seen where slugs were removed. Though the experimental system is a relatively simple one with only four components (sheep, slugs, seedlings and the matrix vegetation), higher order interactions, a combination of direct and indirect effects and possible switching behaviour by slugs are all suggested by our results.

We analyse demographic data from a seven-year study of the annual crucifer Erophila verna which showed two-year cycles of abundance in the field. The unusual behaviour of this population is shown to be the consequence of overcompensating density-dependence. Very local differences in germination succes between plots can account for observed differences in their population dynamics over the long term.