Demographic heterogeneity, cohort selection, and population growth

Demographic heterogeneity--variation among individuals in survival and reproduction--is ubiquitous in natural populations. Structured population models address heterogeneity due to age, size, or major developmental stages. However, other important sources of demographic heterogeneity, such as genetic variation, spatial heterogeneity in the environment, maternal effects, and differential exposure to stressors, are often not easily measured and hence are modeled as stochasticity. Recent research has elucidated the role of demographic heterogeneity in changing the magnitude of demographic stochasticity in small populations. Here we demonstrate a previously unrecognized effect: heterogeneous survival in long-lived species can increase the long-term growth rate in populations of any size. We illustrate this result using simple models in which each individual's annual survival rate is independent of age but survival may differ among individuals within a cohort. Similar models, but with nonoverlapping generations, have been extensively studied by demographers, who showed that, because the more "frail" individuals are more likely to die at a young age, the average survival rate of the cohort increases with age. Within ecology and evolution, this phenomenon of "cohort selection" is increasingly appreciated as a confounding factor in studies of senescence. We show that, when placed in a population model with overlapping generations, this heterogeneity also causes the asymptotic population growth rate lambda to increase, relative to a homogeneous population with the same mean survival rate at birth. The increase occurs because, even integrating over all the cohorts in the population, the population becomes increasingly dominated by the more robust individuals. The growth rate increases monotonically with the variance in survival rates, and the effect can be substantial, easily doubling the growth rate of slow-growing populations. Correlations between parent and offspring phenotype change the magnitude of the increase in lambda, but the increase occurs even for negative parent-offspring correlations. The effect of heterogeneity in reproductive rate on lambda is quite different: growth rate increases with reproductive heterogeneity for positive parent-offspring correlation but decreases for negative parent-offspring correlation. These effects of demographic heterogeneity on lambda have important implications for population dynamics, population viability analysis, and evolution.     

A spatiotemporal individual-based fish model to investigate emergent properties at the organismal and the population level

A spatiotemporal individual-based model (IBM) of roach (Rutilus rutilus) including bioenergetic principles was used to study emergent properties at the individual and the population level which appeared as a result of resource allocation and time scheduling of activities related to maintenance, growth, and reproduction in a seasonally changing environment. The model was used as a virtual laboratory to consider the impact of various parameters on vital rates and spatial behaviour of roach, which is particularly difficult to study in the field. The parameterisation based on field studies performed at Lake Belau (Schleswig-Holstein, Germany) and laboratory measurements. This allowed us to explore the relationship between population structure and environmental heterogeneity on an integrated base. At the individual level emergent properties such as spatial behaviour, growth, and food consumption could be identified. Emergent properties at the population level resulted as phenotypic consequences of a trophic bottleneck, the influence of lake morphology on the phenotype as well as size-dependent winter mortality rates and post-reproductive mortality rates.     

Comparison of growth performance of Lolium perenne L., Dactylis glomerata L. and Agropyron elongatum (Host.) P. Beauv. for erosion control in Turkey

This study was carried out in plastic containers to compare growth performances of perennial ryegrass, orchardgrass and tall wheatgrass to be given priority in revegetation studies in Turkey. Three pre-germinated seeds of each grass species were planted separately into the soil in the black plastic containers. Seedlings were harvested 2, 4 and 6 months after planting pre-germinated seeds and measured for percentage of seedling emergence, rooting depth, height growth, leaf and tiller development and shoot and root weights. Germination percentage was 97.8% for perennial ryegrass, 64.1% for orchardgrass and 11.6% for tall wheatgrass and perennial ryegrass had the greatest whereas tall wheatgrass had the lowest seedling emergence. Two months old rooting depth was 25.66 cm for perennial ryegrass, 20.56 cm for orchardgrass and 30.10 cm for tall wheatgrass. At the end of the study, perennial ryegrass developed about 104 tillers per plant while they were 21.4 and 36.6 tillers per plant for orchardgrass and tall wheatgrass, respectively. Orchardgrass produced greater shoot and root biomasses than tall wheatgrass and similar to perennial ryegrass. All these meant that perennial ryegrass had a better growth performance than orchardgrass and tall wheatgrass to be used for erosion control.     

