An analytical model of stand dynamics as a function of tree growth, mortality and recruitment: the shade tolerance-stand structure hypothesis revisited

On hierarchical competition through reduction of individual growth

We consider a population organised hierarchically with respect to size in such a way that the growth rate of each individual depends only on the presence of larger individuals. As a concrete example one might think of a forest, in which the incidence of light on a tree (and hence how fast it grows) is affected by shading by taller trees. The classic formulation of a model for such a size-structured population employs a first order quasi-linear partial differential equation equipped with a non-local boundary condition. However, the model can also be formulated as a delay equation, more specifically a scalar renewal equation, for the population birth rate. After discussing the well-posedness of the delay formulation, we analyse how many stationary birth rates the equation can have in terms of the functional parameters of the model. In particular we show that, under reasonable and rather general assumptions, only one stationary birth rate can exist besides the trivial one (associated to the state in which there are no individuals and the population birth rate is zero). We give conditions for this non-trivial stationary birth rate to exist and analyse its stability using the principle of linearised stability for delay equations. Finally, we relate the results to the alternative, partial differential equation formulation of the model.

Phytoindication assessment of the effect of reconstruction on the light regime of an urban park

The ecological restoration of urban parks is used to increase their recreational attractiveness, improve air quality, mitigate urban heat island effects, improve stormwater infiltration, and provide other social and environmental benefits. The dynamics of plant communities after urban forest restoration requires investigation. The study assessed the impact of urban park reconstruction on the state of grass cover, phytoindication of changes in light regime caused by park reconstruction and found out the dependence of reliability of phytoindication assessment on the number of species in the relevant area. The study was conducted in the recreational area of the Botanical Garden of the Oles Honchar Dnipro National University (Ukraine). A tree plantation was created after the Second World War in the location of a natural oak forest. In 2019, a 2.8 ha area of the park was reconstructed. The samples were taken within polygons, two of which were placed in the reconstruction area and two of which were placed in a similar section of the park where no reconstruction was performed. During the reconstruction process, walkways were rebuilt, shrubs were removed, old, damaged trees were removed, and tree crowns were trimmed. Juvenile trees were planted in place of the removed old trees. Old outbuildings, which greatly impaired the aesthetic perception of the park, were also removed. Transport and construction machinery was involved in the reconstruction. A total of 65 plant species were found within the studied polygons. The number of herbaceous species in the park area after reconstruction was higher than without reconstruction. The crown closure in the reconstructed area was significantly lower than that in the untreated conditions. The phytoindication assessment showed that the light regime varies from the conditions suitable for the scyophytes (plants of typical foliage forests) to the conditions suitable for the sub-heliophytes (plants of light forests and shrubberies, or high herbaceous communities; lower layers are in the shade). The light regime in the park area after reconstruction was statistically significantly different from the regime in the untreated park area. The lighting regime after the reconstruction was favourable to sub-heliophytes, and without reconstruction the regime favoured hemi-scyophytes. Tree canopy crown closure negatively correlated with grass height and herbaceous layer projective cover. The tree canopy crown closure, grass height, and herbaceous layer projective cover were able to explain 86% of the phytoindication assessment of the lighting regime variation. These parameters negatively affected the light regime. The prospect of further research is to investigate the dependence of indicative reliability of the assessment of other environmental factors with the help of phytoindication depending on the number of species. In addition to the indication of traditional ecological factors it is of particular interest to clarify the aspect of the dynamics of hemeroby indicators as a result of park reconstruction.

Comparing shade tolerance measures of woody forest species

Shade tolerance, the minimum light requirement for plant survival, is a key trait for understanding community assembly and forest dynamics. However, it is poorly defined for tree species to date. Current methods of measuring shade tolerance vary considerably in their performance. For instance, some measures of shade tolerance are unreliable except under some specific conditions. Therefore, it is necessary to compare the performance of these methods to provide guidance of choosing appropriate shade tolerance measures in future studies. We collected a large dataset of light traits and other life history traits for 137 understory wood species in a subtropical forest and tested the performance of five commonly used shade-tolerance indices. Results showed that all the shade-tolerance measures, except the low-light abundance index, performed poorly in distinguishing and ranking shade tolerance of the tested species. The shade tolerance quantified by the low-light abundance was consistent with empirical classification of shade-tolerance/intolerance groups and successional seral stages of species. Comparison of the shade tolerance between trees of different diameter at breast height (DBH) or height classes further confirmed the reliability of low-light abundance. We conclude that low-light abundance is the most objective and practical of the five most commonly-used methods for measuring and ranking shade tolerance of understory wood species in our study forest, and likely in other forests as well. The simplicity of the method should greatly facilitate the assessment of light niche differentiation between species and thus contribute to understanding coexistence of tree species in forests.

