Fixed point sensitivity analysis of interacting structured populations

Sensitivity analysis of structured populations is a useful tool in population ecology. Historically, methodological development of sensitivity analysis has focused on the sensitivity of eigenvalues in linear matrix models, and on single populations. More recently there have been extensions to the sensitivity of nonlinear models, and to communities of interacting populations. Here we derive a fully general mathematical expression for the sensitivity of equilibrium abundances in communities of interacting structured populations. Our method yields the response of an arbitrary function of the stage class abundances to perturbations of any model parameters. As a demonstration, we apply this sensitivity analysis to a two-species model of ontogenetic niche shift where each species has two stage classes, juveniles and adults. In the context of this model, we demonstrate that our theory is quite robust to violating two of its technical assumptions: the assumption that the community is at a point equilibrium and the assumption of infinitesimally small parameter perturbations. Our results on the sensitivity of a community are also interpreted in a niche theoretical context: we determine how the niche of a structured population is composed of the niches of the individual states, and how the sensitivity of the community depends on niche segregation.     

Competitive exclusion and limiting similarity: a unified theory

Robustness of coexistence against changes of parameters is investigated in a model-independent manner by analyzing the feedback loop of population regulation. We define coexistence as a fixed point of the community dynamics with no population having zero size. It is demonstrated that the parameter range allowing coexistence shrinks and disappears when the Jacobian of the dynamics decreases to zero. A general notion of regulating factors/variables is introduced. For each population, its impact and sensitivity niches are defined as the differential impact on, and the differential sensitivity towards, the regulating variables, respectively. Either the similarity of the impact niches or the similarity of the sensitivity niches results in a small Jacobian and in a reduced likelihood of coexistence. For the case of a resource continuum, this result reduces to the usual "limited niche overlap" picture for both kinds of niche. As an extension of these ideas to the coexistence of infinitely many species, we demonstrate that Roughgarden's example for coexistence of a continuum of populations is structurally unstable.     

Studying Individual Patterns of Development Using I-States as Objects Analysis (ISOA)

An approach is presented for studying individual pattern development in person-oriented terms focusing on the concept of i-state, i.e. an individual's configuration of information at a specific point in time. The procedure is called I-States as Objects Analysis (ISOA). First common i-states (typical states) are identified using cluster analysis of subindividuals and then this information is used for describing typical developmental patterns. Both a general procedure and a specific procedure used on a demonstration data set were developed. Using ISOA, change and stability can be studied both with regard to structure and with regard to individual variation. An empirical example was given which concerned longitudinal data about school grades at four different ages for 333 boys and girls. The data were split into a test sample and a replication sample of equal sizes. It was contended from the empirical study that ISOA functioned reasonably well on the sample studied. In the discussion, it was pointed out that ISOA can be a powerful method to use for small samples with many measurement occasions and that the method is optimal for studying short-term change.     

Two-patch model of spatial niche segregation

Spatial niche segregation between two habitats and the related adaptive dynamics are investigated. Independent population regulations operate in the two patches by a single resource in each. The populations migrate between the habitats with a constant rate. In line with a general mathematical concept published elsewhere, the niche of a species is described by the measures of the two-way interactions between the species and the resources. Increasing migration rate tends to equalize the population sizes between the habitats and diminish the dependence of the niches on the environmental tolerances of the species. In line with the expectations, when two species coexist, their realized niches are more segregated than their fundamental ones. We demonstrate that robust coexistence requires sufficient niche segregation. That is, the parameter range that allows coexistence of the two species shrinks to nil when the niche-differences between the species disappear. In turn, niche segregation requires separation of tolerances and sufficiently low migration rate. For the evolutionary study we assume a continuous, clonally inherited character that has different optima at the two patches. Evolution of this trait may end up in an intermediate “generalist” optimum, or it can branch and leads to a dimorphic population. The condition of the latter outcome is in line with the conditions that allow niche segregation: the patches have to be sufficiently different and the migration has to be sufficiently low. Electronic supplementary material  The online version of this article () contains supplementary material, which is available to authorized users.     

