The effects of salt stress and arbuscular mycorrhiza on plant neighbour effects and self-thinning

Abiotic and biotic factors can alter the nature and strength of plant–plant interactions and therefore self-thinning (density-dependent mortality), but few studies have looked at how such factors interact. We investigated how salt stress and arbuscular mycorrhizal fungi (AMF) influence plant neighbour effects and self-thinning in experimental populations of Medicago sativa. We obtained two mycorrhizal levels by applying the fungicide benomyl (low AMF) or not (high AMF) at three salinity levels (0.05%, 0.2% and 0.5%). In experiment 1, we investigated how salinity and AMF interact to influence plant interaction intensity using a neighbour removal treatment. In experiment 2, we investigated how self-thinning dynamics vary under salinity conditions and different AMF levels at two initial plant densities (6000 and 17,500 seeds m^?2). Shoot biomass and plant density were measured 30, 60 and 90 days after sowing. Standardized major axis regression was used to estimate self-thinning parameters. In experiment 1, AMF increased competitive plant neighbour effects when there was no salinity stress, but this enhancement was not significant with increasing salinity. In experiment 2, there were effects of salinity and AMF on the self-thinning trajectory. The slope of the log (mean shoot biomass per unit area) vs. log density relationship was significantly steeper for the high AMF treatment than for the low AMF treatment without salinity, but the effect of AMF level on the self-thinning exponent was not significant under the two higher salinity levels. The effect of AMF treatments on the intercept of the self-thinning line was not significant at 0.2% salinity but was significant at 0.5% salinity, higher elevation for high AMF treatment. In self-thinning populations, AMF decreased the survival rate without salinity, but increased the survival rate at the highest salinity level. Our results support the hypothesis that salinity and AMF interact to influence plant neighbour effects and self-thinning. Under no-salinity conditions, AMF increased competition, steepened the self-thinning line and decreased survival rate, but these effects of AMF were not significant in the presence of salinity.     

数据点选择与参数估计方法对杉木人工林自疏边界线的影响

自疏边界线是指植物种群发生密度依赖死亡时种群最大收获量的上边界线。已有研究由于在拟合自疏边界线的过程中对数据点的选择和参数估计的方法存在诸多的差异,进而导致产生对自疏法则的争议。该研究采用26年生杉木(Cunninghamia lanceolata)人工林的定位观测数据,对视觉法、死亡率法、等距区间法和相对密度法等4种数据点选择方法以及最小二乘法、降维分析法、分位数回归法和随机边界方程等4种参数拟合方法进行对比分析,以探寻客观选择自疏拟合数据和正确拟合方法的途径。比较4种不同的数据选择方法得出:视觉法具有较强的主观性;对于没有发生非密度依赖死亡的林分,死亡率法可以准确地确定林分自疏的起始点;等距区间法可以减少非密度依赖死亡的影响,得到的数据点能充分反映林分的自疏过程;相对密度法可以保证临界密度阈值以上的数据点拟合林分自疏边界线的有效性,并能排除非密度依赖死亡的影响。比较分析4种不同的拟合方法发现:最小二乘法和降维分析法拟合的林分自疏边界线均从实测数据"中心"穿过,与林分自疏边界线为林分收获量上边界线的涵义不相符合,无法真实反映林分的自疏进程;分位数回归和随机边界方程的拟合结果均与实测数据一致,能够较为准确地反映林分自疏的真实过程,但二者的统计推断要求都比较严格。分位数值的正确选取和残差足够小且趋于0,是分位数回归法和随机边界方程能否正确反映林分自疏动态的前提。     

Effect of Localized Placement of Nutrients on Root Competition in Self-thinning Populations