Self-organized spatial patterns of vegetation in alpine grasslands

There is increased interest in vegetation spatial pattern as an indicator of transition shifts following catastrophes. Much, however, remains unknown about the mechanisms that underlie spatial pattern formations. In this study, we examined how the spatial heterogeneity of species distributions in the grasslands of the Central Pyrenees and Middle Atlas Mountains is associated with plant species diversity and the importance of self-organizing processes in the control of pattern formations. In the grasslands of the Central Pyrenees and Middle Atlas, the spatial heterogeneity of species distributions increased along a habitat degradation gradient defined by an increase in bare soil. In Central Pyrenees grasslands, however, the increase in heterogeneity was associated with self-organizing bare soil formations, rather than the self-organizing distribution of plant species. In Middle Atlas grasslands, the increased heterogeneity of species spatial distributions was a consequence of the self-organizing capacity of the composing species; the increase in bare soil was randomly distributed. In the more heavily grazed grasslands (Middle Atlas), but not in the more lightly grazed and better preserved ecosystem (Central Pyrenees), plant species richness and diversity declined significantly with an increase in grazing pressure because fewer species were able to colonize empty space. On the contrary, the colonization of bare soil by new species increased the diversity and spatial organization of new colonizing species in Central Pyrenees grassland.     

A phenomenological model without dispersal kernel to model species migration

Phenomenological approaches to model species migration are usually based on kernel-based methods. These methods require a good knowledge of the dispersal agent behaviour for a given species. They also calculate the location of individuals independently to each other (except the mother plant) and then suppress some of them according to additional interactions such as competition, facilitation and recruitment. In this paper, we propose to use a new phenomenological method, the Gibbs method, to model tree species migration at large scale. The Gibbs method handles the location of adult individuals in terms of pairwise interactions described by a potential function. This function summarizes the set of known and unknown factors determining the spatial distribution of the individuals (or cohorts). The principle of the Gibbs method is to minimize the sum of all pairwise interactions, also called the cost function, in order to optimize the spatial point pattern according to the chosen potential function.     

Incorporating dormancy in dynamic microbial community models

Biogeochemical activity in natural and engineered systems depends on the abundances, functional capabilities and physiological states of the indigenous microorganisms. Typically, only a fraction of the microbial population is active at any given time. As environmental conditions change, previously active microorganisms may switch to an inactive or dormant state, while dormant ones may become active. Here, we present an extended modeling concept for the growth and decay of microorganisms that explicitly accounts for their ability to switch between active and dormant states. The equations describing the switching between physiological states are implemented into a biogeochemical reaction simulator. The model was used to reproduce published data from two laboratory experiments in which microorganisms were subjected to intermittent substrate supply or reactivated after a prolonged period of starvation. Parameter values obtained from the simulation of these experiments were used for subsequent sensitivity analyses and for the simulation of hypothetical scenarios. Results for hypothetical microbial communities consisting of two competing species exposed to periodic feeding imply that, under certain conditions, an effective dormancy-reactivation strategy may have a competitive advantage over a fast growth strategy. That is, organisms that can switch rapidly in response to fluctuations in external conditions may outcompete fast-growing organisms. Furthermore, certain combinations of growth and dormancy strategies may lead to the long-term coexistence of the two competing species. Overall, the simulated population dynamics show that dormancy is an important feature of microbial communities, which can lead to complex responses to environmental fluctuations.     

