Resource competition in stage-structured populations

Two models are made to account for the dynamics of a consumer-resource system in which the consumers are divided into juveniles and adults. The resource grows logistically and a type II functional response is assumed for consumers. Resource levels determine fecundity and maturation rates in one model, and mortality rates in the other. The analysis of the models shows that the condition for establishment of consumers is that the product of per capita fecundity rate and maturation rates is higher than the product of juvenile and adult per capita decay rates at a resource level equal to its carrying capacity. This result imposes a minimal abundance of resource able to maintain the consumers. A second result shows an equilibrium stage structure, with a small instability when juveniles and adults mean saturation constants are different. The implications of these results for community dynamics are discussed.     

Alternative dynamical states in stage-structured consumer populations

The population dynamics of a consumer population with an internal structure is investigated. The population is divided into juvenile and adult individuals that consume different resources and do not interfere with each other. Over a broad range of external conditions (varying mortality and different resource levels), alternative stable states exist. These population states correspond to domination of juveniles and domination of adults, respectively. When mortality is varied, hysteresis between the alternative states only occurs if juveniles have more resources than adults. In the opposite case the juvenile-dominated state is stable for all values of mortality, but the adult-dominated state is not. When the population is modelled with more than one juvenile stage, the adult-dominated state becomes a periodic orbit due to a delay in the regulatory mechanism of the population dynamics. It is shown numerically that the stage-structured model converges to a model with continuous size structure for very large numbers of successive juvenile stages.     

Estimating growth and mortality in stage-structured populations

This paper presents a practical numerical method for separatingand estimating growth and mortality coefficients in stage- orsize-structured populations using only observations of the relativeor absolute abundance of each stage. The method involves writinga system of linear ordinary differential equations (ODEs) modellingthe rate of change of abundance. The solution of the differentialsystem can be numerically approximated using standard (e.g.sixth-order Runge-Kutta-Felhberg) methods. An optimization problemwhose solutions yield ‘optimal’ coefficients fora given model is formulated. The ODE numerical integration techniquecan then be employed to furnish required function and gradientinformation to the optimization algorithm. The data-fittingsoftware package ODRPACK is then successfully employed to estimateoptimal coefficients for the ODE population model. Simulationexperiments with four- and eight-stage model populations illustratethat the method results in the successful estimation of coefficientsof mortality and growth from abundance data.     

Persistence and spread of stage-structured populations in heterogeneous landscapes

Journal of Mathematical Biology - Conditions for population persistence in heterogeneous landscapes and formulas for population spread rates are important tools for conservation ecology and...     

Theorems on the invasion process in stage-structured populations with density-dependent dynamics

 Several theoretical results on evolution in stage-structured models with density-dependent dynamics are obtained. The first one concerns the invadable condition of mutant types when ‘density’ is considered as the weighted sum of the population densities at each stage. In the second and third results, it is shown that the invadability is equivalent to the increase of the weighted sum at equilibrium when certain conditions are satisfied. It is also shown that the sensitivity for the dominant eigenvalue is proportional to that for the weighted sum at equilibrium. Finally, a theorem on the coexistence of a wild and the mutant types is obtained and the condition for coexistence is discussed. A part of these results are the extended theorems of what Charlesworth (1971, 1980, 1994) has already obtained. Received: 26 October 1996     

Qualitative behavior of stage-structured populations: application to structural validation

 The transient behavior of a class of nonlinear differential systems representing stage-structured populations is studied. The qualitative dynamics are described in terms of succession of extrema for the state variables, or for the integrated difference between two trajectories. The rules giving the possibilities of extrema are derived, they characterize the classical stage-structured models. These rules can be compared with experiments to validate the structure of the model. An explanation for the disagreement of this transition scheme with some experiments could be an unexpected interaction with another variable. A new model taking the interaction into account thus engenders new transition rules, which are to be compared with experiments. These results are illustrated with experiments on copepods, showing how the qualitative experimental features can help the construction and the validation of the models. Received: 13 May 1996 / Revised version: 20 March 1998     

Thinking inside the box: community-level consequences of stage-structured populations