The hypothesis that increased root competition can lower theslope and/or intercept of the self-thinning line traversed byplant populations was tested using localized placement of nutrientsto increase root competition. Localized placement of nutrientswill result in increased root competition, if average inter-rootdistances are reduced, and if nutrients are in limiting supply.It was predicted that high-density, nutrient-limited populationsof Ocimum basilicum L. grown with localized placement of nutrientswould self-thin along a lower biomass–density line thannon-localized controls. This was tested at two fertility levelson a soil-based potting medium in expt 1, and at one fertilitylevel on washed sand in expt 2. Localized placement of nutrients significantly reduced the elevation(intercept) of the self-thinning line for both shoot and rootbiomass in expt 2. In expt 1, at the higher-fertility level,localized placement of nutrients had no significant effect;at the lower fertility level, localization had no significanteffect on thinning lines for shoot biomass, and resulted ina zero slope of the thinning line for root biomass. Canopy-based models of self-thinning failed to account for thereduction in the thinning-line intercept observed in expt 2.In both experiments, localized placement of nutrients resultedin a higher proportion of total root length being located inthe localization zone, which would result in a reduction inthe average inter-root distance. This would intensify root competitionunder conditions of nutrient limitation. The hypothesis thatintensified root competition would lower the self-thinning lineis supported by the results of expt 2. Localized placement of nutrients; root competition; shoot competition; root–shoot allocation; self-thinning; Ocimum basilicum ; sweet basil     

A method of selecting data points for fitting the maximum biomass-density line for stands undergoing self-thinning

Abstract A problem that has always existed in self-thinning studies is the lack of objectivity in determining which data points to include when fitting the maximum biomass-density line. This paper demonstrates a more objective method of selecting data points using data from 12 even-aged Pinus radiata stands undergoing self-thinning. The method involves the division of a cluster of data points into a specified number of intervals. From each interval, that point having the maximum stand biomass is selected to contribute to the fitting process. This process is repeated a specified number of times using an increasing number of intervals. Each time an estimate of the line is obtained. From these estimates, one can be chosen to represent the maximum biomass-density line. The method may also be useful in other areas involving the definition of a boundary condition.     

Self-thinning lines differ with fertility level

The effect of variations in fertility level of the substrate on the self-thinning lines followed by populations of Ocimum basilicum L. was investigated experimentally by establishing populations over a range of densities at two fertility levels. Populations from each fertility level followed different self-thinning lines for shoot biomass. Self-thinning began at a lower biomass in populations grown at the higher fertility level; the subsequent slope of the thinning line was –0.5 for these stands on a log shoot biomass versus log density plot. The slope of the self-thinning line was flatter (–0.29) at the lower fertility level. Fitting the self-thinning line by the Structural Relationship rather than the Major Axis made little difference to line estimates. Biomass packing differed with fertility level, with plants from the higher fertility stands requiring more canopy volume for given shoot biomass than plants from lower fertility levels. Biologically, this would mean shoot competition intensified more rapidly at the higher fertility level as biomass accumulated in stands. The difference in slope between fertility levels was associated with changes above- and belowground. The radial extension of the canopy versus shoot mass relationships of individual plants differed with fertility level. Plants at the lower fertility level allocated more biomass to root growth, and had less leaf area per unit root length. The differences in slope of the self-thinning lines may have been because of differences in the radial extension of the canopy versus shoot mass relationships of individual plants at each fertility level, and/or to an increase in root competition at the lower fertility level.     

Comparison of self-thinning models: an exercise in reasoning

Self-thinning of forest stands is one of the clearest and best-documented examples of natural selection. Besides their theoretical interest, understanding of self-thinning is important for forest practice because it produces estimates of stand density and stocking. There is a considerable diversity of views on the processes causing self-thinning, predicting variables, and analytical form of models. The most popular model was proposed by Reineke (J Agric Res 46(7):627–638, 1933) over 70 years ago. This study compares existing models of self-thinning and provides evidence that the virtually unknown model developed by Artur Nilson describes self-thinning more realistically than Reineke’s. While in the Reineke model the rate of mortality (the slope of self-thinning line) is assumed to be constant, it changes from 0 to −2 in Nilson’s model. As a result, Nilson’s model is slightly but consistently more accurate than Reineke’s. Although both models are empirical, their analysis suggests several general conclusions about self-thinning.     