Spatial uncertainty analysis of population models

This paper describes an approach for conducting spatial uncertainty analysis of spatial population models, and illustrates the ecological consequences of spatial uncertainty for landscapes with different properties. Spatial population models typically simulate birth, death, and migration on an input map that describes habitat. Typically, only a single “reference” map is available, but we can imagine that a collection of other, slightly different, maps could be drawn to represent a particular species’ habitat. As a first approximation, our approach assumes that spatial uncertainty (i.e., the variation among values assigned to a location by such a collection of maps) is constrained by characteristics of the reference map, regardless of how the map was produced. Our approach produces lower levels of uncertainty than alternative methods used in landscape ecology because we condition our alternative landscapes on local properties of the reference map. Simulated spatial uncertainty was higher near the borders of patches. Consequently, average uncertainty was highest for reference maps with equal proportions of suitable and unsuitable habitat, and no spatial autocorrelation. We used two population viability models to evaluate the ecological consequences of spatial uncertainty for landscapes with different properties. Spatial uncertainty produced larger variation among predictions of a spatially explicit model than those of a spatially implicit model. Spatially explicit model predictions of final female population size varied most among landscapes with enough clustered habitat to allow persistence. In contrast, predictions of population growth rate varied most among landscapes with only enough clustered habitat to support a small population, i.e., near a spatially mediated extinction threshold. We conclude that spatial uncertainty has the greatest effect on persistence when the amount and arrangement of suitable habitat are such that habitat capacity is near the minimum required for persistence.     

Spatial connectivity in a large river system: resolving the sources and fate of dissolved organic matter

Large rivers are generally heterogeneous and productive systems that receive important inputs of dissolved organic matter (DOM) from terrestrial and in situ sources. Thus, they are likely to play a significant role in the biogeochemical cycling of the DOM flowing to the oceans. The asymmetric spatial gradient driven by directional flow and environmental heterogeneity contributes to the fate of DOM flowing downstream. Yet, the relative effects of spatial connectivity and environmental heterogeneity on DOM dynamics are poorly understood. For example, since environmental variables show spatial heterogeneity, the variation explained by environmental and spatial variables may be redundant. We used the St. Lawrence River (SLR) as a representative large river to resolve the unique influences of environmental heterogeneity and spatial connectivity on DOM dynamics. We used three-dimensional fluorescence matrices combined with parallel factor analysis (PARAFAC) to characterize the DOM pool in the SLR. Seven fluorophores were modeled, of which two were identified to be of terrestrial origin and three from algal exudates. We measured a set of environmental variables that are known to drive the fate of DOM in aquatic systems. Additionally, we used asymmetric eigenvector map (AEM) modeling to take spatial connectivity into account. The combination of spatial and environmental models explained 85% of the DOM variation. We show that spatial connectivity is an important driver of DOM dynamics, as a large fraction of environmental heterogeneity was attributable to the asymmetric spatial gradient. Along the longitudinal axis, we noted a rapid increase in dissolved organic carbon (DOC), mostly controlled by terrestrial input of DOM originating from the tributaries. Variance partitioning demonstrated that freshly produced protein-like DOM was found to be the preferential substrate for heterotrophic bacteria undergoing rapid proliferation, while humic-like DOM was more correlated to the diffuse attenuation coefficient of UVA radiation.     

Scale-dependent interaction of fire and grazing on community heterogeneity in tallgrass prairie

Natural disturbances affect spatial and temporal heterogeneity in plant communities, but effects vary depending on type of disturbance and scale of analysis. In this study, we examined the effects of fire frequency (1-, 4-, and 20-yr intervals) and grazing by bison on spatial and temporal heterogeneity in species composition in tallgrass prairie plant communities. Compositional heterogeneity was estimated at 10-, 50-, and 200-m2 scales. For each measurement scale, we used the average Euclidean Distance (ED) between samples within a year (2000) to measure spatial heterogeneity and between all time steps (1993-2000) for each sample to measure temporal heterogeneity. The main effects of fire and grazing were scale independent. Spatial and temporal heterogeneity were lowest on annually burned sites and highest on infrequently burned (20-yr) sites at all scales. Grazing reduced spatial heterogeneity and increased temporal heterogeneity at all scales. The rate of community change over time decreased as fire frequency increased at all scales, whereas grazing had no effect on rate of community change over time at any spatial scale. The interactive effects of fire and grazing on spatial and temporal heterogeneity differed with scale. At the 10-m2 scale, grazing increased spatial heterogeneity in annually burned grassland but decreased heterogeneity in less frequently burned areas. At the 50-m2 scale, grazing decreased spatial heterogeneity on 4-yr burns but had no effect at other fire frequencies. At the 10-m scale, grazing increased temporal heterogeneity only on 1- and 20-yr burn sites. Our results show that the individual effects of fire and grazing on spatial and temporal heterogeneity in mesic prairie are scale independent, but the interactive effects of these disturbances on community heterogeneity change with scale of measurement. These patterns reflect the homogenizing impact of fire at all spatial scales, and the different frequency, intensity, and scale of patch grazing by bison in frequently burned vs. infrequently burned areas.     

