Size-dependent mortality induces life-history changes mediated through population dynamical feedbacks

The majority of taxa grow significantly during life history, which often leads to individuals of the same species having different ecological roles, depending on their size or life stage. One aspect of life history that changes during ontogeny is mortality. When individual growth and development are resource dependent, changes in mortality can affect the outcome of size-dependent intraspecific resource competition, in turn affecting both life history and population dynamics. We study the outcome of varying size-dependent mortality on two life-history types, one that feeds on the same resource throughout life history and another that can alternatively cannibalize smaller conspecifics. Compensatory responses in the life history dampen the effect of certain types of size-dependent mortality, while other types of mortality lead to dramatic changes in life history and population dynamics, including population (de-)stabilization, and the growth of cannibalistic giants. These responses differ strongly among the two life-history types. Our analysis provides a mechanistic understanding of the population-level effects that come about through the interaction between individual growth and size-dependent mortality, mediated by resource dependence in individual vital rates.     

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

Light competition and interspecific differences in shade tolerance are considered key determinants of forest stand structure and dynamics. Specifically two main stand diameter distribution types as a function of shade tolerance have been proposed based on empirical observations. All-aged stands of shade tolerant species tend to have steeply descending, monotonic diameter distributions (inverse J-shaped curves). Shade intolerant species in contrast typically exhibit normal (unimodal) tree diameter distributions due to high mortality rates of smaller suppressed trees. In this study we explore the generality of this hypothesis which implies a causal relationship between light competition or shade tolerance and stand structure. For this purpose we formulate a partial differential equation system of stand dynamics as a function of individual tree growth, recruitment and mortality which allows us to explore possible individual-based mechanisms--e.g. light competition-underlying observed patterns of stand structure--e.g. unimodal or inverse J-shaped equilibrium diameter curves. We find that contrary to expectations interspecific differences in growth patterns can result alone in any of the two diameter distributions types observed in the field. In particular, slow growing species can present unimodal equilibrium curves even in the absence of light competition. Moreover, light competition and shade intolerance evaluated both at the tree growth and mortality stages did not have a significant impact on stand structure that tended to converge systematically towards an inverse J-shaped curves for most tree growth scenarios. Realistic transient stand dynamics for even aged stands of shade intolerant species (unimodal curves) were only obtained when recruitment was completely suppressed, providing further evidence on the critical role played by juvenile stages of tree development (e.g. the sampling stage) on final forest structure and composition. The results also point out the relevance of partial differential equations systems as a tool for exploring the individual-level mechanisms underpinning forest structure, particularly in relation to more complex forest simulation models that are more difficult to analyze and to interpret from a biological point of view.     

Size-dependent sex change can be the ESS without any size advantage of reproduction when mortality is size-dependent

Almost all models of sex change evolution assume that reproductive rate increases with body size. However, size-dependent sex changing plants often show size-independent reproductive success, presumably due to pollen limitation. Can the observed size-dependent sex change pattern be the ESS in this case? To answer this question, we analyze a game model of size-dependent sex expression in plants. We assume: (1) reproductive rate is perfectly independent of size; (2) mortality decreases with size in the same way for both sexes; (3) growth rates decrease at maturity, more for females than males. We show that the ESS is size-dependent sex expression: small individuals are vegetative, intermediate individuals are male, and large individuals are female. These results demonstrate that mortality is important in size-dependent sex allocation even when mortality rate is independent of sex. They also offer an explanation of why we see populations in poor environments to have sex ratios more biased toward the first sex relative to high quality environments.     