Ecologists have historically represented consumer-resource interactions with boxes and arrows. A key assumption of this conceptualization is that all individuals inside a box are functionally equivalent. Demographic stage structure, however, is a widespread source of heterogeneity inside the boxes. Synthesizing recent studies, we show that stage structure can modify the dynamics of consumer-resource communities owing to stage-related shifts in the nature and strength of interactions that occur within and between populations. As a consequence, stage structure can stabilize consumer-resource dynamics, create possibilities for alternative community states, modify conditions for coexistence of competitors, and alter the strength and direction of trophic cascades. Consideration of stage structure can thus lead to outcomes that are not expected based on unstructured approaches.     

Environmental fluctuations and the maintenance of genetic diversity in age or stage-structured populations

The ability of random fluctuations in selection to maintain genetic diversity is greatly increased when generations overlap. This result has been derived previously using genetic models with very special assumptions about the population age structure. Here we explore its robustness in more realistic population models, with very general age structure or physiological structure. For a range of genetic models (haploid, diploid, single and multilocus) we find that the condition for maintaining genetic diversity generalizes almost without change. Genetic diversity is maintained by selection if a product of the form (generation overlap)×(selection intensity)×(variability in the selection regime) is sufficiently large, where the generation overlap is measured in units of Fisher's reproductive value. This conclusion is based on a local evolutionary stability analysis, which differs from the standard “protected polymorphism” criterion for the maintenance of genetic diversity. Simulation results match the predictions from the local stability analysis, but not those from the protected polymorphism criterion. The condition obtained here for maintaining genetic diversity requires fitness fluctuations that are substantial but well within the range observed in many studies of natural populations.     

A method for the estimation of parameters for natural stage-structured populations

A relatively simple method is proposed for the estimation of parameters of stage-structured populations from sample data for situation where (a) unit time survival rates may vary with time, and (b) the distribution of entry times to stage 1 is too complicated to be fitted with a simple parametric model such as a normal or gamma distribution. The key aspects of this model are that the entry time distribution is approximated by an exponential function withp parameters, the unit time survival rates in stages are approximated by anr parameter exponential polynomial in the stage number, and the durations of stages are assumed to be the same for all individuals. The new method is applied to four Zooplankton data sets, with parametric bootstrapping used to assess the bias and variation in estimates. It is concluded that good estimates of demographic parameters from stagefrequency data from natural populations will usually only be possible if extra information such as the durations of stages is known.     

Colour of environmental noise affects the nonlinear dynamics of cycling, stage-structured populations

Populations fluctuate because of their internal dynamics, which can be nonlinear and stochastic, and in response to environmental variation. Theory predicts how the colour of environmental stochasticity affects population means, variances and correlations with the environment over time. The theory has not been tested for cycling populations, commonly observed in field systems. We applied noise of different colours to cycling laboratory beetle populations, holding other statistical properties of the noise fixed. Theory was largely validated, but failed to predict observations in sufficient detail. The main period of population cycling was shifted up to 33% by the colour of environmental stochasticity. Noise colour affected population means, variances and dominant periodicities differently for populations that cycled in different ways without noise. Our results show that changes in the colour of climatic variability, partly caused by humans, may affect the main periodicity of cycling populations, possibly impacting industry, pest management and conservation.     

Estimation of survival rate and extinction probability for stage-structured populations with overlapping life stages

The development of methods providing reliable estimates of demographic parameters (e.g., survival rates, fecundity) for wild populations is essential to better understand the ecology and conservation requirements of individual species. A number of methods exist for estimating the demographics of stage-structured populations, but inherent mathematical complexity often limits their uptake by conservation practitioners. Estimating survival rates for pond-breeding amphibians is further complicated by their complex migratory and reproductive behaviours, often resulting in nonobservable states and successive cohorts of eggs and tadpoles. Here we used comprehensive data on 11 distinct breeding toad populations (Bufo calamita) to clarify and assess the suitability of a relatively simple method [the Kiritani–Nakasuji–Manly (KNM) method] to estimate the survival rates of stage-structured populations with overlapping life stages. The study shows that the KNM method is robust and provides realistic estimates of amphibian egg and larval survival rates for species in which breeding can occur as a single pulse or over a period of several weeks. The study also provides estimates of fecundity for seven distinct toad populations and indicates that it is essential to use reliable estimates of fecundity to limit the risk of under- or overestimating the survival rates when using the KNM method. Survival and fecundity rates for B. calamita populations were then used to define population matrices and make a limited exploration of their growth and viability. The findings of the study recently led to the implementation of practical conservation measures at the sites where populations were most vulnerable to extinction.     

