Modeling the growth of individuals in crowded plant populations

Aims We present an improved model for the growth of individuals in plant populations experiencing competition.Methods Individuals grow sigmoidally according to the Birch model, which is similar to the more commonly used Richards model, but has the advantage that initial plant growth is always exponential. The individual plant growth models are coupled so that there is a maximum total biomass for the population. The effects of size-asymmetric competition are modeled with a parameter that reflects the size advantage that larger individual have over smaller individuals. We fit the model to data on individual growth in crowded populations of Chenopodium album .Important findings When individual plant growth curves were not coupled, there was a negative or no correlation between initial growth rate and final size, suggesting that competitive interactions were more important in determining final plant size than were plants' initial growth rates. The coupled growth equations fit the data better than individual, uncoupled growth models, even though the number of estimated parameters in the coupled competitive growth model was far fewer, indicating the importance of modeling competition and the degree of size-asymmetric growth explicitly. A quantitative understanding of stand development in terms of the growth of individuals, as altered by competition, is within reach.     

Effects of variation in individual growth on plant species coexistence

Abstract. Both size structure and variability (spatial heterogeneity, disturbance, stochasticity, variation in species attributes, etc.) are regarded as regulatory mechanisms of species coexistence. However, none of the models so far proposed consider both size structure and variability simultaneously. A size-structured variation model for plant-community dynamics is proposed, which is based on the diffusion model for growth dynamics of plant populations. This model has four functions: (1) mean growth rate of individuals of size x at time t, G(t, x) (species-specific mean traits, e.g. competitive ability); (2) variance in growth rate of individuals of size x at time t, D(t, x) (stochastic factors due to genetic variation, environmental heterogeneity, spatial variation of individuals, etc.); (3) mortality rate of individuals of size x at time t, M(t, x); and (4) recruitment rate at time t, R(t), as a boundary condition. The interference function for individuals of size x at time t, C(t, x), is introduced, which expresses the degree of interactions between individuals and hence averaged effects of local neighbourhood competition; the G(t, x), D(t, x), M(t, x) and R(t) functions are given in terms of C(t, x). These four functions describe the growth dynamics of individuals of each species in the plant community. Effects of the G(t, x), D(t, x), M(t, x) and R(t) functions on species coexistence in plant communities were evaluated by simulation and the relative importance of the D(t, x) function as well as size structure was shown for species coexistence especially in plant communities where competition among species is non-transitive or niche limitation does not work.     

Heterogeneous growth of plant tissues

KORN, R., 1993. Heterogeneous growth of plant tissues. Heterogeneous growth is defined as different rates or patterns of growth in adjacent tissue regions, in contrast to homogeneous growth where a region expresses a uniform rate or pattern of growth. Heterogeneous growth is inspected in a variety of plant tissues and the pattern of expansion is characterized for each. In the case of epidermal cell proliferation, different growth rates for cell plates and old walls lead to the feature of coordinated growth in which slow growth of the former is compensated for by a faster rate of the latter. Examples include leaf epidermal cells above veins growing differently from those above areole regions, and pairs of guard cells of stomata ceasing to expand before other epidermal cells. In the alga Coleochaete only marginal walls grow, and at different rates around the colony, to generate a fractal, stochastic type of coordinated growth. In the fern gametophyte there are complex gradients of differential growth rates. Epidermal cells of apices are often of mixed growth, as cells at the summit undergo two dimensional expansion while cells along the flanks express one dimensional expansion. Coordinated growth requires matched rates where the constraining effect of the slower growing region is compensated for by a faster rate in an encircling region compared to the average rate of the overall tissue. Mixed and differential growth patterns do not necessarily create constraints and so lead to smooth tissue expansion. Emergence of some constraints leads to breaking of symmetry and disruptive growth as in the appearance of new axes found in organs and epidermal derivatives. In planar development heterogeneous growth appears to be the rule, and homogeneous growth the exception.     