POPULATION STRUCTURE, DYNAMICS, AND PRODUCTION OF THE MEDITERRANEAN MACROALGA CODIUM BURSA (CHLOROPHYCEAE)

The biochemical composition and metabolism of the balloonlike Mediterranean macroalga Codium bursa J. Agardh are strongly size dependent and constrained by the spherical geometry of its thallus. Changes in reproductive phenology, population structure, density, biomass, and production of this widespread alga were followed over an annual cycle to examine whether mortality rate was size and age dependent. Examination of size and age distributions showed the population to be in quasi-steady state. A main recruitment event occurred in winter, with the highest gametangial densities observed in October, and the peak of recruits observed in December. The small recruits (0–2 cm in diameter) exhibited high growth (1 cm in <1 month) and mortality rates. High exponential mortality rate was also observed in the larger individuals (>12 cm, or 6 years old). Intermediate size C. bursa showed the lowest mortality rate, indicating that organisms within this size range (3–12 cm) escape advective and grazing losses that decimate small recruits and that they, unlike larger organisms, maintain an adequate physiological status. Asexual gemmation within the intermediate size classes may also contribute to maintain stable populations of this species in the NW Mediterranean littoral zone, since recruits derived from sexual reproduction experience extremely high mortality rates.     

Abundance, diversity and body size: patterns from a grassland arthropod community

1. The empirical relationships among body size, species richness and number of individuals may give insight into the factors controlling species diversity and the relative abundances of species. To determine these relationships, we sampled the arthropods of grasslands and savannahs at Cedar Creek, MN using sweep nets (90 525 individuals of 1225 species) and pitfall traps (12 721 individuals of 92 species). Specimens were identified, enumerated and measured to determine body size.
2. Both overall and within abundant taxonomic orders, species richness and numbers of individuals peaked at body sizes intermediate for each group. Evolution could create unimodal diversity patterns by random diversification around an ancestral body size or from size-dependent fitness differences. Local processes such as competition or predation could also create unimodal diversity distributions.
3. The average body size of a species depended significantly on its taxonomic order, but on contemporary trophic role only within the context of taxonomic order.
4. Species richness ( S _i) within size classes was related to the number of individuals ( I _i) as S _i =  I i^0·5. This relationship held across a 100 000-fold range of body sizes. Within size classes, abundance distributions of size classes were all similar power functions. A general rule of resource division, together with similar minimum population sizes, is sufficient to generate the relationship between species richness and number of individuals.
5. Smaller bodied species had slightly shallower abundance distributions and may, in general, persist at lower densities than larger species.
6. Our results suggest there may be fewer undescribed small arthropod species than previously thought and that most undescribed species will be smaller than arthropods.     

Cell Growth and Size Homeostasis in Silico

Cell growth in size is a complex process coordinated by intrinsic and environmental signals. In a research work performed by a different group, size distributions of an exponentially growing population of mammalian cells were used to infer cell-growth rate in size. The results suggested that cell growth was neither linear nor exponential, but subject to size-dependent regulation. To explain the observed growth pattern, we built a mathematical model in which growth rate was regulated by the relative amount of mRNA and ribosomes in a cell. Under the growth model and a stochastic division rule, we simulated the evolution of a population of cells. Both the sampled growth rate and size distribution from this in silico population agreed well with experimental data. To explore the model space, alternative growth models and division rules were studied. This work may serve as a starting point to understand the mechanisms behind cell growth and size regulation using predictive models.     

Cell Growth and Size Homeostasis in Silico

Cell growth in size is a complex process coordinated by intrinsic and environmental signals. In a research work performed by a different group, size distributions of an exponentially growing population of mammalian cells were used to infer cell-growth rate in size. The results suggested that cell growth was neither linear nor exponential, but subject to size-dependent regulation. To explain the observed growth pattern, we built a mathematical model in which growth rate was regulated by the relative amount of mRNA and ribosomes in a cell. Under the growth model and a stochastic division rule, we simulated the evolution of a population of cells. Both the sampled growth rate and size distribution from this in silico population agreed well with experimental data. To explore the model space, alternative growth models and division rules were studied. This work may serve as a starting point to understand the mechanisms behind cell growth and size regulation using predictive models.     

