Comparing tropical forest tree size distributions with the predictions of metabolic ecology and equilibrium models

Tropical forests vary substantially in the densities of trees of different sizes and thus in above-ground biomass and carbon stores. However, these tree size distributions show fundamental similarities suggestive of underlying general principles. The theory of metabolic ecology predicts that tree abundances will scale as the −2 power of diameter. Demographic equilibrium theory explains tree abundances in terms of the scaling of growth and mortality. We use demographic equilibrium theory to derive analytic predictions for tree size distributions corresponding to different growth and mortality functions. We test both sets of predictions using data from 14 large-scale tropical forest plots encompassing censuses of 473 ha and > 2 million trees. The data are uniformly inconsistent with the predictions of metabolic ecology. In most forests, size distributions are much closer to the predictions of demographic equilibrium, and thus, intersite variation in size distributions is explained partly by intersite variation in growth and mortality.     

Testing metabolic ecology theory for allometric scaling of tree size, growth and mortality in tropical forests

The theory of metabolic ecology predicts specific relationships among tree stem diameter, biomass, height, growth and mortality. As demographic rates are important to estimates of carbon fluxes in forests, this theory might offer important insights into the global carbon budget, and deserves careful assessment. We assembled data from 10 old-growth tropical forests encompassing censuses of 367 ha and > 1.7 million trees to test the theory's predictions. We also developed a set of alternative predictions that retained some assumptions of metabolic ecology while also considering how availability of a key limiting resource, light, changes with tree size. Our results show that there are no universal scaling relationships of growth or mortality with size among trees in tropical forests. Observed patterns were consistent with our alternative model in the one site where we had the data necessary to evaluate it, and were inconsistent with the predictions of metabolic ecology in all forests.     

A general combined model to describe tree‐diameter distributions within subtropical and temperate forest communities

The size distribution of trees in natural forests is a fundamental attribute of forest structure. Previous attempts to model tree size distributions using simple functions (such as power or Weibull functions) have had limited success, typically overestimating the number of large stems observed. We describe a model which assumes that the dominant mortality process is asymmetric competition when trees are smaller, and size‐independent processes (e.g. disturbance) when trees are larger. This combination of processes leads to a size distribution which takes the form of a power distribution in the small tree phase and a Weibull distribution in the large tree phase. Analyses of data from four large‐scale (≥ 24 ha each) subtropical and temperate forest plots totalling 99 ha and approximately 0.4 million trees provide support for this model in two respects: (a) the combined function provided unbiased predictions and (b) power‐law functions fitted to small trees had exponents that deviated from the universal exponent of –2 predicted by metabolic scaling theory, gradually decreasing from subtropical evergreen to temperate deciduous forests along the latitudinal gradient.     

Species–habitat associations and demographic rates of forest trees

Niche‐driven effects on demographic processes generated in response to habitat heterogeneity partly shape local distributions of species. Thus, tree distributions are commonly studied in relation to habitat conditions to understand how niche differentiation contributes to species coexistence in forest communities. Many such studies implicitly assume that local abundance reflects habitat suitability, and that abundance is relatively stable over time. We compared models based on abundance with those based on demographic performance for making inferences about habitat association for 287 tree species from three large dynamic plots located in tropical, subtropical and temperate forests. The correlation between the predictions of the abundance‐based models and the demography‐based models varied widely, with correlation coefficients ranging nearly from ?1 to 1.This suggests that the two types of models capture different information about species–habitat associations. Demography‐based models evaluate habitat quality by focusing on population processes and thus should be preferred for understanding responses of tree species to habitat conditions, especially when habitat conditions are changing and species–habitat interactions cannot be considered to be at equilibrium.     

Linking canopy leaf area and light environments with tree size distributions to explain Amazon forest demography

Forest biophysical structure – the arrangement and frequency of leaves and stems – emerges from growth, mortality and space filling dynamics, and may also influence those dynamics by structuring light environments. To investigate this interaction, we developed models that could use LiDAR remote sensing to link leaf area profiles with tree size distributions, comparing models which did not (metabolic scaling theory) and did allow light to influence this link. We found that a light environment‐to‐structure link was necessary to accurately simulate tree size distributions and canopy structure in two contrasting Amazon forests. Partitioning leaf area profiles into size‐class components, we found that demographic rates were related to variation in light absorption, with mortality increasing relative to growth in higher light, consistent with a light environment feedback to size distributions. Combining LiDAR with models linking forest structure and demography offers a high‐throughput approach to advance theory and investigate climate‐relevant tropical forest change.     