Individualism in plant populations: using stochastic differential equations to model individual neighbourhood-dependent plant growth

We study individual plant growth and size hierarchy formation in an experimental population of Arabidopsis thaliana, within an integrated analysis that explicitly accounts for size-dependent growth, size- and space-dependent competition, and environmental stochasticity. It is shown that a Gompertz-type stochastic differential equation (SDE) model, involving asymmetric competition kernels and a stochastic term which decreases with the logarithm of plant weight, efficiently describes individual plant growth, competition, and variability in the studied population. The model is evaluated within a Bayesian framework and compared to its deterministic counterpart, and to several simplified stochastic models, using distributional validation. We show that stochasticity is an important determinant of size hierarchy and that SDE models outperform the deterministic model if and only if structural components of competition (asymmetry; size- and space-dependence) are accounted for. Implications of these results are discussed in the context of plant ecology and in more general modelling situations.     

Modeling the growth of individuals in plant populations: local density variation in a strand population of Xanthium strumarium (Asteraceae)

We studied the growth of individual Xanthium strumarium plants growing at four naturally occurring local densities on a beach in Maine: (1) isolated plants, (2) pairs of plants ≤1 cm apart, (3) four plants within 4 cm of each other, and (4) discrete dense clumps of 10-39 plants. A combination of nondestructive measurements every 2 wk and parallel calibration harvests provided very good estimates of the growth in aboveground biomass of over 400 individual plants over 8 wk and afforded the opportunity to fit explicit growth models to 293 of them. There was large individual variation in growth and resultant size within the population and within all densities. Local crowding played a role in determining plant size within the population: there were significant differences in final size between all densities except pairs and quadruples, which were almost identical. Overall, plants growing at higher densities were more variable in growth and final size than plants growing at lower densities, but this was due to increased variation among groups (greater variation in local density and/or greater environmental heterogeneity), not to increased variation within groups. Thus, there was no evidence of size asymmetric competition in this population. The growth of most plants was close to exponential over the study period, but half the plants were slightly better fit by a sigmoidal (logistic) model. The proportion of plants better fit by the logistic model increased with density and with initial plant size. The use of explicit growth models over several growth intervals to describe stand development can provide more biological content and more statistical power than "growth-size" methods that analyze growth intervals separately.     

Plant compensatory growth: a conquering strategy in plant–herbivore interactions?

We present a theoretical analysis that considers the phenotypic trait of compensatory growth ability in a context of population dynamics. Our model depicts a system of three interactors: herbivores and two different plant types referred to as ordinary and compensating. The compensating plant type has the ability to increase its intrinsic rate of biomass increase as a response to damage. This compensatory growth ability is maintained at the expense of a reduced growth rate in the absence of damage, where the ordinary plant type has the higher growth rate. Analysis of this system suggests that, even though a compensatory capacity of this kind will not imply an increase in equilibrium plant density, it will give a competitive advantage in relation to other plants, in the presence of a sufficiently efficient herbivore. Invasion of compensating plants into a population of non-compensating plants is facilitated by a high compensatory growth ability and a high intrinsic rate of plant biomass increase. Conversely, an ordinary plant can invade and outcompete a compensating plant when the herbivore is characterised by a relatively low attack rate, and/or when plant intrinsic growth rate is decreased.     

Modelling the uptake of nitrate by a growing plant with an adjustable root nitrate uptake capacity