Community robustness and limiting similarity in periodic environments

Temporal environmental variation has long been considered as one of the potential factors that could promote species coexistence. A question of particular interest is how the ecology of fluctuating environments relates to that of equilibrium systems. Equilibrium theory says that the more similar two species are in their modes of regulation, the less robust their coexistence will be; that is, the volume of external parameters for which all populations persist shrinks with increasing similarity. In this study, we will attempt to generalize these results to temporally varying situations and establish the precise mathematical relationship between the two. Our treatment considers unstructured populations in continuous time with periodic attractors of fixed period length, where the periodic behavior is due to external forcing. Within these conditions, our treatment is general. We provide a coherent theoretical framework for defining measures of species similarity and niche. Our main conclusion is that all factors that function to regulate population growth may be considered as separate regulating factors for each moment of time. In particular, a single resource becomes a resource continuum, along which species may segregate in the same manner as along classical resource continua. Therefore, we provide a mathematical underpinning for considering fluctuation-mediated coexistence as temporal niche segregation.     

Global realized niche divergence in the African clawed frog Xenopus laevis

Although of crucial importance for invasion biology and impact assessments of climate change, it remains widely unknown how species cope with and adapt to environmental conditions beyond their currently realized climatic niches (i.e., those climatic conditions existing populations are exposed to). The African clawed frog Xenopus laevis, native to southern Africa, has established numerous invasive populations on multiple continents making it a pertinent model organism to study environmental niche dynamics. In this study, we assess whether the realized niches of the invasive populations in Europe, South, and North America represent subsets of the species’ realized niche in its native distributional range or if niche shifts are traceable. If shifts are traceable, we ask whether the realized niches of invasive populations still contain signatures of the niche of source populations what could indicate local adaptations. Univariate comparisons among bioclimatic conditions at native and invaded ranges revealed the invasive populations to be nested within the variable range of the native population. However, at the same time, invasive populations are well differentiated in multidimensional niche space as quantified via n‐dimensional hypervolumes. The most deviant invasive population are those from Europe. Our results suggest varying degrees of realized niche shifts, which are mainly driven by temperature related variables. The crosswise projection of the hypervolumes that were trained in invaded ranges revealed the south‐western Cape region as likely area of origin for all invasive populations, which is largely congruent with DNA sequence data and suggests a gradual exploration of novel climate space in invasive populations.     

Sexual Segregation in Juvenile New Zealand Sea Lion Foraging Ranges: Implications for Intraspecific Competition,Population Dynamics and Conservation

Sexual segregation (sex differences in spatial organisation and resource use) is observed in a large range of taxa. Investigating causes for sexual segregation is vital for understanding population dynamics and has important conservation implications, as sex differences in foraging ecology may affect vulnerability to area-specific human activities. Although behavioural ecologists have proposed numerous hypotheses for this phenomenon, the underlying causes of sexual segregation are poorly understood. We examined the size-dimorphism and niche divergence hypotheses as potential explanations for sexual segregation in the New Zealand (NZ) sea lion (Phocarctos hookeri), a nationally critical, declining species impacted by trawl fisheries. We used satellite telemetry and linear mixed effects models to investigate sex differences in the foraging ranges of juvenile NZ sea lions. Male trip distances and durations were almost twice as long as female trips, with males foraging over the Auckland Island shelf and in further locations than females. Sex was the most important variable in trip distance, maximum distance travelled from study site, foraging cycle duration and percent time at sea whereas mass and age had small effects on these characteristics. Our findings support the predictions of the niche divergence hypothesis, which suggests that sexual segregation acts to decrease intraspecific resource competition. As a consequence of sexual segregation in foraging ranges, female foraging grounds had proportionally double the overlap with fisheries operations than males. This distribution exposes female juvenile NZ sea lions to a greater risk of resource competition and bycatch from fisheries than males, which can result in higher female mortality. Such sex-biased mortality could impact population dynamics, because female population decline can lead to decreased population fecundity. Thus, effective conservation and management strategies must take into account sex differences in foraging behaviour, as well as differential threat-risk to external impacts such as fisheries bycatch.     