A new approach to spatial entropy measures

Entropy is widely employed in many applied sciences to measure the heterogeneity of observations. Recently, many attempts have been made to build entropy measures for spatial data, in order to capture the influence of space over the variable outcomes. The main limit of these developments is that all indices are computed conditional on a single distance and do not cover the whole spatial configuration of the phenomenon under study. Moreover, most of them do not satisfy the desirable additivity property between local and global spatial measures. This work reviews some recent developments, based on univariate distributions, and compares them to a new approach which considers the properties of entropy measures linked to bivariate distributions. This perspective introduces substantial innovations. Firstly, Shannon’s entropy may be decomposed into two terms: spatial mutual information, accounting for the role of space in determining the variable outcome, and spatial global residual entropy, summarizing the remaining heterogeneity carried by the variable itself. Secondly, these terms both satisfy the additivity property, being sums of partial entropies measuring what happens at different distance classes. The proposed indices are used for measuring the spatial entropy of a marked point pattern on rainforest tree species. The new entropy measures are shown to be more informative and to answer a wider set of questions than the current proposals of the literature.     

Birth sex ratios in sheep over six lambing seasons

Summary The birth sex ratio of a commercial flock of Suffolk × sheep, Ovis aries, were studied over six consecutive lambing seasons. In all, data from 1820 lambs were recorded and analysed. The overall birth sex ratio was 49.56% male lambs. Significantly more males (56.23%) were born to ewes with single lambs than to ewes with like-sex twins (47.73%). Significantly more female lambs were born to ewes with triplet births (41.79% male). A significant difference in the birth sex ratio was observed between the first and second half of the lambing season, among like-sex pairs of twin lambs. More males were born in the first half (51.43%) and significantly more females (43.59% male) in the second half of the lambing season. The results are discussed with reference to the theory of Trivers and Willard (1973).     

Spatial and temporal variability modify density dependence in populations of large herbivores

A central challenge in ecology is to understand the interplay of internal and external controls on the growth of populations. We examined the effects of temporal variation in weather and spatial variation in vegetation on the strength of density dependence in populations of large herbivores. We fit three subsets of the model ln(Nt) = a + (1 + b) x ln(N(t-1)) + c x ln(N(t-2)) to five time series of estimates (Nt) of abundance of ungulates in the Rocky Mountains, USA. The strength of density dependence was estimated by the magnitude of the coefficient b. We regressed the estimates of b on indices of temporal heterogeneity in weather and spatial heterogeneity in resources. The 95% posterior intervals of the slopes of these regressions showed that temporal heterogeneity strengthened density-dependent feedbacks to population growth, whereas spatial heterogeneity weakened them. This finding offers the first empirical evidence that density dependence responds in different ways to spatial heterogeneity and temporal heterogeneity.     

