Trees species’ dispersal mode and habitat heterogeneity shape negative density dependence in a temperate forest

Conspecific negative density dependence(CNDD)is a potentially important mechanism in maintaining species diversity.While previous evidence showed habitat heterogeneity and species’dispersal modes affect the strength of CNDD at early life stages of trees(e.g.,seedlings),it remains unclear how they affect the strength of CNDD at later life stages.We examined the degree of spatial aggregation between saplings and trees for species dispersed by wind and gravity in four topographic habitats within a 25-ha temperate forest dynamic plot in the Qinling Mountains of central China.We used the replicated spatial point pattern(RSPP)analysis and bivariate paircorrelation function(PCF)to detect the spatial distribution of saplings around trees at two scales,15 and 50 m,respectively.Although the signal was not apparent across the whole study region(or 25-ha),it is distinct on isolated areas with specific characteristics,suggesting that these characteristics could be important factors in CNDD.Further,we found that the gravity-dispersed tree species experienced CNDD across habitats,while for wind-dispersed species CNDD was found in gully,terrace and low-ridge habitats.Our study suggests that neglecting the habitat heterogeneity and dispersal mode can distort the signal of CNDD and community assembly in temperate forests.

STRONG LIMIT THEOREMS FOR EXTENDED INDEPENDENT RANDOM VARIABLES AND EXTENDED NEGATIVELY DEPENDENT RANDOM VARIABLES UNDER SUB-LINEAR EXPECTATIONS

Limit theorems for non-additive probabilities or non-linear expectations are challenging issues which have attracted a lot of interest recently.The purpose of this paper is to study the strong law of large numbers and the law of the iterated logarithm for a sequence of random variables in a sub-linear expectation space under a concept of extended independence which is much weaker and easier to verify than the independence proposed by Peng[20].We introduce a concept of extended negative dependence which is an extension of the kind of weak independence and the extended negative independence relative to classical probability that has appeared in the recent literature.Powerful tools such as moment inequality and Kolmogorov’s exponential inequality are established for these kinds of extended negatively independent random variables,and these tools improve a lot upon those of Chen,Chen and Ng[1].The strong law of large numbers and the law of iterated logarithm are also obtained by applying these inequalities.

LARGE DEVIATIONS AND MODERATE DEVIATIONS FOR SUMS OF NEGATIVELY DEPENDENT RANDOM VARIABLES

In this article, we obtain the large deviations and moderate deviations for negatively dependent （ND） and non-identically distributed random variables defined on （-∞, ＋∞）. The results show that for some non-identical random variables, precise large deviations and moderate deviations remain insensitive to negative dependence structure.

SELF-NORMALIZED CENTRAL LIMIT THEOREM AND ESTIMATION OF VARIANCE OF PARTIAL SUMS FOR NEGATIVE DEPENDENT RANDOM VARIABLES

Let ｛X n,n≥1｝ be a stationary LNQD or NA sequence satisfying EX 1=μ,EX 2 1<∞ and (Var S n)/n→σ 2 as n→∞.In this paper a class of self-normalized central limit theorems and estimators of Var S n are studied.The weak and strong consistency of the estimators of Var S n are presented.

A NONCLASSICAL LAW OF ITERATED LOGARITHM FOR NEGATIVELY ASSOCIATED RANDOM VARIABLES

A nonclassical law of iterated logarithm that holds for a stationary negatively associated sequence of random variables with finite variance is proved in this paper. The proof is based on a Rosenthal type maximal inequality and the subsequence method.This result extends the work of Klesov,Rosalsky (2001) and Shao,Su (1999).