Size and temperature dependent foraging capacities and metabolism: consequences for winter starvation mortality in fish

The foraging related capacities, energy requirements and the ability of individuals to withstand starvation are strongly dependent on body size and temperature. In this study, we estimated size-dependent foraging rates and critical resource density (CRD) in small Arctic char ( Salvelinus alpinus ) under winter conditions and compared these with previous observations under summer conditions. We investigated if starvation mortality is size-dependent in the laboratory, and we assessed the potential for winter growth and the occurrence and size dependency of winter mortality both in a large scale pond experiment and in natural lakes. The efficiency of foraging on macroinvertebrates increased with size but was lower at 4 than 12°C, still CRD was lower at 4 than 12°C as metabolic rates decreased faster than foraging efficiency with temperature. When starved, small char died before large and at rates which suggest that YOY char need to feed during winter to avoid starvation. Results from both our pond experiment and field study indicate that survival of YOY char over winter is high, despite severe winter conditions, because YOY char are able to feed and grow during winter. In seasonal environments with declining resources, the size scaling and temperature dependency of foraging and metabolic demands may provide conditions which can favour either small or large individuals. This size advantage dichotomy relates to that larger individual's by having a higher CRD are more likely to start starving, but once resource levels are below CRD for all size classes, small individuals starve to death at a higher rate. Negative size-dependent winter mortality from starvation is suggested to be more pronounced in species that are not adapted to feed at low temperatures and in species feeding on zooplankton, since zooplankton abundance, in contrast to macroinvertebrate abundance, is generally low during winter.     

Live fast,die young: estimating size-age relations and mortality pattern of shrubs species in the semi-arid Karoo,South Africa

We present a technique for estimating size-age relations and size-dependent mortality patterns of long-lived plants. The technique requires two sets of size data of individual (non-marked) plants that should be collected with a time-lag of several years in the same area of a study site. The basic idea of our technique is to assume general (three parameter) families of size-dependent functions which describe growth and mortality that occurred between the two data gathering events. We apply these growth and mortality functions to the size data of the early data set and construct predicted size-class distributions to compare it, in a systematic way, to the size-class distribution of the later data set. In a next step we calculate the size-age relations from the resulting growth functions, which yield the smallest difference between observed and predicted size-class distribution. Applying this technique to size data of five dominant shrub species at the Tierberg study site in the semiarid Karoo, South Africa produced new insight into the biology of these species which otherwise cannot be obtained without frequent measurements of marked plants. We could relate characteristics of growth behavior and mortality, for certain subgroups of the five species, to the life-history attributes evergreen vs. deciduous, succulent vs. woody, and early reproductive vs. late reproductive. The results of our pilot-study suggest a broad applicability of our technique to other shrublands of the world. This requires at least one older record of (individual) shrub-size data and performance of resampling.     

Size symmetry of competition alters biomass-density relationships

As crowded populations of plants develop, the growth of some plants is accompanied by the death of others, a process called density-dependent mortality or 'self-thinning'. During the course of density-dependent mortality, the relationship between total population biomass (B) and surviving plant density (N) is allometric: B = aN(b). Essentially, increasing population biomass can be achieved only through decreasing population density. Variation in the allometric coefficient a among species has been recognized for many years and is important for management, assessment of productivity and carbon budgets, but the causes of this variation have not been elucidated. Individual-based models predict that size-dependent competition causes variation in the allometric coefficient. Using transgenic Arabidopsis with decreased plasticity, we provide experimental evidence that morphological plasticity of wild-type populations decreases the size asymmetry of competition for light and thereby decreases density-dependent mortality. This decrease in density-dependent mortality results in more biomass at a given density under size-symmetric compared with size-asymmetric competition.     

Comparison of population structures and ecology of a congeneric pair of common and rare neotropical tree species

We compared the general ecology and population profiles of Jatropha standleyi and J. chamelensis, two ecologically similar, dioecious forest trees in order to illuminate why they differ in range size, an important measure of relative commonness and rarity. Jatropha standleyi is widespread throughout the tropical deciduous forest in Mexico and the endangered J. chamelensis is restricted to a small region on the Pacific coast of Mexico. Using data collected over the same time period from a site central to the distributions of both species, we found significant differences in population size distributions and seedling mortality, but no discernible differences in seedling or adult growth rates, local abundance or local distribution. The observed difference in relative rarity could be explained by a number of hypotheses depending on whether the populations are at a stable equilibrium or not. The high ratio of pre-reproductive individuals may indicate a growing, rather than stable, population for J. chamelensis. Jatropha standleyi is more widespread and has a significantly lower ratio of pre-reproductive to mature individuals. Alternatively, both populations may be at equilibrium with J. chamelensis restricted to its limited range by large-scale environmental constraints or niche differences not elucidated in this study. In either case however, the greater and less variable seed output of the J. standleyi population will also mean a greater number of rare long-distance dispersal events and a better chance of establishing a persistent remote population for J. standleyi than for J. chamelensis. The dioecy to be found in both these species would exacerbate the limiting effects of low seed production on the ability of a species to travel successfully. A more extensive field investigation of mortality and factors contributing to mortality in sub-canopy and pre-reproductive individuals would allow more light to be shed on relative population processes in these species.     