Spatial scale of the patchiness of plant poisons: a critical influence on foraging efficiency

Generalist mammalian browsers and folivores feed on a range of chemically different plant species, which may assist them in diluting toxins and diversifying nutrient consumption. The frequency and order in which their diets are mixed are important determinants of intake. As a result, the degree of plant heterogeneity in an environment, and the spatial scale at which this occurs, should directly influence herbivore foraging decisions. We tested whether altering the Spatial scale of plants, and thus plant secondary metabolites (PSMs), affected foraging efficiency of a generalist folivore, the common brushtail possum (Trichosurus vulpecula). First, we demonstrated that possums were able to consume more from a mixed diet of two chemically different species, Eucalyptus globulus and E. tenuiramis, than when either of these species was offered alone. We then tested whether altering the spatial scale between E. globulus and E. tenuiramis, as small- or large-scale plant heterogeneity "patches," affected possum foraging behavior and, ultimately, their foraging efficiency. Possums increased their foraging efficiency when the spatial scale of plant heterogeneity was small rather than large. We argue that the ability to regularly switch diets, when plant spatial distribution is at a small scale, reduces the negative effects of PSM ingestion. We predict that the heterogeneity of plant patches, in relation to PSM distribution, and the scale at which this occurs across a landscape, are critical factors that influence foraging efficiency and, ultimately, fitness of mammalian herbivores. This research provides a fundamental link between plant chemistry, foraging, and habitat heterogeneity.     

Effect of Small‐Scale Heterogeneity of Prey and Hunter Distributions on the Sustainability of Bushmeat Hunting

Abstract: Bushmeat is the main source of protein and the most important source of income for rural people in the Congo Basin, but intensive hunting of bushmeat species is also a major concern for conservationists. Although spatial heterogeneity in hunting effort and in prey populations at the landscape level plays a key role in the sustainability of hunted populations, the role of small‐scale heterogeneity within a village hunting territory in the sustainability of hunting has remained understudied. We built a spatially explicit multiagent model to capture the dynamics of a system in which hunters and preys interact within a village hunting territory. We examined the case of hunting of bay duikers (Cephalophus dorsalis) in the village of Ntsiété, northeastern Gabon. The impact of hunting on prey populations depended on the spatial heterogeneity of hunting and prey distribution at small scales within a hunting area. Within a village territory, the existence of areas hunted throughout the year, areas hunted only during certain seasons, and unhunted areas contributed to the sustainability of the system. Prey abundance and offtake per hunter were particularly sensitive to the frequency and length of hunting sessions and to the number of hunters sharing an area. Some biological parameters of the prey species, such as dispersal rate and territory size, determined their spatial distribution in a hunting area, which in turn influenced the sustainability of hunting. Detailed knowledge of species ecology and behavior, and of hunting practices are crucial to understanding the distribution of potential sinks and sources in space and time. Given the recognized failure of simple biological models to assess maximum sustainable yields, multiagent models provide an innovative path toward new approaches for the assessment of hunting sustainability, provided further research is conducted to increase knowledge of prey species’ and hunter behavior.     

广州白云山风景区植被景观异质性分析

采用信息论的线性抽样方法对白云山风景区的景观要素进行了景观异质性分析,结果表明,白云山风景区景观的异质性较大,并与景观要素的空间分布密切相关。阔叶林类型的相对频率与平均信息量最大,已在白云山风景区处于景观基质的地位,对白云山的景观结构和景观生态的变化起着决定性的作用。     

Resource partitioning among savanna grazers mediated by local heterogeneity: an experimental approach

Recent theoretical studies predict that body size-related interspecific differences in spatial scale of perception and resource use may contribute to coexistence of species that compete for the same class of resources. These studies provide a new theoretical framework for explaining resource partitioning patterns among African ungulates that coexist in spatially heterogeneous savanna grasslands. According to these studies, different-sized ungulates can coexist because larger species forage at a coarser scale but can tolerate lower quality food, whereas smaller species need higher quality food but forage at a finer scale. To test this hypothesis in an African savanna, we created an experimental mosaic with variation in grain (spatial detail) and quality of short-grass patches and directly observed the visitation of naturally occurring grazers to this mosaic over a two-year period (total of 903 observation hours). Of the seven species that visited our experiment, warthog, impala, zebra, and white rhino visited long enough to allow data analysis. We showed that warthog and impala avoided plots with a finer grain of short grass and that warthog preferred fertilized plots to unfertilized plots. Zebra and white rhino did not avoid the finer grain plots. Our results suggest that differences in grain and quality of a resource might indeed contribute to partitioning of this resource by savanna ungulates. Although four focal species is unusually high for an experimental study on resource partitioning among naturally occurring savanna ungulates, this number is too low to evaluate the allometric basis of our hypothesis. Our results, however, encourage wider experimental testing of the role of spatial heterogeneity in facilitating the coexistence of potentially competing savanna herbivores.     