The role of breeding system in community dynamics: Growth and mortality in forests of different successional stages

Plant sexual systems appear to play an important role in community assembly: Dioecious species are found to tend to have a higher propensity to colonize communities in early successional stages. Here, we test two demographic hypotheses to explain this pattern in temperate forests. First, we test demographic differences between hermaphrodite and dioecious species in stressful younger successional stages: Previous theory predicts that hermaphrodite seed production is more harmed in stressful environments than that of dioecious populations leading to an advantage for females of dioecious species. Second, in primary forest, we hypothesized that dioecious species would show demographic advantage over monomorphic ones. We used data from two temperate forest plots in Northeast China surveyed over 10 years to compare the rates of growth and mortality of tree species with contrasting breeding systems in both secondary and primary forests. We assessed the effect of breeding system on the growth‐mortality trade‐off, while controlling for other traits usually considered as correlates of growth and mortality rates. We show that in the secondary forest, dioecious species showed weak advantage in demographic rates compared with monomorphic species; dioecious species showed considerably both lower relative growth and mortality rates compared to the hermaphrodites in the primary forest over 10 years, consistent with a priori predictions. Hermaphrodites showed strong growth‐mortality trade‐offs across forest stages, even when possibly confounding factors had been accounted for. These results suggest that sexual system influences community succession and assembly by acting on the rates of growth and mortality, and the trade‐off between them. As vegetation develops, the demographic differences between breeding systems are much larger. Our results demonstrate the association between breeding system, succession, and community assembly and that this relationship is succession‐stage dependent. Our findings support the suggestion that the demographic advantage of dioecious species facilitates the coexistence of sexual systems in primary forest.     

Metabolic partitioning across individuals in ecological communities

The mechanistic origin and shape of body‐size distributions within communities are of considerable interest in ecology. A recently proposed light‐limitation model provides a good fit to the distribution of tree sizes in a tropical forest plot. The maximum entropy theory of ecology (METE) also predicts size distributions, but without explicit mechanistic assumptions, and thus its predictions should hold in ecosystems generally, regardless of whether they are light limited. A comparison of the form and success of the predictions of the model and the theory can provide insight into the role that mechanisms play in shaping patterns in macroecology. The prediction by the METE of the size distribution of organisms is remarkably similar in form to that of the model: power‐law behaviour in the size range where the light‐limitation model predicts a power law, and exponential behaviour in the size range where the model predicts an exponential tail. The METE prediction matches data widely, including data in ecosystems where light is not limiting. We show examples for three disparate communities: trees in a tropical forest plot; herbaceous plants in a treeless subalpine meadow; and island arthropods. We conclude that the success of METE's predicted form across systems, including those that are clearly not light limited, enriches our capacity to predict patterns in macroecology without making explicit mechanistic assumptions and provides a unified framework that can capture ubiquitous features of those patterns across diverse ecosystems governed by a variety of mechanisms.     

Non‐neutrality in forest communities: evolutionary and ecological determinants of tree species abundance distributions

The unified neutral theory of biodiversity and biogeography provides a promising framework that can be used to integrate stochastic and ecological processes operating in ecological communities. Based on a mechanistic non‐neutral model that incorporates density‐dependent mortality, we evaluated the deviation from a neutral pattern in tree species abundance distributions and explored the signatures of historical and ecological processes that have shaped forest biomes. We compiled a dataset documenting species abundance distributions in 1168 plots encompassing 16 973 tree species across tropical, temperate, and boreal forests. We tested whether deviations from neutrality of species abundance distributions vary with climatic and historical conditions, and whether these patterns differ among regions. Non‐neutrality in species abundance distributions was ubiquitous in tropical, temperate, and boreal forests, and regional differences in patterns of non‐neutrality were significant between biomes. Species abundance evenness/unevenness caused by negative density‐dependent or abiotic filtering effects had no clear macro‐scale climatic drivers, although temperature was non‐linearly correlated with species abundance unevenness on a global scale. These findings were not significantly biased by heterogeneity of plot data (the differences of plot area, measurement size, species richness, and the number of individuals sampled). Therefore, our results suggest that environmental filtering is not universally increasing from warm tropical to cold boreal forests, but might affect differently tree species assembly between and within biomes. Ecological processes generating particularly dominant species in local communities might be idiosyncratic or region‐specific and may be associated with geography and climate. Our study illustrates that stochastic dynamical models enable the analysis of the interplay of historical and ecological processes that influence community assemblies and the dynamics of biodiversity.     

