Summary1. Large variation in the size of individuals is a ubiquitous feature of natural plant populations. While the role of competition in generating this variation has been studied extensively, the potential effects of positive interactions among plants, which are common in high-stress environments, have not been investigated. 2. Using an individual-based 'zone-of-influence' model, we investigate the effects of competition, abiotic stress and facilitation on size inequality in plant monocultures. In the model, stress reduces the growth rate of plants, and facilitation ameliorates the effects of stress. Both facilitation and competition occur in overlapping zones of influence. We tested some of the model's predictions with a field experiment using the clonal grass Elymus nutans in an alpine meadow. 3. Facilitation increased the size inequality of model populations when there was no density-dependent mortality. This effect decreased with density as competition overwhelmed facilitation. The lowest size inequality was found at intermediate densities both with the model and in the field. 4. When density-dependent mortality was included in the model, stress delayed its onset and reduced its rate by reducing growth rates, so the number of survivors at any point in time was higher under harsh than under more benign conditions. Facilitation increased size inequality during selfthinning. 5. Synthesis. Our results demonstrate that facilitation interacts with abiotic stress and competition to influence the degree of size inequality in plant populations. Facilitation increased size inequality at low to intermediate densities and during self-thinning.
Conventional outputs of physics-based landslide forecasting models are presented as deterministic 9warnings by calculating the safety factor (Fs) of potentially dangerous slopes. However, these models are highly 10 dependent on variables such as cohesion force and internal friction angle which are affected by high degree of 11 uncertainty especially at a regional scale, which result in unacceptable uncertainties of Fs. Under such circum-12 stances, the outputs of physical models are more suitable if presented in the form of landslide probability values. 13In order to develop such models, a method to link the uncertainty of soil parameter values with landslide probabil-14 ity is devised. This paper proposes the use of Monte Carlo method to quantitatively express uncertainty by as-15signing random values to physical variables inside a defined interval. The inequality Fs<1 is tested for each pixel 16 in n simulations which are integrated in a unique parameter. This parameter links the landslide probability to the 17 uncertainties of soil mechanical parameters and is used to create a physics-based probabilistic forecasting model 18 for rainfall-induced shallow landslides. The prediction ability of this model was tested in a case study, in which 19 simulated forecasting of landslide disasters associated to heavy rainfalls on July 9 of 2013 in the Wenchuan 20 earthquake region of Sichuan province, China was performed. The proposed model successfully forecasted land-21 slides in 159 of the 176 disaster points registered by the geo-environmental monitoring station of Sichuan prov-22 ince. Such testing results indicate that the new model can be operated in a high efficient way and show more reli-23 able results attributing to its high prediction accuracy. Accordingly, the new model can be potentially packaged 24 into a forecasting system for shallow landslides providing technological support for the mitigation of these disas-25 ters at regional scale. 26
Comparisons between competing and non-competing sunflower (Helianthus annuus L.) populations demonstrate pronounced effects of density on plant height growth, height-to-crown width ratio, and a population's height inequality. In the present study, non-destructive measurements of height and the projected crown area of sunflower plants were taken at seven times from emergence to fruit maturation in even-aged monospecific stands with initial densities of 1, 4, 16, and 64 plants/m 2 . The mean height of populations increased and then decreased with increasing population density; the height inequalities of uncrowded populations decreased during stand growth, whereas the height inequalities of crowded populations decreased first and then increased during stand development. The interindividual relationships between the relative height growth rate and height within uncrowded populations became significantly negative during population growth, whereas these relationships were negative first and then became positive during the development of crowded populations. In the uncrowded populations, the static interindividual relationship between height-to-crown width ratio and volume was positive, whereas for the crowded population these relationships became negative with increasing competition for light. The data suggest that the plastic responses of plant height and height-to-crown width ratio to light competition will become more intense with increasing competition intensity. The results of the present study argue strongly for the importance of size-dependent individual-level plastic responses due to size-asymmetric light competition in generating the variations in population height inequality.
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