Fire and forest landscapes in the Georgia Piedmont: an assessment of spatial modeling assumptions

Landscape simulation models are widely used to study the behavior of ecological systems. As computing power has increased, these models have become more complex and incorporated more realistic spatial representations of landscape patterns and ecological processes. The goal of this research was to examine the sensitivity of simulated landscape patterns to fundamental spatial modeling assumptions. The LANDIS simulator was parameterized for forests of the Georgia Piedmont and used to model landscape-scale community dynamics at fire return intervals from 20 to 100 years. A base scenario incorporating localized seed dispersal along with landform-related variation in species establishment rates and disturbance regimes was contrasted with three alternative scenarios. The uniform habitat scenario applied the same set of species establishment coefficients across all landforms. The uniform dispersal scenario removed the effects of seed source abundance and pattern on species establishment. The uniform disturbance scenario assumed identical disturbance regimes on all landforms.At the shortest fire return intervals, fire severities were low and the stand age distribution was dominated by older forests. At longer fire return intervals, fire severities were high and the stand age distribution was skewed toward younger forests. Species composition generally followed a gradient from fire-resistant species at short fire return intervals to fire-sensitive species at longer fire return intervals. However, some species exhibited bimodal distributions with high abundances at both short and long fire return intervals. Landscape responses to fire were similar in the uniform habitat scenario and the base scenario. Communities were less sensitive to fire return interval and had more fire-sensitive species in the uniform dispersal scenario than in the base scenario. Species composition in the uniform disturbance scenario was similar to the base scenario for the longest fire-intervals, but was more sensitive to changes in the fire regime at shorter fire return intervals. In models of Piedmont forest landscapes, accurate spatial representations of dispersal and fire regime heterogeneity are essential for predicting landscape-scale species composition under changing fire regimes. In contrast, the precise spatial representation of species–habitat relationships may be considerably less important.     

Modelling the horizontal spatial structure of planktonic community in Lake Trasimeno (Umbria,Italy) using multivariate geostatistical methods

Spatial heterogeneity of ecological systems has been recognised in recent years as an important ecological feature of an ecosystem, rather than a mere statistical nuisance. However, although considerable interest has been paid to the development of statistical methods for the analysis of spatial environmental data, when in presence of more species or environmental variables common analyses still fail to recognise the necessity of a joint modelling of the whole correlation structure. In this paper, we propose to study the multivariate spatial autocorrelation of a plankton community by making explicit reference to a spatial linear factor model entailing a set of constraints for the spatial structure of the planktonic species. The data set examined come from an intensive 2-day sampling survey performed in July 1991 on Lake Trasimeno (Italy) to investigate the horizontal spatial heterogeneity and distribution of the planktonic community, from small (50 m) to large (1000–10,000 m) scale. The analysis revealed that zooplankton and phytoplankton essentially have different degrees of heterogeneity and different spatial structures which required separate modelling. On the other hand, the similarity of the spatial autocorrelation found within zooplankton and phytoplankton communities, indicates that at the investigated scales of observation the horizontal organisation of both components is not appreciably affected by species-specific behaviours. The analysis of the multivariate spatial patterns emerging from the mapping of the extracted factors suggested an interpretation of the distribution of macrozooplankton and phytoplankton assemblages in terms of planktonic responses to environmental factors of a lake-size scale.