Sapling biomass allocation and growth in the understory of a deciduous hardwood forest

Above- and belowground tissues of co-occurring saplings (0.1-1 m height) of Acer saccharum Marsh. (very shade tolerant), Acer rubrum L. (shade tolerant), Fraxinus americana L. (intermediate shade tolerant), and Prunus serotina Ehrh. (shade intolerant) were harvested from a forest understory to test the hypothesis that the pattern of biomass allocation varied predictably with shade-tolerance rank. The placement and length of branches along the main axis were consistent with the formation of a monolayer of foliage for the tolerant and intermediate species. Other morphological characteristics did not vary predictably with shade-tolerance rank. The maintenance of high specific leaf area (SLA; leaf area/leaf mass) and leaf area ratio (LAR; leaf area/sapling mass) is considered important for growth under extreme shade, yet these traits were not clearly related to the shade-tolerance rank of these species. Fraxinus americana, an intermediate species, had the highest LAR and growth rate in the understory, and with the exception of P. serotina, the very shade-tolerant A. saccharum had the lowest LAR. Prunus serotina maintained a large starch-rich tap root and shoot dieback was common, yielding the largest root/shoot ratio for these species. The observed allocation patterns were not similar to the long-standing expectation for the phenotypic response of juvenile trees to shade, but were consistent with three hypothetical "growth strategies" in the understory: (1) the low SLA and LAR of A. saccharum may provide a measure of defense against herbivores and pathogens and thus promote persistence in the understory, (2) the high SLA for F. americana and high LAR for F. americana and A. rubrum may enable these species to achieve high growth rates in shade, and (3) the large carbohydrate stores of P. serotina may poise this species for opportunistic growth following disturbance. The relative importance of resistance to herbivores and pathogens vs. the maintenance of high growth rates may be important in evaluating the patterns of biomass allocation in the understory.     

Characterization of Nanocrystal Size Distribution using Raman Spectroscopy with a Multi-particle Phonon Confinement Model

Analysis of the size distribution of nanocrystals is a critical requirement for the processing and optimization of their size-dependent properties. The common techniques used for the size analysis are transmission electron microscopy (TEM), X-ray diffraction (XRD) and photoluminescence spectroscopy (PL). These techniques, however, are not suitable for analyzing the nanocrystal size distribution in a fast, non-destructive and a reliable manner at the same time. Our aim in this work is to demonstrate that size distribution of semiconductor nanocrystals that are subject to size-dependent phonon confinement effects, can be quantitatively estimated in a non-destructive, fast and reliable manner using Raman spectroscopy. Moreover, mixed size distributions can be separately probed, and their respective volumetric ratios can be estimated using this technique. In order to analyze the size distribution, we have formulized an analytical expression of one-particle PCM and projected it onto a generic distribution function that will represent the size distribution of analyzed nanocrystal. As a model experiment, we have analyzed the size distribution of free-standing silicon nanocrystals (Si-NCs) with multi-modal size distributions. The estimated size distributions are in excellent agreement with TEM and PL results, revealing the reliability of our model.     