Simulating Stationary Size Distribution of Trees in Rain Forests

A simple dynamic model of the distribution of tree size (trunkdiameter) in natural rain forests is presented. Based on dataof permanent plot measurements in a tropical rain forest anda warm-temperate rain forest, the cumulative basal area densityof trees larger than a given tree, at any particular time, isused to express the effect of suppression, or one-sided competition,on the growth rate of that tree. It also shows that increasingthe basal area density of all trees in the stand depresses therate of recruitment from the pool of seedlings. Mortality istreated as independent of the cumulative basal area. Simulationwith the model, applying the one-dimensional drift-diffusionequation, reproduces the observed course of reforestation afterclear-felling and leads to convergence to a unique stationarysize distribution by 200 years. This concuts with the size distributionobserved in primary forest stands. The present model representsan extension of density-dependent population growth models tosize-structured tree populations. Competition, cumulative basal area, density dependence, equilibrium, population, simulation, size distribution, tropical rain forest, warm—temperate rain forest     

Contrasting demographics of tropical savanna and temperate forest eucalypts provide insight into how savannas and forests function. A case study using Corymbia clarksoniana from north‐eastern Australia

Eucalypts (Eucalyptus spp. and Corymbia spp.) dominate many communities across Australia, including frequently burnt tropical savannas and temperate forests, which receive less frequent but more intense fires. Understanding the demographic characteristics that allow related trees to persist in tropical savannas and temperate forest ecosystems can provide insight into how savannas and forests function, including grass–tree coexistence. This study reviews differences in critical stages in the life cycle of savanna and temperate forest eucalypts, especially in relation to fire. It adds to the limited data on tropical eucalypts, by evaluating the effect of fire regimes on the population biology of Corymbia clarksoniana, a tree that dominates some tropical savannas of north‐eastern Australia. Corymbia clarksoniana displays similar demographic characteristics to other tropical savanna species, except that seedling emergence is enhanced when seed falls onto recently burnt ground during a high rainfall period. In contrast to many temperate forest eucalypts, tropical savanna eucalypts lack canopy‐stored seed banks; time annual seed fall to coincide with the onset of predictable wet season rain; have very rare seedling emergence events, including a lack of mass germination after each fire; possess an abundant sapling bank; and every tropical eucalypt species has the ability to maintain canopy structure by epicormically resprouting after all but the most intense fires. The combination of poor seedling recruitment strategies, coupled with characteristics allowing long‐term persistence of established plants, indicate tropical savanna eucalypts function through the persistence niche rather than the regeneration niche. The high rainfall‐promoted seedling emergence of C. clarksoniana and the reduction of seedling survival and sapling growth by fire, support the predictions that grass–tree coexistence in savannas is governed by rainfall limiting tree seedling recruitment and regular fires limiting the growth of juvenile trees to the canopy.     

Temperate forest termites: ecology,biogeography, and ecosystem impacts

1. Wood decomposition in temperate forests is dominated by termites, fungi, and some species of ants and beetles. Outside of urban areas, temperate termite ecology is largely unknown, particularly when compared to tropical termites and other temperate organisms in the functional guild of wood‐decomposing animals. 2. This review combines climate habitat modelling with knowledge of species physiology, behaviour, and community interactions to identify and prioritise future research on temperate termite ecology and biogeography. 3. Using a correlative climate model, the regional distributions of three common temperate forest termite species are shown to correlate with different aspects of climate (e.g. mean versus minimum monthly temperature), but that overall their distributions within temperate systems correlate more strongly with temperature variables than with precipitation variables. 4. Existing data are synthesised to outline how the subterranean, wood‐nesting behaviour of most temperate forest termite species links their activity to an additional set of non‐climate controls: wood type and tree species, soil depth, fungal activity, ant abundances and phenology, and competitive asymmetries among termite species. 5. Although fine‐scale estimates of temperate termite abundances are rare, we provide upper bounds on their ecosystem impacts and illustrate how their regional abundances may influence forest structure and habitat availability for other organisms. 6. This review highlights that rigorous ecological studies in non‐urban, intact ecosystems – with a particular focus on community interactions – are critically needed to accurately project future abundances, economic impacts, and ecosystem effects of temperate forest termites.     