Potential mechanisms of coexistence in closely related forbs

The stable coexistence of very similar species has perplexed ecologists for decades and has been central to the development of coexistence theory. According to modern coexistence theory, species can coexist stably (i.e. persist indefinitely with no long‐term density trends) as long as species' niche differences exceed competitive ability differences, even if these differences are very small. Recent studies have directly quantified niche and competitive ability differences in experimental communities at small spatial scales, but provide limited information about stable coexistence across spatial scales in heterogeneous natural communities. In this study, we use experimental and observational approaches to explore evidence for niche and competitive ability differences between two closely related, ecologically similar and widely coexisting annual forbs: Trachymene cyanopetala and T. ornata. We experimentally tested for stabilizing niche differences and competitive ability differences between these species by manipulating species' frequencies, under both well‐watered and water‐stressed conditions. We considered these experimental results in light of extensive field observations to explore evidence of niche segregation at a range of spatial scales. We found little evidence of intra‐specific stabilization or competitive ability differences in laboratory experiments while observational studies suggested niche segregation across pollinator assemblages and small‐scale microclimate heterogeneity. Though we did not quantify long‐term stabilization of coexisting populations of these species, results are consistent with expectations for stable coexistence of similar species via a spatial storage effect allowing niche differences to overcome even small (to absent) competitive ability differences.     

Resource partitioning among competing species—A coevolutionary approach

A reasonably general theory for predicting the outcome of coevolution among interacting species is developed. It is applied to a model for resource partitioning among competing species.Current theory for resource partitioning is based on derivations of a “limiting similarity”—i.e., a limit to how similar competitors can be to one another consistent with coexistence. This theory presumes there is a mechanism, perhaps invasion and extinction, which causes competitors to attain the limiting similarity. The view taken in this paper is that partitioning is an evolutionary compromise between pressures for character displacement and disadvantages inherent in the shift to different resource types.A set of principles is offered for the evolution of the parameters in ecological models. (1) For single population models natural selection causes the parameters ultimately to assume those values which produce the highest equilibrium population size. (2) For models of interacting populations, but without interspecific frequency-dependence, natural selection causes the parameters to assume values which produce either the highest or lowest equilibrium population size for any species depending on the sign of the “feedback” in the community obtained by deleting that species. (3) For models of interacting populations with interspecific frequency dependence natural selection leads to parameter values which produce intermediate equilibrium population sizes. A function called the conditional equilibrium population size is introduced. Provided (a) the mean fitness is a maximum in each species at a stable coevolutionary equilibrium and (b) there is negative density-dependence in each species then natural selection causes the parameters to assume values which produce the highest conditional equilibrium population size for each species.These coevolutionary principles, applied to a model for resource partitioning, entail that the niche separation between species relative to given niche widths, increases with the variety of available resources and decreases with the number of competing populations. Also, the evolution of character displacement between two species does not proceed far enough to maximize the equilibrium population sizes of the species involved. These results imply that the relationship between the niche overlap (of nearest neighbors) and species diversity is qualitatively different depending on whether the variety of resources at any place covaries with the species diversity there. Without covariation niche overlap increases with species diversity; with covariation overlap may decrease with species diversity. This study provides the beginning of a theory for the convergent evolution of community structure.     

Short-and long term niche segregation and individual specialization of brown trout (Salmo trutta) in species poor Faroese lakes