Tree Biomass Estimation of Chinese fir (Cunninghamia lanceolata) Based on Bayesian Method

Chinese fir (Cunninghamia lanceolata (Lamb.) Hook.) is the most important conifer species for timber production with huge distribution area in southern China. Accurate estimation of biomass is required for accounting and monitoring Chinese forest carbon stocking. In the study, allometric equation was used to analyze tree biomass of Chinese fir. The common methods for estimating allometric model have taken the classical approach based on the frequency interpretation of probability. However, many different biotic and abiotic factors introduce variability in Chinese fir biomass model, suggesting that parameters of biomass model are better represented by probability distributions rather than fixed values as classical method. To deal with the problem, Bayesian method was used for estimating Chinese fir biomass model. In the Bayesian framework, two priors were introduced: non-informative priors and informative priors. For informative priors, 32 biomass equations of Chinese fir were collected from published literature in the paper. The parameter distributions from published literature were regarded as prior distributions in Bayesian model for estimating Chinese fir biomass. Therefore, the Bayesian method with informative priors was better than non-informative priors and classical method, which provides a reasonable method for estimating Chinese fir biomass.     

-3/2方自疏法则的机理与普适性

根据植物构件性理论,对经验规律-3/2方自疏法则进行了理论推导,对-3/2方自疏法则以前不能解释的实验结果进行了理论分析,并以春小麦（Triticum aestiunm L.）为材料,设置了4个密度梯度的实验,定期测定个体形态及种群数量指标,证明了-3/2方自疏法法则对春小麦作物种群的适用性,同时,基于所测定的植株形态数据,结合数值的量纲变化特点对-3/2方自疏法则的普适性进行了理论解释。     

Additive genetic variance and covariance between relatives in synthetic wheat crosses with variable parental ploidy levels

Cultivated bread wheat (Triticum aestivum L.) is an allohexaploid species resulting from the natural hybridization and chromosome doubling of allotetraploid durum wheat (T. turgidum) and a diploid goatgrass Aegilops tauschii Coss (Ae. tauschii). Synthetic hexaploid wheat (SHW) was developed through the interspecific hybridization of Ae. tauschii and T. turgidum, and then crossed to T. aestivum to produce synthetic hexaploid wheat derivatives (SHWDs). Owing to this founding variability, one may infer that the genetic variances of native wild populations vs improved wheat may vary due to their differential origin and evolutionary history. In this study, we partitioned the additive variance of SHW and SHWD with respect to their breed origin by fitting a hierarchical Bayesian model with heterogeneous covariance structure for breeding values to estimate variance components for each breed category, and segregation variance. Two data sets were used to test the proposed hierarchical Bayesian model, one from a multi-year multi-location field trial of SHWD and the other comprising the two species of SHW. For the SHWD, the Bayesian estimates of additive variances of grain yield from each breed category were similar for T. turgidum and Ae. tauschii, but smaller for T. aestivum. Segregation variances between Ae. tauschii—T. aestivum and T. turgidum—T. aestivum populations explained a sizable proportion of the phenotypic variance. Bayesian additive variance components and the Best Linear Unbiased Predictors (BLUPs) estimated by two well-known software programs were similar for multi-breed origin and for the sum of the breeding values by origin for both data sets. Our results support the suitability of models with heterogeneous additive genetic variances to predict breeding values in wheat crosses with variable ploidy levels.     

How does fertility of the substrate affect intraspecific competition? Evidence and synthesis from self-thinning

When dense populations of even-aged plant monocultures are subject to intense competition, mortality can occur in a process known as self-thinning, in which changes in biomass are accompanied by decreases in density. On a plot of log biomass versus log density, self-thinning populations show a linear relationship called the self-thinning line. Variations in the fertility level of the substrate are known to affect self-thinning in a number of ways. Populations from substrates with different fertility levels have been observed to self-thin along the same line, or along different lines. A review of several experiments using the one species grown at different fertility levels was undertaken to look for any mechanisms that might account for the different patterns observed. It was postulated that the critical difference between whether populations followed a common or different line was the way in which competition developed in the stands as biomass accumulated. For the common-line pattern, data on the canopy volume required to support a given biomass showed that biomass packing did not differ between fertility levels, supporting the model of a common competitive mechanism operating at all fertility levels. When different lines were observed, the development of competition differed as plants increased in size and biomass accumulated at each fertility level. Over the upper range of fertility levels, biomass packing values per plant increased as fertility declined and the position of self-thinning lines followed predictions from biomass packing data. At the low end of the fertility scale, biomass packing values still decreased with fertility level, but the position of self-thinning lines was not linked to the biomass packing of individual plants: root interactions were presumed to dominate competition and the trajectory of self-thinning lines.     