Effects of functional phylogeny of light-response-related orthologous genes on seedling survival in a subtropical forest

Background: Light is an important environmental factor affecting the growth and survival of plants in forest communities. The competition for light resources and divergent responses to light may affect plant species coexistence in natural forests through niche partitioning and environmental filtering, respectively.Methods: In the present study, sequences of light-response-related functional genes were extracted from transcriptomic data of 99 tree species in a subtropical forest and average and nearest taxon phylogenetic diversity of adult(A_Apd’, A_NTpd’) and seedling neighbors(S_Apd’, S_NTpd’) around each focal seedling were calculated to evaluate effects of differentiation in light-response-related genes on community assembly processes.Results: The results showed that seedling survival was related to S_NTpd’, S_Apd’and A_Apd’of two chlorophyll ab-binding proteins involved in the assembly of photosystem Ⅱ and two genes responsive to light intensity,indicating seedlings surrounded by neighbors with distinct light responses tended to have high survival rates.Conclusions: Our results indicated that niche partitioning due to competition for light resources between plants may act as the key mechanism in determining seedling dynamics in subtropical forests.

Estimates for the ruin probability of a time-dependent renewal risk model with dependent by-claims

Consider a continuous-time renewal risk model, in which every main claim induces a delayed by-claim. Assume that the main claim sizes and the inter-arrival times form a sequence of identically distributed random pairs, with each pair obeying a dependence structure, and so do the by-claim sizes and the delay times. Supposing that the main claim sizes with by-claim sizes form a sequence of dependent random variables with dominatedly varying tails, asymptotic estimates for the ruin probability of the surplus process are investigated, by establishing a weakly asymptotic formula, as the initial surplus tends to infinity.

Species abundance is jointly determined by functional traits and negative density dependence in a subtropical forest in southern China

Aims The factors affecting species abundance are a subject of ongoing debates in community ecology.Empirical studies have demonstrated that tree abundance is affected by plant functional traits and negative density dependence(NDD).However,few studies have focused on the combined effects of NDD and plant functional traits on species abundance.Methods In this study,we used tree functional traits and two census data from a 50-ha forest dynamic plot in the Heishiding(HSD)Nature Reserve to explore the combined effects of functional traits and NDD on species abundance.Using hierarchical Bayesian models,we analyzed how neighbor densities affected the survival of saplings from 130 species and extracted posterior means of the coefficients to represent NDD.The structural equation modeling(SEM)analysis was then applied to investigate the causal relationships among species functional traits,NDD and species abundance.Important Findings SEM showed that tree functional traits,including specific leaf area(SLA),leaf area(LA),leaf dry matter content(LDMC),leaf N content(LNC),maximum electron transport rate(ETRmax)and conspecific adult negative density dependence(CNDDadult),together explained 20%of the total variation in tree abundance.Specifically,SLA affected tree abundance both directly and indirectly via CNDDadult,with a totally negative influence on abundance.LDMC and LNC had only indirect effects mediated by CNDDadult on tree abundance.ETRmax and LA had directly negative effects on abundance,but their direct connections with CNDDaduIt were not observed.In addition,CNDDadult was negatively correlated with species abundance,indicating that abundant species are under stronger NDD.Among these investigated traits,SLA contributed the most to the variation in CNDDaduIt and abundance.We argued that our findings of trait-CNDDadult-abundance relationships can improve our understanding of the determinants of species commonness and rarity in forests.

On the convergence for PNQD sequences with general moment conditions

Let fX;Xn;n≥1g be a sequence of identically distributed pairwise negative quadrant dependent(PNQD)random variables and fan;n1g be a sequence of positive constants with an=f(n)and f(θ^k)=f(θ^k-1)for all large positive integers k,where 1<θ≤βand f(x)>0(x≥1)is a non-decreasing function on[b;+1)for some b≥1:In this paper,we obtain the strong law of large numbers and complete convergence for the sequence fX;Xn;n≥1g,which are equivalent to the general moment conditionΣ∞n=1P(|X|>an)<1.Our results extend and improve the related known works in Baum and Katz[1],Chen at al.[3],and Sung[14].