Linking fine root morphology, hydraulic functioning and shade tolerance of trees

Background and Aims

Understanding root traits and their trade-off with other plant processes is important for understanding plant functioning in natural ecosystems as well as agricultural systems. The aim of the present study was to determine the relationship between root morphology and the hydraulic characteristics of several orders of fine roots (<2 mm) for species differing in shade tolerance (low, moderate and high).

Methods

The morphological, anatomical and hydraulic traits across five distal root orders were measured in species with different levels of shade tolerance and life history strategies. The species studied were Acer negundo, Acer rubrum, Acer saccharum, Betula alleghaniensis, Betula lenta, Quercus alba, Quercus rubra, Pinus strobus and Pinus virginiana.

Key Results

Compared with shade-tolerant species, shade-intolerant species produced thinner absorptive roots with smaller xylem lumen diameters and underwent secondary development less frequently, suggesting that they had shorter life spans. Shade-tolerant species had greater root specific hydraulic conductance among these roots due to having larger diameter xylems, although these roots had a lower calculated critical tension for conduit collapse. In addition, shade-intolerant species exhibited greater variation in hydraulic conductance across different root growth rings in woody transport roots of the same root order as compared with shade-tolerant species.

Conclusions

Plant growth strategies were extended to include root hydraulic properties. It was found that shade intolerance in trees was associated with conservative root hydraulics but greater plasticity in number of xylem conduits and hydraulic conductance. Root traits of shade-intolerant species were consistent with the ability to proliferate roots quickly for rapid water uptake needed to support rapid shoot growth, while minimizing risk in uncertain environments.

Competition for light in forest population dynamics: From computer simulator to mathematical model

In this article we build a mathematical model for forest growth and we compare this model with a computer forest simulator named SORTIE. The main ingredient taken into account in both models is the competition for light between trees. The parameters of the mathematical model are estimated by using SORTIE model, when the parameter values of SORTIE model correspond to the ones previously evaluated for the Great Mountain Forest in USA. We see that the best fit of the parameters of the mathematical model is obtained when the competition for light influences only the growth rate of trees. We construct a size structured population dynamics model with one and two species and with spatial structure.

Responses to shading of naturalized and non-naturalized exotic woody species

BACKGROUND AND AIMS

Recent studies have suggested that responses to shading gradients may play an important role in establishment success of exotic plants, but hitherto few studies have tested this. Therefore, a common-garden experiment was conducted using multiple Asian woody plant species that were introduced to Europe >100 years ago in order to test whether naturalized and non-naturalized species differ in their responses to shading. Specifically, a test was carried out to determine whether naturalized exotic woody species maintained better growth under shaded conditions, and whether they expressed greater (morphological and physiological) adaptive plasticity in response to shading, relative to non-naturalized species.

METHODS

Nineteen naturalized and 19 non-naturalized exotic woody species were grown under five light levels ranging from 100 to 7 % of ambient light. For all plants, growth performance (i.e. biomass), morphological and CO2 assimilation characteristics were measured. For the CO2 assimilation characteristics, CO2 assimilation rate was measured at 1200 μmol m(-2) s(-1) (i.e. saturated light intensity, A1200), 50 μmol m(-2) s(-1) (i.e. low light intensity, A50) and 0 μmol m(-2) s(-1) (A0, i.e. dark respiration).

KEY RESULTS

Overall, the naturalized and non-naturalized species did not differ greatly in biomass production and measured morphological and CO2 assimilation characteristics across the light gradient. However, it was found that naturalized species grew taller and reduced total leaf area more than non-naturalized species in response to shading. It was also found that naturalized species were more capable of maintaining a high CO2 assimilation rate at low light intensity (A50) when grown under shading.

CONCLUSIONS

The results indicate that there is no clear evidence that the naturalized species possess a superior response to shading over non-naturalized species, at least not at the early stage of their growth. However, the higher CO2 assimilation capacity of the naturalized species under low-light conditions might facilitate early growth and survival, and thereby ultimately favour their initial population establishment over the non-naturalized species.

Matrix models for size-structured populations: unrealistic fast growth or simply diffusion?