Trophic niche divergence is considered to be a major process by which species coexistence is facilitated. When studying niche segregation in lake ecosystems, we tend to view the niche on a one-dimensional pelagic-littoral axis. In reality, however, the niche use may be more complex and individual fidelity to a niche may be variable both between and within populations. In order to study this complexity, relative simple systems with few species are needed. In this paper, we study how competitor presence affects the resource use of brown trout (Salmo trutta) in 11 species-poor Faroese lakes by comparing relative abundance, stable isotope ratios and diet in multiple habitats. In the presence of three-spined sticklebacks (Gasterosteus aculeatus), a higher proportion of the trout population was found in the pelagic habitat, and trout in general relied on a more pelagic diet base as compared to trout living in allopatry or in sympatry with Arctic charr (Salvelinus alpinus). Diet analyses revealed, however, that niche-segregation may be more complex than described on a one-dimensional pelagic-littoral axis. Trout from both littoral and offshore benthic habitats had in the presence of sticklebacks a less benthic diet as compared to trout living in allopatry or in sympatry with charr. Furthermore, we found individual habitat specialization between littoral/benthic and pelagic trout in deep lakes. Hence, our findings indicate that for trout populations interspecific competition can drive shifts in both habitat and niche use, but at the same time they illustrate the complexity of the ecological niche in freshwater ecosystems.     

Coexistence in a fluctuating environment by the effect of relative nonlinearity: A minimal model

The minimal model of the “relative nonlinearity” type fluctuation-maintained coexistence is investigated. The competing populations are affected by an environmental white noise. With quadratic density dependence, the long-term growth rates of the populations are determined by the average and the variance of the (fluctuating) total density. At most two species can coexist on these two “regulating” variables; competitive exclusion would ensue in a constant environment. A numerical study of the expected time until extinction of any of the two species reveals that the criterion of mutual invasibility predicts the parameter range of long-term coexistence correctly in the limit of zero extinction threshold. However, any extinction threshold consistent with a realistic population size will allow only short-term coexistence. Therefore, our simulations question the biological relevance of mutual invasibility, as a sufficient condition of coexistence, for large density fluctuations. We calculate the average and the variance of the fluctuating density of the coexisting populations analytically via the moment-closure approximation; the results are reasonably close to the simulated behavior. Based on this treatment, robustness of coexistence is studied in the limit of infinite population size. We interpret the results of this analysis in the context of necessity of niche segregation with respect to the regulating variables using a framework theory published earlier.     

Environmental stability increases relative individual specialisation across populations of an aquatic top predator

The concept of the niche has long been a central pillar in ecological theory, with a traditional focus on quantifying niches at the species or population level. However, the importance of individual‐level niche variation is increasingly being recognised, with a strong focus on individual specialisation. While examples illustrating the contribution of the individual niche to whole population niche structure are accumulating rapidly, surprisingly little is known about the conditions that shape the differences between these two potentially divergent components. Though theory predicts that stability should influence the extent of such intra‐specific specialisation, we know of no previous study that has investigated its role in individual specialisation, and the differentiation between individual‐ and population niches. Here, we studied the diet of individuals from multiple populations of an aquatic top‐predator, Salmo trutta, inhabiting contrasting stable, groundwater fed and unstable, surface water fed pre‐alpine streams. Based on stomach content analysis, we found that individuals living in stable environments displayed a higher degree of specialisation than those in unstable environments, with the between‐individual component of niche width being approximately twice as high in the former. We subsequently validated these results by evidence gained from stable isotope analysis of muscle tissue. As such, we reveal that environmental stability can significantly influence individual niches within populations, leading to increased specialisation.     

Chromosomal regions associated with segregation distortion in maize

Segregation distortion skews the genotypic frequencies from their Mendelian expectations. Our objectives in this study were to assess the frequency of occurrence of segregation distortion in maize, identify chromosomal regions consistently associated with segregation distortion, and examine the effects of gametophytic factors on linkage mapping. We constructed a simple sequence repeat (SSR) linkage map for a LH200/LH216 F₂Syn3 (i.e., random-mated three times) population, and compared the segregation distortion in this map with the segregation distortion in three published linkage maps. Among 1,820 codominant markers across the four mapping populations, 301 (17%) showed segregation distortion (P < 0.05). The frequency of markers showing segregation distortion ranged from 19% in the Tx303/CO159 mapping population to 36% in the B73/Mo17 mapping population. A positive relationship was found between the number of meioses and the frequency of segregation distortion detected in a population. On a given chromosome, nearly all of the markers showing segregation distortion favored the allele from the same parent. A total of 18 chromosomal regions on the ten maize chromosomes were associated with segregation distortion. The consistent location of these chromosomal regions in four populations suggested the presence of segregation distortion regions (SDRs). Three known gametophytic factors are possible genetic causes of these SDRs. As shown in previous research, segregation distortion does not affect the estimate of map distance when only one gametophytic factor is present in an SDR.     