The size distribution of conspecific populations: the peoples of New Guinea

The size distribution of the language populations in New Guinea, which represent over 15% of the world's languages, is analysed using models analogous to the resource division models of species abundance distribution in ecological communities. A model distribution of resource segments reflecting population size is created by repeated selection of an existing resource segment and its division into two. We found that any dependency of the selection probability on the size of the segment generated negatively skewed abundance distributions after log transformation. Asymmetric segment division further exacerbated the negative skewness. Size-independent selection produced lognormal abundance distributions, irrespective of the segment division method. Size-dependent selection and asymmetric division were deemed reasonable assumptions since large language populations are more likely to generate isolates, which develop into new populations, than small ones, and these isolates are likely to be small relative to the progenitor population. A negatively skewed distribution of the log-transformed population sizes was therefore expected. However, the observed distributions were lognormal, scale invariant for areas containing between 100 and over 1000 language populations. The dynamics of language differentiation, as reflected by the models, may therefore be unimportant relative to the effect of variable growth rates among populations. All lognormal distributions from resource division models had a higher variance than the observed one, where half of the 1053 populations had between 350 and 3000 individuals. The possible mechanisms maintaining such a low variance around a modal population size of 1000 are discussed.     

Mutation Size Optimizes Speciation in an Evolutionary Model

The role of mutation rate in optimizing key features of evolutionary dynamics has recently been investigated in various computational models. Here, we address the related question of how maximum mutation size affects the formation of species in a simple computational evolutionary model. We find that the number of species is maximized for intermediate values of a mutation size parameter μ; the result is observed for evolving organisms on a randomly changing landscape as well as in a version of the model where negative feedback exists between the local population size and the fitness provided by the landscape. The same result is observed for various distributions of mutation values within the limits set by μ. When organisms with various values of μ compete against each other, those with intermediate μ values are found to survive. The surviving values of μ from these competition simulations, however, do not necessarily coincide with the values that maximize the number of species. These results suggest that various complex factors are involved in determining optimal mutation parameters for any population, and may also suggest approaches for building a computational bridge between the (micro) dynamics of mutations at the level of individual organisms and (macro) evolutionary dynamics at the species level.     

Predicting population trends from size distributions: a direct test in a tropical tree community

ABSTRACT Forest ecologists often evaluate how well the species composition of saplings in the understory matches that of the canopy: absence of juveniles suggests that a tree species is suffering population decline. Here we offer a theoretical and empirical test of this assertion using data from a 50-ha census plot in Panama. Theory indicates that higher rates of population change, lambda, lead to more steeply declining size distributions (more juveniles relative to adults). But other parameters also affect the size distribution: lower growth rate of juveniles and lower survival at any size pro duce more steeply declining size distributions as well. Empirical evaluation of 216 tree populations showed that juvenile growth was the strongest predictor of size distribution, in the direction predicted by theory. Size distribution did correlate with population growth, but weakly and only in understory species, not canopy seecies. Size distribution did not correlate with the growth rate of larger individuals nor with survival. Results suggest that static in formation on the size distribution is not a good predictor of future population trends, while demographic information is. Fast-growing species will have fewer juveniles in the understory than slow growing species, even when population growth is equal.     

Effects of Group Membership and Size Distribution within a Group on Growth Rates of Juvenile Sablefish Anoplopoma fimbria

Group membership can confer both advantages and disadvantages to growth in juvenile fishes. The balance between costs and benefits of social interactions can shift depending on such factors as the composition of the group (density and size disparity) and the availability of food. We examined the effect of these factors on absolute growth and growth depensation in juvenile sablefish, Anoplopoma fimbria. Increasing density and increasing size disparity had little influence on absolute growth rates of juvenile sablefish and the effects of these social factors were not modified by ration level. In experiments testing density effects, absolute growth did not differ among groups of 1, 3, or 10 fish held at high rations, but at low rations single fish exhibited a different pattern of size-dependent growth compared to fish in groups. In experiments testing disparity effects, absolute growth did not differ between groups with an even size distribution and groups with a mixed size distribution. The relative size of an individual within a group, i.e., small, medium, or large, also did not modify growth, despite evidence of higher chasing behavior in mixed size distributions. Although the growth of small fish was not diminished in the presence of large fish, negative impacts of size disparity were expressed in high levels of cannibalism, which occurred in 42% of groups with a mixed size distribution. Significant growth depensation over time occurred in the density experiment, but not in the size disparity experiment, possibly due to the shorter duration of the latter experiment. We suggest that growth depensation was generated by individual variability in growth capacity rather than social effects on growth rates. Schooling behavior, measured by group cohesion indices, increased with fish size and was higher in groups with an even vs. a mixed size distribution. These results for sablefish are consistent with other schooling species in which growth variability is determined by exploitative competition and/or genetic variability in growth capacity rather than interference competition.     