Matrix population models are widely used to study population dynamics but have been criticized because their outputs are sensitive to the dimension of the matrix (or, equivalently, to the class width). This sensitivity is concerning for the population growth rate (λ) because this is an intrinsic characteristic of the population that should not depend on the model specification. It has been suggested that the sensitivity of λ to matrix dimension was linked to the existence of fast pathways (i.e. the fraction of individuals that systematically move up a class), whose proportion increases when class width increases. We showed that for matrix population models with growth transition only from class i to class i + 1, λ was independent of the class width when the mortality and the recruitment rates were constant, irrespective of the growth rate. We also showed that if there were indeed fast pathways, there were also in about the same proportion slow pathways (i.e. the fraction of individuals that systematically remained in the same class), and that they jointly act as a diffusion process (where diffusion here is the movement in size of an individual whose size increments are random according to a normal distribution with mean zero). For 53 tree species from a tropical rain forest in the Central African Republic, the diffusion resulting from common matrix dimensions was much stronger than would be realistic. Yet, the sensitivity of λ to matrix dimension for a class width in the range 1-10 cm was small, much smaller than the sampling uncertainty on the value of λ. Moreover, λ could either increase or decrease when class width increased depending on the species. Overall, even if the class width should be kept small enough to limit diffusion, it had little impact on the estimate of λ for tree species.

Stand dynamics and tree coexistence in an analytical structured model: the role of recruitment

Understanding the mechanisms of coexistence and niche partitioning in plant communities is a central question in ecology. Current theories of forest dynamics range between the so-called neutral theories which assume functional equivalence among coexisting species to forest simulators that explain species assemblages as the result of tradeoffs in species individual strategies at several ontogenetic stages. Progress in these questions has been hindered by the inherent difficulties of developing analytical size-structured models of stand dynamics. This precludes examination of the relative importance of each mechanism on tree coexistence. In previous simulation and analytical studies emphasis has been given to interspecific differences at the sapling stage, and less so to interspecific variation in seedling recruitment. In this study we develop a partial differential equation model of stand dynamics in which competition takes place at the recruitment stage. Species differ in their size-dependent growth rates and constant mortality rates. Recruitment is described as proportional to the basal area of conspecifics, to account for fecundity and seed supply per unit of basal area, and is corrected with a decreasing function of species specific basal area to account for competition. We first analyze conditions for population persistence in monospecific stands and second we investigate conditions of coexistence for two species. In the monospecific case we found a stationary stand structure based on an inequality between mortality rate and seed supply. In turn, intra-specific competition does not play any role on the asymptotic extinction or population persistence. In the two-species case we found that coexistence can be attained when the reciprocal negative effect on recruitment follows a given relation with respect to intraspecific competition. Specifically a tradeoff between recruitment potential (i.e. shade tolerance or predation avoidance) and fecundity or growth rate. This is to our knowledge the first study that describes coexistence mechanisms in an analytical size-structured model in terms of competitive differences at the regeneration state.

M. Structure and dynamics of a Cariniana estrellensis (Lecythidaceae) population in a fragment of Atlantic Forest in Minas Gerais, Brazil

We aimed to describe population structure and dynamics of Cariniana estrellensis (Raddi) Kuntze to test the hypothesis that this species survives in the forest by forming a seedling bank. We evaluated seed germination, spatial distribution, and recruitment, growth and mortality rates of young individuals. To characterize population structure a 1.2-ha plot was defined, where reproductive adults were mapped; also 100 6 m² sub-plots were established to characterize structure and monitor dynamics of young individuals. We estimated seed production using seed collectors and determined the percentage of canopy cover by hemispherical photographs. Seed rain and saplings showed clustered distribution indicating habitat-patch formation. Sapling mortality occurred mainly during the initial establishment phase. Size structure was characterized by many saplings (X = 9,763 individuals ha-1) and few adults (X = 5 individuals ha-1), associated with a high rate of seed production (X = 60,800 seeds ha-1), low growth rates (X = 2.37 cm ano-1) and mortality (15.66%) of established saplings, showing that species invest in seedling bank formation as a reproductive strategy.

Co-dominance and succession in forest dynamics: the role of interspecific differences in crown transmissivity

Forests that are composed of two or more tree species with similar ecological strategies appear to contradict the competitive exclusion principle. Beech-maple communities are a well-known example of such a system. On a local scale, a number of mechanisms have been proposed to explain the coexistence of these two species. These are reciprocal replacement, external factors that favour alternatively one or the other species and demographic stochasticity. This paper presents and analyses a simple mathematical model that shows that external factors are not an essential requirement for coexistence. Rather, coexistence requires interspecific differences in light transmissivity through the crowns of adult trees. However, all the three mechanisms mentioned above can be interpreted within the framework of the model. Furthermore, many models of forest dynamics make use of shade tolerance as a key feature in describing successional dynamics. Despite its importance, however, shade tolerance does not have a commonly accepted quantitative definition. Here, a simple scheme is proposed where the relationship between shade tolerance, individual traits (growth and survival) and successional status is defined. This might have important implications in understanding the overall dynamics. Theoretical results have been compared with a number of studies carried out in North American forests. In particular, coexistence in beech-maple communities and the relation between shade tolerance and successional status in a beech-hemlock-birch community have been discussed.