On population abundance and niche structure

Recent published evidence indicates a negative correlation between density of populations and the distance of their environments to a suitably defined ‘niche centroid’. This empirical observation lacks theoretical grounds. We provide a theoretical underpinning for the empirical relationship between population density and position in niche space, and use this framework to understand the circumstances under which the relationship will fail. We propose a metapopulation model for the area of distribution, as a system of ordinary differential equations coupled with a dispersal kernel. We present an analytical approximation to the solution of the system as well as R code to solve the full model numerically. We use this tool to analyze various scenarios and assumptions. General and realistic demographic assumptions imply a good correlation between position in niche space and population abundance. Factors that modify this correlation are: transitory states, a heterogeneous spatial structure of suitability, and Allee effects. We also explain why the raw output of the niche modeling algorithm MaxEnt is not a good predictor of environmental suitability. Our results elucidate the empirical results for spatial patterns of population size in niche terms, and provide a theoretical basis for a structured theory of the niche.     

MULTIDIMENSIONAL ANALYSIS OF RESOURCE UTILIZATION IN ASSEMBLAGES OF RANGELAND GRASSHOPPERS (ORTHOPTERA: ACRIDIDAE)

Abstract  A study was conducted in a typical steppe area in central Inner Mongolia to determine resource utilization in time, space, and food by grasshopper assemblages. Pattern of use for these resources was analyzed from three vegetation types by examining species-specific niche breadths, overlaps and partitions of resource utilization as well as population sizes. Popular niche indices and the principal components analysis (PCA) procedure were used to indicate the interrelations among grasshopper species. In the heterogeneous grassland environments resulting from livestock grazing, eleven grasshopper species were categorized respectively based on the 3-dimensional niche segregation and overlap degree. Population sizes were determined by the calorific values of their realized population biomass. Comparison in niche breadth displayed that species which had a broad niche along one dimension at least had a narrow niche along another one. There were sufficient differences between species for overall overlap associated with resource use to explain coexistence in the assemblages by resource segregation. Distinct rule of niche complementarity in overlap was not found. Evidence from this study implied that the species-specific use of resource may be due primarily to grasshopper adaptive differentiation and to coevolutionary interactions between grasshopper and plant rather than interspecific competition among grasshopper species.     

草原蝗虫种团资源利用的多维分析(直翅目:蝗科)(英文)

本文研究了内蒙古典型草原蝗虫在时间、空间和食物资源利用方面的特点。对于这些资源利用的格局是通过对存在于三种类型植被中蝗虫种的生态位宽度、资源利用的分化和重叠以及每种蝗虫的种群大小来分析的。常用的生态位指数和主成份分析技术用来阐明蝗虫种间的关系。在放牧形成的异质性草原环境中,11种蝗虫根据它们在三维生态位方面的分化和重叠程度被划分成数个种组。种群的大小是根据种群实际生物量所含热能值来确定的。生态位宽度比较说明,在某一维生态位宽的种,在另一维上必定变窄。生态位重叠的差异说明共存的蝗虫种在资源利用上的分化。生态位重叠的补偿规律在本项研究中并不明显。本项研究结果说明,蝗虫种资源利用的分化主要归因于蝗虫的适应性分化和蝗虫——植物协同进化的相互作用关系,而不是蝗虫种间竞争所造成的。     

Genetic linkage map of Coffea canephora: effect of segregation distortion and analysis of recombination rate in male and female meioses.