Ice‐storm disturbance and long‐term forest dynamics in the Adirondack Mountains

Ice storms cause periodic disturbance to temperate forests of eastern North America. They are the primary agents of disturbance in some eastern forests. In this paper, a forest gap model is employed to explore consequences of ice storms for the long‐term dynamics of Tsuga canadensis‐northem hardwoods forests. The gap model LINKAGES was modified to simulate periodic ice storm disturbance in the Adirondack Mountains of New York. To adapt the gap model for this purpose, field data on ice storm disturbance are used to develop a polytomous logistic regression model of tree damage. The logistic regression model was then incorporated into the modified forest gap model, LINK ADIR, to determine the type of damage sustained by each simulated tree. The logistic regression model predicts high probabilities of bent boles or severe bole damage (leaning, snapping, or uprooting) in small‐diameter trees, and increasing probability of canopy damage as tree size increases. Canopy damage is most likely on gentle slopes; the probability of severe bole damage increases with increasing slope angle. In the LINKADIR simulations, tree damage type determines the probability of mortality; trees with severe bole damage are assigned the highest mortality rate. LINKADIR predicts Tsuga canadensis dominance in mesophytic old‐growth forests not disturbed by ice storms. When ice storms are simulated, the model predicts Acer saccharum‐dominated forests with higher species richness. These results suggest that ice storms may function as intermediate disturbances that enhance species richness in forested Adirondack landscapes.     

Neutral theory: a historical perspective

To resolve a panselectionist paradox, the population geneticist Kimura invented a neutral theory, where each gene is equally likely to enter the next generation whatever its allelic type. To learn what could be explained without invoking Darwinian adaptive divergence, Hubbell devised a similar neutral theory for forest ecology, assuming each tree is equally likely to reproduce whatever its species. In both theories, some predictions worked; neither theory proved universally true. Simple assumptions allow neutral theorists to treat many subjects still immune to more realistic theory. Ecologists exploit far fewer of these possibilities than population geneticists, focussing instead on species abundance distributions, where their predictions work best, but most closely match non-neutral predictions. Neutral theory cannot explain adaptive divergence or ecosystem function, which ecologists must understand. By addressing new topics and predicting changes in time, however, ecological neutral theory can provide probing null hypotheses and stimulate more realistic theory.     

Global species–energy relationship in forest plots: role of abundance,temperature and species climatic tolerances

Aim To evaluate the strength of evidence for hypotheses explaining the relationship between climate and species richness in forest plots. We focused on the effect of energy availability which has been hypothesized to influence species richness: (1) via the effect of productivity on the total number of individuals (the more individuals hypothesis, MIH); (2) through the effect of temperature on metabolic rate (metabolic theory of biodiversity, MTB); or (3) by imposing climatic limits on species distributions. Location Global. Methods We utilized a unique ‘Gentry‐style’ 370 forest plots data set comprising tree counts and individual stem measurements, covering tropical and temperate forests across all six forested continents. We analysed variation in plot species richness and species richness controlled for the number of individuals by using rarefaction. Ordinary least squares (OLS) regression and spatial regressions were used to explore the relative performance of different sets of environmental variables. Results Species richness patterns do not differ whether we use raw number of species or number of species controlled for number of individuals, indicating that number of individuals is not the proximate driver of species richness. Productivity‐related variables (actual evapotranspiration, net primary productivity, normalized difference vegetation index) perform relatively poorly as correlates of tree species richness. The best predictors of species richness consistently include the minimum temperature and precipitation values together with the annual means of these variables. Main conclusion Across the world's forests there is no evidence to support the MIH, and a very limited evidence for a prominent role of productivity as a driver of species richness patterns. The role of temperature is much more important, although this effect is more complex than originally assumed by the MTB. Variation in forest plot diversity appears to be mostly affected by variation in the minimum climatic values. This is consistent with the ‘climatic tolerance hypothesis’ that climatic extremes have acted as a strong constraint on species distribution and diversity.     