Predicting predation through prey ontogeny using size-dependent functional response models

The functional response is a critical link between consumer and resource dynamics, describing how a consumer's feeding rate varies with prey density. Functional response models often assume homogenous prey size and size-independent feeding rates. However, variation in prey size due to ontogeny and competition is ubiquitous, and predation rates are often size dependent. Thus, functional responses that ignore prey size may not effectively predict predation rates through ontogeny or in heterogeneous populations. Here, we use short-term response-surface experiments and statistical modeling to develop and test prey size-dependent functional responses for water bugs and dragonfly larvae feeding on red-eyed treefrog tadpoles. We then extend these models through simulations to predict mortality through time for growing prey. Both conventional and size-dependent functional response models predicted average overall mortality in short-term mixed-cohort experiments, but only the size-dependent models accurately captured how mortality was spread across sizes. As a result, simulations that extrapolated these results through prey ontogeny showed that differences in size-specific mortality are compounded as prey grow, causing predictions from conventional and size-dependent functional response models to diverge dramatically through time. Our results highlight the importance of incorporating prey size when modeling consumer-prey dynamics in size-structured, growing prey populations.     

A model for the dynamics of an annual plant population

A model for the dynamics of a single species population of plants is proposed and its use demonstrated by the analysis of a simple example. The model incorporates the effects of microsite variation by allowing for individual differences in growth and death rates within each season. We demonstrate that an increase in the variance in individual growth rates may increase both the chances that a plant population will persist and the equilibrium size of that population. We also show that even if size-dependent death is occurring, it may not have a significant effect on the shape of the size frequency distribution. An extension of the model to multispecies communities of plants suggests an experimental procedure to determine whether competition is responsible for excluding a particular plant species from a community that appears otherwise to be suitable. A more detailed analysis of the model for a two-species community produces conditions for competitive coexistence reminiscent of those from the Lotka-Volterra competition equations. Another extension suggests that selection will favor those genotypes that maximize the product of germination probability and mass of seeds produced, if survivorship and growth are not substantially altered. Finally, an analog to r- and K-selection theory for animal populations is developed. Selection in low-density populations favors increasing growth rate, and in high-density populations favors minimizing the effect of neighbors on one's own growth rate.     

Tree Size Inequality Reduces Forest Productivity: An Analysis Combining Inventory Data for Ten European Species and a Light Competition Model

Plant structural diversity is usually considered as beneficial for ecosystem functioning. For instance, numerous studies have reported positive species diversity-productivity relationships in plant communities. However, other aspects of structural diversity such as individual size inequality have been far less investigated. In forests, tree size inequality impacts directly tree growth and asymmetric competition, but consequences on forest productivity are still indeterminate. In addition, the effect of tree size inequality on productivity is likely to vary with species shade-tolerance, a key ecological characteristic controlling asymmetric competition and light resource acquisition. Using plot data from the French National Geographic Agency, we studied the response of stand productivity to size inequality for ten forest species differing in shade tolerance. We fitted a basal area stand production model that included abiotic factors, stand density, stand development stage and a tree size inequality index. Then, using a forest dynamics model we explored whether mechanisms of light interception and light use efficiency could explain the tree size inequality effect observed for three of the ten species studied. Size inequality negatively affected basal area increment for seven out of the ten species investigated. However, this effect was not related to the shade tolerance of these species. According to the model simulations, the negative tree size inequality effect could result both from reduced total stand light interception and reduced light use efficiency. Our results demonstrate that negative relationships between size inequality and productivity may be the rule in tree populations. The lack of effect of shade tolerance indicates compensatory mechanisms between effect on light availability and response to light availability. Such a pattern deserves further investigations for mixed forests where complementarity effects between species are involved. When studying the effect of structural diversity on ecosystem productivity, tree size inequality is a major facet that should be taken into account.