Two complementary segregating plant populations of Coffea canephora were produced from the same clone. One population (DH) comprised 92 doubled haploids derived from female gametes, while the other population (TC) was a test cross consisting of 44 individuals derived from male gametes. Based on the DH population, a genetic linkage map comprising 160 loci was constructed. Eleven linkage groups that putatively correspond to the 11 gametic chromosomes of C. canephora were identified. The mapped loci included more than 40 specific sequence-tagged site markers, either single-copy RFLP probes or microsatellites, that could serve as standard landmarks in coffee-genome analyses. Furthermore, comparisons for segregation distortion and recombination frequency between the two populations were performed. Although segregation distortions were observed in both populations, the frequency of loci exhibiting a very pronounced degree of distortion was especially high in the DH population. This observation is consistent with the hypothesis of strong zygotic selection among the DH population. The recombination frequencies in both populations were found to be almost indistinguishable. These results offer evidence in favour of the lack of significant sex differences in recombination in C. canephora.     

NICHE DIMENSIONALITY AND THE GENETICS OF ECOLOGICAL SPECIATION

Niche dimensionality is suggested to be a key determinant of ecological speciation (“multifarious selection” hypothesis), but genetic aspects of this process have not been investigated theoretically. We use Fisher's geometrical model to study how niche dimensionality influences the mean fitness of hybrids formed upon secondary contact between populations adapting in allopatry. Gaussian selection for an optimum generates two forms of reproductive isolation (RI): an extrinsic component due to maladaptation of the mean phenotype, and an intrinsic variance load resulting from what we term transgressive incompatibilities between mutations fixed in different populations. We show that after adaptation to a new environment, RI increases with (1) the mean initial maladaptation of diverging population, and (2) niche dimensionality, which increases the phenotypic variability of fixed mutations. Under mutation selection drift equilibrium in a constant environment, RI accumulates steadily with time, at a rate that also increases with niche dimensionality. A similar pattern can be produced by successive shifts in the optimum phenotype. Niche dimensionality thus has an effect per se on postzygotic isolation, beyond putative indirect effects (stronger selection, more genes). Our mechanism is consistent with empirical evidence about transgressive segregation in crosses between divergent populations, and with patterns of accumulation of RI with time in many taxa.     

Effects of missing marker and segregation distortion on QTL mapping in F2 populations

Missing marker and segregation distortion are commonly encountered in actual quantitative trait locus (QTL) mapping populations. Our objective in this study was to investigate the impact of the two factors on QTL mapping through computer simulations. Results indicate that detection power decreases with increasing levels of missing markers, and the false discovery rate increases. Missing markers have greater effects on smaller effect QTL and smaller size populations. The effect of missing markers can be quantified by a population with a reduced size similar to the marker missing rate. As for segregation distortion, if the distorted marker is not closely linked with any QTL, it will not have significant impact on QTL mapping; otherwise, the impact of the distortion will depend on the degree of dominance of QTL, frequencies of the three marker types, the linkage distance between the distorted marker and QTL, and the mapping population size. Sometimes, the distortion can result in a higher genetic variance than that of non-distortion, and therefore benefits the detection of linked QTL. A formula of the ratio of genetic variance explained by QTL under distortion and non-distortion was given in this study, so as to easily determine whether the segregation distortion marker (SDM) increases or decreases the QTL detection power. The effect of SDM decreases rapidly as its linkage relationship with QTL becomes looser. In general, distorted markers will not have a great effect on the position and effect estimations of QTL, and their effects can be ignored in large-size mapping populations.     

The effect of population structure on the adaptive radiation of microbial populations evolving in spatially structured environments

Spatial structure is thought to be an important factor influencing the emergence and maintenance of genetic diversity. Previous studies have demonstrated that environmental heterogeneity, provided by spatial structure, leads to adaptive radiation of populations. In the present study, we investigate not only the impact of environmental heterogeneity on adaptive radiation, but also of population fragmentation and niche construction. Replicate populations founded by a single genotype of Escherichia coli were allowed to evolve for 900 generations by serial transfer in either a homogeneous environment, or a spatially structured environment that was either kept intact or destroyed with each daily transfer. Only populations evolving in the structured environment with intact population structure diversified: clones are significantly divergent in sugar catabolism, and show frequency-dependent fitness interactions indicative of stable coexistence. These findings demonstrate an important role for population fragmentation, a consequence of population structure in spatially structured environments, on the diversification of populations.