The allometric interpretation of the self-thinning rule

Plant populations growing at high densities undergo density-dependent mortality or self-thinning. The density of survivors ({ρ}) is related to their mean biomass (w) by the power equation w = K_ρ^?a, where a is $\text{3}\text{2}$. This is known as the “self-thinning rule”. This relationship is very general for plant populations and represents both an asymptotic time-trajectory for a particular population and a boundary line for juxtaposed joint values of w and p of separate populations. The traditional allometric derivation of the rule is outlined and shown to be unrealistic. An attempt to reformulate the self-thinning rule, based on the traditional allometric derivation, is shown to be unsatisfactory and an alternative allometric derivation is presented. The rule in its traditional statement $\text{w = K}{}_{\mathrm{\rho }}{}^{\mathrm{?3}}\text{2}$ is still its best expression. The nature of the constant K is discussed with particular reference to its dimensionality.     

When mechanism matters: Bayesian forecasting using models of ecological diffusion

Ecological diffusion is a theory that can be used to understand and forecast spatio‐temporal processes such as dispersal, invasion, and the spread of disease. Hierarchical Bayesian modelling provides a framework to make statistical inference and probabilistic forecasts, using mechanistic ecological models. To illustrate, we show how hierarchical Bayesian models of ecological diffusion can be implemented for large data sets that are distributed densely across space and time. The hierarchical Bayesian approach is used to understand and forecast the growth and geographic spread in the prevalence of chronic wasting disease in white‐tailed deer (Odocoileus virginianus). We compare statistical inference and forecasts from our hierarchical Bayesian model to phenomenological regression‐based methods that are commonly used to analyse spatial occurrence data. The mechanistic statistical model based on ecological diffusion led to important ecological insights, obviated a commonly ignored type of collinearity, and was the most accurate method for forecasting.     

A long-term study of Pinus banksiana population dynamics

Abstract. The long-term population dynamics of a pure, naturally-established stand of Pinus banksiana (jack pine) in southeastern Manitoba, Canada is described. The study was initiated at stand age 15, when all 468 trees in a plot were mapped and their trunk diameter at breast height (DBH) measured. The plot was remeasured eight times — every five years (six years in one case) — and mortality and DBH changes recorded. Total mortality over the 41-yr study period was ca. 84 %. Mortality was initially very low, increased once the stand entered the self-thinning stage from ages 25–46, and declined at ages 46–56. Mortality was restricted to the smallest size classes throughout. The stand reached the self-thinning line at ca. age 30. The self-thinning slope was significantly less steep than the theoretically expected value of ?0.5. The distribution of DBH values was initially symmetric, showed increasing positive skewness during the period of highest mortality, and became symmetric again at later stages. Size (DBH) inequality was highest just prior to the onset of density-dependent mortality, and subsequently declined. Tree DBH values were positively autocorrelated both initially and at later stages of stand development, but were spatially independent during the period of highest density-dependent mortality. The stand initially had a strongly clumped pattern at all spatial scales. Patterns of mortality were non-random during stand development, however, resulting in increased spatial regularity over time. Mortality was initially restricted to high density patches of the stand, but occurred throughout the plot once the self-thinning line was reached. Mortality during the self-thinning stage deviated from random expectation at local spatial scales (1–2m radius), suggesting that individuals were competing with their immediate neighbours. It is argued that an integrated approach, incorporating both population size and spatial structures, is essential in improving our understanding of long-term plant population dynamics.     