A new model is presented to predict the plant uptake of nitrate supplied by diffusion and mass flow to its roots. Plant growth, root-shoot ratio and the plant's nitrate uptake capacity are all set dependent on the plant's N nutrition state. By thoroughly integrating processes occurring in both plant and soil, the model enables to control the relative importance of both under a wide range of different nutritional scenarios.Soil parameters D₀ diffusion coefficient in water (m² day^-1) - D_e diffusion coefficient in soil (m² day^-1) - C nitrate concentration in soil (mol m^-3) - f tortuosity (-) - volumetric moisture content (-) - R radial distance from root axis (m) Plant parameters b₁, b₂ parameters of biomass partitioning Equation (10) - IR interroot distance (m) - K_mU Michaelis-Menten constant of the uptake system (mol m^-3) - K_mNRA Michaelis-Menten constant of nitrogen reduction system (mol g^-1) - k₁, k₂, k₃ parameters of growth model Equation (9) - L_v Root length density (m m^-3) - NO_{3 set} ^- Set point of the cytoplasmatic nitrate pool (mol g^-1 dw) - NO_{3 c} ^- cytoplasmatic nitrate concentration (mol g^-1 dw) - NO_{3 v} ^- vacuolar nitrate concentration (mol g^-1 dw) - NRA_max maximum nitrate reductase activity (mol g^-1 dw day^-1) - N_re reduced nitrogen content (mol) - N_remax maximum reduced N concentration in the plant (mol g^-1 dw) - P partitioning coefficient of nitrate between cyplasm and vacuole - R(1) root radius (m) - RGR relative growth rate (day^-1) - U uptake rate (mol day^-1 m^-2) - U_max maximum uptake rate (Eq. 6) (day^-1 m^-2) - Vo water flux at root surface (m day^-1) - W_r root dry weight (g) - W_sh shoot dry weight (g) - X model parameter: number of root compartments - Y model parameter: number of nodes     

Modelling attention in individual cells leads to a system with realistic saccade behaviours

Single cell recordings in monkey inferior temporal cortex (IT) and area V4 during visual search tasks indicate that modulation of responses by the search target object occurs in the late portion of the cell’s sensory response (Chelazzi et al. in J Neurophysiol 80:2918–2940, 1998; Cereb Cortex 11:761–772, 2001) whereas attention to a spatial location influences earlier responses (Luck et al. in J Neurophysiol 77:24–42, 1997). Previous computational models have not captured differences in the latency of these attentional effects and yet the more protracted development of the object-based effect could have implications for behaviour. We present a neurodynamic biased competition model of visual attention in which we aimed to model the timecourse of spatial and object-based attention in order to simulate cellular responses and saccade onset times observed in monkey recordings. In common with other models, a top-down prefrontal signal, related to the search target, biases activity in the ventral visual stream. However, we conclude that this bias signal is more complex than modelled elsewhere: the latency of object-based effects in V4 and IT, and saccade onset, can be accurately simulated when the target object feedback bias consists of a sensory response component in addition to a mnemonic response. These attentional effects in V4 and IT cellular responses lead to a system that is able to produce search scan paths similar to those observed in monkeys and humans, with attention being guided to locations containing behaviourally relevant stimuli. This work demonstrates that accurate modelling of the timecourse of single cell responses can lead to biologically realistic behaviours being demonstrated by the system as a whole.     

黄土丘陵半干旱区柠条林密度对土壤水分和柠条生长的影响

研究密度对土壤水分和植物生长的影响对森林植被恢复和生态建设具有重要的意义。以黄土丘陵半干旱区人工柠条为研究对象,对相同立地条件下不同密度柠条林生长与林地土壤水分进行了长期定位观测和分析。研究表明,1—5年生柠条不同密度林地土壤水资源量差异显著,从第3年开始,土壤水资源量随着密度增加而增加;10—12年生柠条密度越低土壤水资源量越高(Treatment4除外,T4),不同密度之间水资源量差异不显著。1—3年生柠条密度越高会促进其株高生长;从第四年开始,柠条密度过高会抑制其株高生长;1—5年生柠条密度越高基径生长越快,不同密度生长差异不显著;10—12年生密度过高(Treatment1,T1)或过低(T4)均会抑制柠条株高与基径生长。在柠条播种后第5年,高密度试验小区(T1和Treatment2,T2)柠条林地最大入渗深度土壤水资源量降到水资源利用限度,此时需要依据土壤水分植被承载力通过平茬来降低林分密度,以达到减少土壤水分消耗和可持续利用土壤水资源之目的。     

Modelling the relative growth rate as a function of plant nitrogen concentration

The relationship between the relative growth rate (RGR) and the nitrogen concentration of the whole plant (PNC) was analyzed by using experimentally determined relations (1) between the PNC and the fraction of dry matter (LWR) and nitrogen in leaves, (2) between the specific leaf area (SLA) and the leaf nitrogen concentration (LNC) and (3) between the net assimilation rate (NAR) and the LNC on an area basis. A strong dependence of RGR on nitrogen concentration resulted from the increase in NAR, LWR and SLA with increasing PNC. A curvilinear relationship between RGR and PNC gave an optimum curve for nitrogen productivity against PNC.     