Integrating macroecological metrics and community taxonomic structure

We extend macroecological theory based on the maximum entropy principle from species level to higher taxonomic categories, thereby predicting distributions of species richness across genera or families and the dependence of abundance and metabolic rate distributions on taxonomic tree structure. Predictions agree with qualitative trends reported in studies on hyper‐dominance in tropical tree species, mammalian body size distributions and patterns of rarity in worldwide plant communities. Predicted distributions of species richness over genera or families for birds, arthropods, plants and microorganisms are in excellent agreement with data. Data from an intertidal invertebrate community, but not from a dispersal‐limited forest, are in excellent agreement with a predicted new relationship between body size and abundance. Successful predictions of the original species level theory are unmodified in the extended theory. By integrating macroecology and taxonomic tree structure, maximum entropy may point the way towards a unified framework for understanding phylogenetic community structure.     

Core and Satellite Species in Degraded Habitats: an Analysis Using Malagasy Tree Communities

Core-satellite theory predicts that, via the “rescue effect”, widespread, abundant species should have reduced risk of local extinctions. We test this hypothesis in southeastern Malagasy littoral forest using data on distribution and abundance of trees and woody understory vegetation in tropical forest fragments along a disturbance gradient. We partition the mortality risk into two kinds of extinction factors, separately operating at demographic (local) and landscape (regional) scales, contrary to core-satellite predictions, for both trees and woody understory vegetation, that the relative number of core (abundant) species declined significantly with increasing disturbance. In the least-degraded forest fragments there was a strong mode of core species, while in the moderately- and severely-degraded fragments the species distributions were essentially log-normal, lacking a substantial core mode. While the rescue effect mitigates one kind of extinction risk, namely local environmental and demographic stochasticity, it may not counterbalance widespread pervasive sources of mortality. The amount of internal forest fragmentation appears to have a much greater effect on species richness and diversity than either fragment size or shape.     

Evidence of variant intra- and interspecific scaling of tree crown structure and relevance for allometric theory

General scaling rules or constants for metabolic and structural plant allometry as assumed by the theory of Euclidian geometric scaling (2/3-scaling) or metabolic scaling (3/4-scaling) may meet human's innate propensity for simplicity and generality of pattern and processes in nature. However, numerous empirical works show that variability of crown structure rather than constancy is essential for a tree's success in coping with crowding. In order to link theory and empiricism, we analyzed the intra- and inter-specific scaling of crown structure for 52 tree species. The basis is data from 84 long-term plots of temperate monospecific forests under survey since 1870 and a set of 126 yield tables of angiosperm and gymnosperm forest tree species across the world. The study draws attention to (1) the intra-specific variation and correlation of the three scaling relationships: tree height versus trunk diameter, crown cross-sectional area versus trunk diameter, and tree volume versus trunk diameter, and their dependence on competition, (2) the inter-specific variation and correlation of the same scaling exponents ([Formula: see text] and [Formula: see text]) across 52 tree species, and (3) the relevance of the revealed variable scaling of crown structure for leaf organs and metabolic scaling. Our results arrive at suggesting a more extended metabolic theory of ecology which includes variability and covariation between allometric relationships as prerequisite for the individual plant's competitiveness.     

Responses of species abundance distribution patterns to spatial scaling in subtropical secondary forests

To quantify and assess the processes underlying community assembly and driving tree species abundance distributions(SADs) with spatial scale variation in two typical subtropical secondary forests in Dashanchong state‐owned forest farm, two 1‐ha permanent study plots (100‐m × 100‐m) were established. We selected four diversity indices including species richness, Shannon–Wiener, Simpson and Pielou, and relative importance values to quantify community assembly and biodiversity. Empirical cumulative distribution and species accumulation curves were utilized to describe the SADs of two forests communities trees. Three types of models, including statistic model (lognormal and logseries model), niche model (broken‐stick, niche preemption, and Zipf‐Mandelbrodt model), and neutral theory model, were estimated by the fitted SADs. Simulation effects were tested by Akaike's information criterion (AIC) and Kolmogorov–Smirnov test. Results found that the Fagaceae and Anacardiaceae families were their respective dominance family in the evergreen broad‐leaved and deciduous mixed communities. According to original data and random sampling predictions, the SADs were hump‐shaped for intermediate abundance classes, peaking between 8 and 32 in the evergreen broad‐leaved community, but this maximum increased with size of total sampled area size in the deciduous mixed community. All niche models could only explain SADs patterns at smaller spatial scales. However, both the neutral theory and purely statistical models were suitable for explaining the SADs for secondary forest communities when the sampling plot exceeded 40 m. The results showed the SADs indicated a clear directional trend toward convergence and similar predominating ecological processes in two typical subtropical secondary forests. The neutral process gradually replaced the niche process in importance and become the main mechanism for determining SADs of forest trees as the sampling scale expanded. Thus, we can preliminarily conclude that neutral processes had a major effect on biodiversity patterns in these two subtropical secondary forests but exclude possible contributions of other processes.     