Rosenthal's inequalities for independent and negatively dependent random variables under sub-linear expectations with applications

Classical Kolmogorov's and Rosenthal's inequalities for the maximum partial sums of random variables are basic tools for studying the strong laws of large numbers.In this paper,motived by the notion of independent and identically distributed random variables under the sub-linear expectation initiated by Peng(2008),we introduce the concept of negative dependence of random variables and establish Kolmogorov's and Rosenthal's inequalities for the maximum partial sums of negatively dependent random variables under the sub-linear expectations.As an application,we show that Kolmogorov's strong law of larger numbers holds for independent and identically distributed random variables under a continuous sub-linear expectation if and only if the corresponding Choquet integral is finite.

Central Limit Theorems for Asymptotically Negatively Associated Random Fields

The aim of this paper is to investigate the central limit theorems for asymptotically negatively dependent random fields under lower moment conditions or the Lindeberg condition. Results obtained improve a central limit theorem of Roussas[11]for negatively associated fields and the main results of Su and Chi [18]. and also include a central limit theorem for weakly negatively associated random variables similar to that of Burton et al.[20].

Density dependence and habitat preference shape seedling survival in a subtropical forest in central China

Aims seedlings are vulnerable to many kinds of fatal abiotic and biotic agents,and examining the causes of seedling dynamics can help understand mechanisms of species coexistence.To disentangle the relative importance of neighborhood densities,habitat factors and phylogenetic relatedness on focal seedling survival,we monitored the survival of 5306 seedlings of 104 species>15 months.We address the following questions:(i)How do neighborhood densities,habitat variables and phylogenetic relatedness affect seedling survival?What is the relative importance of conspecific densities,habitat variables and phylogenetic relatedness to seedling survival?(ii)Does the importance of the neighborhood densities,habitat variables and phylogenetic relatedness vary among growth forms,leaf habits or dispersal modes?specially,does the conspecific negative density dependence inhibit tree and decidu-ous seedlings more compared with shrub and evergreen species?Does density dependence affect the wind and animal-dispersed species equally?Methods We established 135 census stations to monitor seedling dynamics in a 25-ha subtropical forest plot in central China.Conspecific and heterospecific seedling density in the 1-m2 seedling plot and adult basal area within a 20-m radius provided neighborhood density var-iables.mean elevation,convexity and aspect of every 5-×5-m grid with seedling plots were used to quantify habitat characteristics.We calculated the relative average phylodiversity between focal seed-ling and heterospecific neighbors to quantify the species related-ness in the neighborhood.Eight candidate generalized linear mixed models with binominal error distribution were used to compare the relative importance of these variables to seedling survival.akaike’s information criteria were used to identify the most parsimonious models.Important Findingsat the community level,both the neighborhood densities and phylogenetic relatedness were important to seedling survival.We found negative effects of increasing conspecific seedlings,which suggested the existence of species-specific density-dependent mortality.Phylodiversity of heterospecific neighbors was negatively related to survival of focal seedlings,indicating similar habitat preference shared among phylogenetically closely related species may drive seedling survival.The relative importance of neighborhood densities,habitat variables and phylogenetic relatedness varied among ecological guilds.Conspecific densities had significant negative effect for deciduous and wind-dispersed species,and marginally significant for tree seedlings>10 cm tall and animal-dispersed species.Habitat variables had limited effects on seedling survival,and only elevation was related to the sur-vival of evergreen species in the best-fit model.We conclude that both negative density-dependent mortality and habitat preference reflected by the phylogenetic relatedness shape the species coex-istence at seedling stage in this forest.

Exponential inequalities under the sub-linear expectations with applications to laws of the iterated logarithm

Kolmogorov's exponential inequalities are basic tools for studying the strong limit theorems such as the classical laws of the iterated logarithm for both independent and dependent random variables. This paper establishes the Kolmogorov type exponential inequalities of the partial sums of independent random variables as well as negatively dependent random variables under the sub-linear expectations. As applications of the exponential inequalities, the laws of the iterated logarithm in the sense of non-additive capacities are proved for independent or negatively dependent identically distributed random variables with finite second order moments.For deriving a lower bound of an exponential inequality, a central limit theorem is also proved under the sublinear expectation for random variables with only finite variances.