Computer simulations support a core prediction of a contentious plant model

? Premise of the study: An overarching but vigorously debated plant model proposed by the West, Brown, Enquist (WBE) theory predicts the scaling relationships for numerous botanical phenomena. However, few studies have evaluated this model's basic assumptions, one of which is that natural selection has resulted in hierarchal networks that minimize the energy required to distribute nutrients internally and have thus produced highly efficient organisms. ? Methods: If these core assumptions are correct, an "idealized" plant complying with all of the scaling relationships emerging from the WBE plant model should rapidly outcompete other plants, even those that differ slightly from it. To test this reasoning, a computer model was used to simulate competition between an idealized WBE plant, a generic "average" angiosperm (GA), and one of seven variants of the idealized WBE plant, each being similar to the GA in one of the GA's scaling parameters. ? Key results: Replicate simulations show that the idealized WBE plant rapidly outcompetes all other plants under light-shade and open-field conditions. However, changing only one of the WBE's scaling parameters results in death or in the coexistence of WBE and GA plants. ? Conclusions: These simulations support a core assumption of the WBE plant model and suggest why this idealized plant has not evolved.     

Habituation of plant cells does not mean insensitivity to plant growth regulators

Summary Fully habituated organogenic and nonorganogenic sugarbeet calluses reacted to application of the synthetic auxin [3-benzo(b) selenienyl] acetic acid by changes in growth and ethylene production. Treatment of fully habituated cells of periwinkle with 2,4-dichlorophenoxyacetic acid led to the decrease of free cytokinin contents (isopentenyl adenine, zeatin riboside, and zeatin) during the late exponential phase of growth. The polyamine contents were also modified and the capacity to biotransform secologanin into ajmalicine was decreased. Treatment of the habituated periwinkle cells with zeatin greatly increased the amount of a polypeptide of 16 kDa; this response was more marked than that displayed by the auxin-dependent line. These data show that hormone-independent calluses and cell suspensions can retain some sensitivity to growth hormones. However, differences of responses were observed between the auxin-dependent lines and the habituated lines.     

Modelling the distribution and compositional variation of plant communities at the continental scale

Aim

We investigate whether (1) environmental predictors allow to delineate the distribution of discrete community types at the continental scale and (2) how data completeness influences model generalization in relation to the compositional variation of the modelled entities.

Location

Europe.

Methods

We used comprehensive datasets of two community types of conservation concern in Europe: acidophilous beech forests and base‐rich fens. We computed community distribution models (CDMs) calibrated with environmental predictors to predict the occurrence of both community types, evaluating geographical transferability, interpolation and extrapolation under different scenarios of sampling bias. We used generalized dissimilarity modelling (GDM) to assess the role of geographical and environmental drivers in compositional variation within the predicted distributions.

Results

For the two community types, CDMs computed for the whole study area provided good performance when evaluated by random cross‐validation and external validation. Geographical transferability provided lower but relatively good performance, while model extrapolation performed poorly when compared with interpolation. Generalized dissimilarity modelling showed a predominant effect of geographical distance on compositional variation, complemented with the environmental predictors that also influenced habitat suitability.

Main conclusions

Correlative approaches typically used for modelling the distribution of individual species are also useful for delineating the potential area of occupancy of community types at the continental scale, when using consistent definitions of the modelled entity and high data completeness. The combination of CDMs with GDM further improves the understanding of diversity patterns of plant communities, providing spatially explicit information for mapping vegetation diversity and related habitat types at large scales.

     

Interacting effects of temperature and density on individual growth performance in a wild population of brown trout

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