Evolution towards dioecy in heterostylous populations

The effective gender of a plant is defined as the proportion of the plant's genes that are transmitted through pollen (its maleness) or through ovules (its femaleness). Formulae are derived that enable the average effective gender of the morphs of a heterostylous population and the gender of individual plants to be estimated. Estimates require a knowledge of the morph ratio and the seed set that results in each morph from self-fertilization and from legitimate and illegitimate cross-fertilizations. If no illegitimate fertilizations occur, the average gender of the morphs can be estimated from their seed production alone; in this situation the average femaleness of one morph is exactly equal to the average maleness of the other morph. The average gender of long- and short-styled morphs is calculated for populations of fiveCordia species (Boraginaceae) from published data ofOpler & al. (1975). In two species, both morphs transmit their genes equally through pollen and ovules. In the other species, the long-styled morph acts predominantly (or in one species exclusively) as an ovule parent and the short-styled morph succeeds predominantly (or exclusively) as a pollen parent.The features of the evolutionary pathway from heterostyly to dioecy and the selective forces that may be responsible are outlined.     

Evolution of cross-feeding in microbial populations

Although limited by a single resource, microbial populations that grow for long periods in continuous culture (chemostat) frequently evolve stable polymorphisms. These polymorphisms may be maintained by cross-feeding, where one strain partially degrades the primary energy resource and excretes an intermediate that is used as an energy resource by a second strain. It is unclear what selective advantage cross-feeding strains have over a single competitor that completely degrades the primary resource. Here we show that cross-feeding may evolve in microbial populations as a consequence of the following optimization principles: the rate of ATP production is maximized, the concentration of enzymes of the pathway is minimized, and the concentration of intermediates of the pathway is minimized.     

Evolution of pleiotropic costs in experimental populations

The fitness of populations adapting to new environments is expected to decline in different environments, but empirical studies often do not lend support for such adaptation costs. We test the idea that the initial fitness of the selected populations in the environment where the cost is estimated is key for interpreting tests of ecological trade‐offs. We isolated single clones of the yeast Saccharomyces cerevisiae every ~250 generations from replicate experimental lineages that had been selected during 5000 generations in a glucose‐limited environment. We then selected these clones in a galactose‐limited environment for ~120 generations. Finally, we estimated single‐clone fitness in both environments, before and after selection on galactose. The pleiotropic effects on glucose of selection on galactose evolved from positive to negative as fitness in glucose increased, providing strong support for the importance of initial fitness for determining the sign and magnitude of pleiotropic effects. This demonstrates that the sign of pleiotropic effects for fitness following adaptation to a new environment can change during long‐term adaptation to an original environment. We also found no relationship between the size of the fitness changes in galactose and glucose, such that pleiotropic effects in glucose became relatively smaller as the sizes of direct effects on galactose increased.     

Evolution of beta-globin haplotypes in human populations

The beta-globin haplotypes of 852 chromosomes from 12 populations in the Asia-Pacific region are described. These data are combined with those from other populations in an investigation of the affinities of regional human populations. Both partial maximum-likelihood and distance Wagner methods indicate that Africans are the most divergent group, with the remaining populations branching in the following order: Australian Aborigines, Highland Melanesians, Lowland Melanesians, Indonesians and Micronesians, Polynesians, east Asians, Indians, and Europeans. This pattern of relationship is consistent with that indicated by other data. Analysis of the evolution and distribution of haplotype occurrence provides some limited support for an origin of modern humans in Africa. Otherwise, however, it was not useful in further elucidating the evolutionary history of human populations.