Relationship between the virtual dynamic thinning line and the self-thinning boundary line in simulated plant populations

The self-thinning rule defines a straight upper boundary line on log-log scales for all possible combinations of mean individual biomass and density in plant populations. Recently, the traditional slope of the upper boundary line, -3/2, has been challenged by -4/3 which is deduced from some new mechanical theories, like the metabolic theory. More experimental or field studies should be carried out to identify the more accurate self-thinning exponent. But it＇s hard to obtain the accurate self-thinning exponent by fitting to data points directly because of the intrinsic problem of subjectivity in data selection. The virtual dynamic thinning line is derived from the competition-density （C-D） effect as the initial density tends to be positive infinity, avoiding the data selection process. The purpose of this study was to study the relationship between the virtual dynamic thinning line and the upper boundary line in simulated plant stands. Our research showed that the upper boundary line and the virtual dynamic thinning line were both straight lines on log-log scales. The slopes were almost the same value with only a very little difference of 0.059, and the intercept of the upper boundary line was a little larger than that of the virtual dynamic thinning line. As initial size and spatial distribution patterns became more uniform, the virtual dynamic thinning line was more similar to the upper boundary line. This implies that, given appropriate parameters, the virtual dynamic thinning line may be used as the upper boundary line in simulated plant stands.     

Effects of self-thinning of shoots on the nutrient budgets of Zizania latifolia

This experimental study focused on the seasonal changes and mobilization of nutrients between plant parts to understand the implications of self-thinning in the ecology of Zizania latifolia (Griseb.) Turcz. ex Stapf. The observations of shoot density, above- and belowground biomass, and total nitrogen and total phosphorus concentrations were conducted from February 2002 to August 2003. The biomass of shoots that died during the period and daily uptake of nutrients were determined. The shoot density sharply increased until mid-April and thereafter decreased significantly due to self-thinning of shoots. Total nitrogen and phosphorus concentrations of rhizomes decreased initially due to translocation to new shoots; however, the nutrients of rhizomes were slightly replenished from dead shoots during self-thinning. In contrast to other species, self-thinning of Z. latifolia shoots reallocates some of the minerals contained in the dead shoots back to the rhizomes, which can be regarded as a strategy to replenish the reduced resources of the rhizomes. The initial intensive growth of shoots can be regarded as a strategy to maintain resource competition.     

Nonparametric approaches for estimating regional lake nutrient thresholds

Nonparametric approaches including a classification and regression tree (CART), a nonparametric changepoint analysis (nCPA) and a Bayesian hierarchical modeling (BHM) method were developed to determine ecoregional nutrient response thresholds. A CART analysis revealed that hierarchical structure was important for predicting Chl a concentrations from total nitrogen (TN) and total phosphorus (TP). The nCPA and BHM methods confirmed the CART results for each node in the tree, and the 90% confidence interval for each threshold was calculated to quantify uncertainty. The CART, nCPA, and BHM methods suggested that the nutrient criteria differed significantly within certain nutrient ecoregions and that numerical nutrient criteria of 0.0150–0.222 mg/L TP and 0.300–1.766 mg/L TN may control Chl a concentrations in the various lake ecoregions. The results of this analysis suggest that the integration of CART, nCPA and BHM might be useful for determining nutrient thresholds.     

Density effect, self-thinning and size distribution in Pinus densiflora Sieb. et Zucc. stands

The competition-density (C-D) effect for given times and self-thinning over time in even-aged, natural, pure stands of Pinus densiflora Sieb. et Zucc. were analyzed with the reciprocal equation of the C-D effect in self-thinning stands, and the equation describing the time-trajectory of mean stem volume and stand density. The C-D effect and self-thinning were consistently well explained by the two equations. Differences in mean stem volume and in stand density among the stands tended to merge with increasing stand age. The self-thinning line with a slope of approximately –3/2 was reached by the higher density stand prior to the medium and lower density stands. The skewness of tree height distribution showed positive values, which means that the distribution is more or less L-shaped, and in addition the skewness decreased with increasing mean tree height, which indicates that smaller trees died as the stands grew. This trend is consistent with the asymmetric (one-sided) competition hypothesis that self-thinning is driven by competition for light. The tree height distribution was analyzed using the Weibull distribution. The location parameter h _min of the Weibull distribution increased with increasing stand age, and the scale parameter a tended to increase slightly with increasing stand age. The range of the shape parameter b of the Weibull distribution corresponded to that of the skewness.     