Precise large deviations for generalized dependent compound renewal risk model with consistent variation

We investigate the precise large deviations of random sums of negatively dependent random variables with consistently varying tails. We find out the asymptotic behavior of precise large deviations of random sums is insensitive to the negative dependence. We also consider the generalized dependent compound renewal risk model with consistent variation, which including premium process and claim process, and obtain the asymptotic behavior of the tail probabilities of the claim surplus process.

The Law of Logarithm for Arrays of Random Variables under Sub-linear Expectations

Under the framework of sub-linear expectation initiated by Peng,motivated by the concept of extended negative dependence,we establish a law of logarithm for arrays of row-wise extended negatively dependent random variables under weak conditions.Besides,the law of logarithm for independent and identically distributed arrays is derived more precisely and the sufficient and necessary conditions for the law of logarithm are obtained.

Differential impacts of adult trees on offspring and non-offspring recruits in a subtropical forest

An important mechanism promoting species coexistence is conspecific negative density dependence(CNDD),which inhibits conspecific neighbors by accumulating host-specific enemies near adult trees.Natural enemies may be genotype-specific and regulate offspring dynamics more strongly than non-offspring,which is often neglected due to the difficulty in ascertaining genetic relatedness.Here,we investigated whether offspring and non-offspring of a dominant species,Castanopsis eyrei,suffered from different strength of CNDD based on parentage assignment in a subtropical forest.We found decreased recruitment efficiency(proxy of survival probability)of offspring compared with non-offspring near adult trees during the seedling-sapling transition,suggesting genotype-dependent interactions drive tree demographic dynamics.Furthermore,the genetic similarity between individuals of same cohort decreased in late life history stages,indicating genetic-relatedness-dependent tree mortality throughout ontogeny.Our results demonstrate that within-species genetic relatedness significantly affects the strength of CNDD,implying genotype-specific natural enemies may contribute to population dynamics in natural forests.

Asymptotic Behavior of Product of Two Heavy-tailed Dependent Random Variables

Let X and Y be positive weakly negatively dependent （WND） random variables with finite expectations and continuous distribution functions F and G with heavy tails, respectively. The asymptotic behavior of the tail of distribution of XY is studied and some closure properties under some suitable conditions on F（x） = 1-F（x） and G（x） = of XY when X and Y are WND random variables 1- G（x） are provided. Moreover, subexponentiality is derived.

The asymmetric relationships of the distribution of conspecific saplings and adults in forest fragments

Aims With the increase of land-use change,habitat fragmentation has become a major factor affecting plant diversity.Generally,when the adult density is high,the survival rate of conspecific saplings may decline and provide more resources and space for other species to maintain a high local species diversity.Therefore,the spatial relationship of conspecific saplings and adults(SRCSA)can regulate plant diversity.However,very few studies have assessed SRCSA within fragmented forests,and we still largely unknown the relationship between SRCSA and species diversity in fragmented landscapes.Methods We calculated the mean strength of SRCSA using the spatial distribution data of saplings and adults with a log-transformed hierarchical offset-power model on 27 islands in a land-bridge island system.The higher strength of SRCSA reflects a more negative relationship between the density of conspecific saplings and adults on an island(i.e.the looser pattern of SRCSA).We tested the relationships among island attributes(i.e.island area,the distance to the mainland—MD,and the distance to the nearest island—ND),SRCSA and species diversity.Important Findings The strength of SRCSA increased with ND.Meanwhile,the species diversity significantly increased with the strength of SRCSA,and island area and the strength of SRCSA independently explained 26%and 6%of variation of species diversity,respectively,and their interactions explained 8%.Shade-intolerant and low-abundant species showed looser patterns of SRCSA.Our study suggests that SRCSA may have the effect of excluding species with a relatively low abundance in isolated island forests,which illustrates the importance of biotic interactions in maintaining plant diversity in fragmented forests.Our results also emphasize that we should consider forest connectivity when testing the conspecific negative density dependence.