长白山温带森林不同演替阶段群落结构特征

原始阔叶红松林是长白山西部地区的地带性顶级植被类型, 经采伐干扰或火烧破坏后形成大面积次生林。参照CTFS (Centre for Tropical Forest Science)样地建设技术规范, 于2005~2007年, 在长白山地区典型次生杨桦林、次生针阔混交林和椴树红松林内各建立了5.2 hm²固定监测样地。调查并鉴定了样地内胸径大于1 cm的木本植物, 初步分析了森林监测样地的群落组成和种群结构, 并应用双相关函数g(r)分析了样地内5个优势树种的空间分布。结果表明: 次生杨桦林样地共监测木本植物32种, 20 949株活个体, 隶属于13科21属。次生针阔混交林样地共监测木本植物31个种, 14 725株活个体, 隶属于12科20属。椴树红松林样地共监测木本植物20个种, 12 062株活个体, 隶属于11科13属。次生杨桦林、次生针阔混交林及椴树红松林中胸径大于1 cm的木本植物胸高断面积之和分别为24.74、32.07和56.64 m²·hm^-2。紫椴(Tilia amurensis)是长白山针阔混交林带的重要组成树种, 其重要值、胸高断面积在3个森林监测样地内均居于前列。白桦(Betula platyphylla)、山杨(Populus daviana)重要值和胸高断面积在次生杨桦林内均处于优势地位, 而在椴树红松林内优势地位为红松(Pinus koraiensis)等顶级树种所取代。次生杨桦林和次生针阔混交林中, 红松、色木槭(Acer mono)、臭松(Abies nephrolepis)、鱼鳞松(Picea jezoensis)和紫椴的径级结构均呈倒J型分布; 而椴树红松林内, 红松和紫椴的径级结构则呈单峰分布, 色木槭、臭松和鱼鳞松呈倒J型分布。g(r)分析表明长白山森林监测样地内5个优势树种的空间格局以聚集分布为主, 聚集强度在同种个体周围(r≤4 m)达到最大, 随着距离增加, 聚集强度逐渐减小。次生林中树种空间格局的环境解释量较高, 而椴树红松林中环境因子对树种空间分布的解释能力较差。     

Unimodal Tree Size Distributions Possibly Result from Relatively Strong Conservatism in Intermediate Size Classes

Tree size distributions have long been of interest to ecologists and foresters because they reflect fundamental demographic processes. Previous studies have assumed that size distributions are often associated with population trends or with the degree of shade tolerance. We tested these associations for 31 tree species in a 20 ha plot in a Dinghushan south subtropical forest in China. These species varied widely in growth form and shade-tolerance. We used 2005 and 2010 census data from that plot. We found that 23 species had reversed J shaped size distributions, and eight species had unimodal size distributions in 2005. On average, modal species had lower recruitment rates than reversed J species, while showing no significant difference in mortality rates, per capita population growth rates or shade-tolerance. We compared the observed size distributions with the equilibrium distributions projected from observed size-dependent growth and mortality. We found that observed distributions generally had the same shape as predicted equilibrium distributions in both unimodal and reversed J species, but there were statistically significant, important quantitative differences between observed and projected equilibrium size distributions in most species, suggesting that these populations are not at equilibrium and that this forest is changing over time. Almost all modal species had U-shaped size-dependent mortality and/or growth functions, with turning points of both mortality and growth at intermediate size classes close to the peak in the size distribution. These results show that modal size distributions do not necessarily indicate either population decline or shade-intolerance. Instead, the modal species in our study were characterized by a life history strategy of relatively strong conservatism in an intermediate size class, leading to very low growth and mortality in that size class, and thus to a peak in the size distribution at intermediate sizes.