Population structure and thinning in natural stands of Atlantic White Cedar (Chamaecyparis thyoides (L.) BSP)

Summary Data from forestry yield tables were used to investigate the population structure of natural stands of Atlantic White Cedar (Chamaecyparis thyoides) in the mid-Atlantic states. The proportion of individuals in three size classes, 1–5 inch dbh, 5–8 inch dbh and > 8 inch dbh was shown to depend on both site age since clearcutting and site quality. Site age and site quality also determined the degree to which cedar populations underwent density dependent mortality (self-thinning). On all sites, the smallest individuals were removed by self-thinning. Analyses of this type allow predictions to be made of forest stand dynamics and further an understanding of population processes in natural communities.     

A Bayesian hierarchical trend analysis finds strong evidence for large-scale temporal declines in stream ecological condition around Melbourne, Australia

Knowledge of temporal change in ecological condition is important for the understanding and management of ecosystems. However, analyses of trends in biological condition have been rare, as there are usually too few data points at any single site to use many trend analysis techniques. We used a Bayesian hierarchical model to analyse temporal trends in stream ecological condition (as measured by the invertebrate-based index SIGNAL) across Melbourne, Australia. The Bayesian hierarchical approach assumes dependency amongst the sampling sites. Results for each site "borrow strength" from the other data because model parameter values are assumed to be drawn from a larger common distribution. This leads to robust inference despite the few data that exist at each site. Utilising the flexibility of the Bayesian approach, we also modelled change over time as a function of catchment urbanisation, allowed for potential temporal and spatial autocorrelation of the data and trend estimates, and used prior information to improve the estimate of data uncertainty. We found strong evidence of a widespread decline in SIGNAL scores for edge habitats (areas of little or no flow). The rate of decline was positively associated with catchment urbanisation. There was no evidence of such declines for riffle habitats (areas with rapid and turbulent flow). Melbourne has experienced a decline in rainfall, indicative of either drought and/or longer-term climate change. The results are consistent with the expected coupled effects of these rainfall changes and increasing urbanisation, but more research is needed to isolate a causal mechanism. More immediately, however, the Bayesian hierarchical approach has allowed us to identify a pattern in a biological monitoring data set that might otherwise have gone un-noticed, and to demonstrate a large-scale temporal decline in biological condition.     

Genetic relationship among wild,landraces and cultivars of hazelnut (Corylus avellana) from Portugal revealed through ISSR and AFLP markers

The genus Corylus, a member of the birch family Betulaceae, includes several species that are widely distributed throughout temperate regions of the Northern Hemisphere. This study assesses the genetic diversity in 26 international cultivars and 32 accessions of Corylus avellana L. from Portugal: 13 wild genotypes and 19 landraces. The genetic relationships among the 58 hazelnuts (Corylus avellana L.) were analyzed using inter simple sequence repeat (ISSR) and amplified fragment length polymorphism (AFLP) markers. Eighteen ISSR primers and seven AFLP primer pairs generated a total of 570 unambiguous and repeatable bands, respectively, from which 541 (95.03 %) were polymorphic for both markers. Genetic similarity index values ranged from 0.239 for wild types and cultivars to 0.143 for landraces and wild types. The genetic relationships were presented as a Neighbor-Joining method dendrogram and a two-dimensional principal coordinate analysis (PCoA) plot. The Neighbor-Joining dendrogram showed three main clusters, and the PCoA analysis has shown to be congruent with the hierarchical analysis. Bayesian analysis clustered all individuals into three groups showing a good separation among wild genotypes, landraces and cultivars. The genetic diversity found on wild genotypes and Portuguese landraces may provide relevant information for the diversity conservation and it will be useful in breeding programs and to identify local selections for preservation.