The age structure of populations of Saccharomyces cerevisiae

A discrete deterministic model is described for the growth of an age-structured population of yeast, Saccharomyces cerevisiae, incorporating recent information on the asymmetry of cell division and control of the cell cycle in this species. Solutions are obtained for the age structure of the population at equilibrium, and for the equilibrium distribution of relative frequency of cells through the cell cycle. The model is applied to experimental data on the changing age structure of nonequilibrium populations of yeast. The model predicts well both the transient behavior and the equilibrium structure of such populations. It is shown that the asymmetry of cell division explains (1) the excess of newly formed daughter cells in the population as compared to the frequency of older cells and (2) the damped oscillations in the frequencies of cells of different ages as demographic equilibrium is approached.     

Transient population dynamics impede restoration and may promote ecosystem transformation after disturbance

The apparent failure of ecosystems to recover from increasingly widespread disturbance is a global concern. Despite growing focus on factors inhibiting resilience and restoration, we still know very little about how demographic and population processes influence recovery. Using inverse and forward demographic modelling of 531 post‐fire sagebrush populations across the western US, we show that demographic processes during recovery from seeds do not initially lead to population growth but rather to years of population decline, low density, and risk of extirpation after disturbance and restoration, even at sites with potential to support long‐term, stable populations. Changes in population structure, and resulting transient population dynamics, lead to a > 50% decline in population growth rate after disturbance and significant reductions in population density. Our results indicate that demographic processes influence the recovery of ecosystems from disturbance and that demographic analyses can be used by resource managers to anticipate ecological transformation risk.     

Unexplained variability among spatial replicates in transient elasticity: implications for evolutionary ecology and management of invasive species

Understanding actual and potential selection on traits of invasive species requires an assessment of the sources of variation in demographic rates. While some of this variation is assignable to environmental, biotic or historical factors, unexplained demographic variation also may play an important role. Even when sites and populations are chosen as replicates, the residual variation in demographic rates can lead to unexplained divergence of asymptotic and transient population dynamics. This kind of divergence could be important for understanding long- and short- term differences among populations of invasive species, but little is known about it. We investigated the demography of a small invasive tree Psidium cattleianum Sabine in the rainforest of Hawaiʻi at four sites chosen for their ecological similarity. Specifically, we parameterized and analyzed integral projection models (IPM) to investigate projected variability among replicate populations in: (1) total population size and annual per capita population growth rate during the transient and asymptotic periods; (2) population structure initially and asymptotically; (3) three key parameters that characterize transient dynamics (the weighted distance of the structure at each time step from the asymptotic structure, the strength of the sub-dominant relative to the dominant dynamics, and inherent cyclicity in the subdominant); and (4) proportional sensitivity (elasticity) of population growth rates (both asymptotic and transient) to perturbations of various components of the life cycle. We found substantial variability among replicate populations in all these aspects of the dynamics. We discuss potential consequences of variability across ecologically similar sites for management and evolutionary ecology in the exotic range of invasive species.     

Biochemical kinetics in changing volumes

The need of taking into account the change of compartment volume when developing chemical kinetics analysis inside the living cell is discussed. Literature models of a single enzymatic Michaelis-Menten process, glycolytic oscillations, and mitotic cyclin oscillations were tested with appropriate theoretical extension in the direction of volume modification allowance. Linear and exponential type of volume increase regimes were compared. Due to the above, in a growing cell damping of the amplitude, phase shift, and time pattern deformation of the metabolic rhythms considered were detected, depending on the volume change character. The perfomed computer simulations allow us to conclude that evolution of the cell volume can be an essential factor of the chemical kinetics in a growing cell. The phenomenon of additional metabolite oscillations caused by the periodic cell growth and division was theoretically predicted and mathematically described. Also, the hypothesis of the periodized state in the growing cell as the generalization of the steady-state was formulated.     

ODE,RDE and SDE models of cell cycle dynamics and clustering in yeast

Biologists have long observed periodic-like oxygen consumption oscillations in yeast populations under certain conditions, and several unsatisfactory explanations for this phenomenon have been proposed. These ‘autonomous oscillations’ have often appeared with periods that are nearly integer divisors of the calculated doubling time of the culture. We hypothesize that these oscillations could be caused by a form of cell cycle synchronization that we call clustering. We develop some novel ordinary differential equation models of the cell cycle. For these models, and for random and stochastic perturbations, we give both rigorous proofs and simulations showing that both positive and negative growth rate feedback within the cell cycle are possible agents that can cause clustering of populations within the cell cycle. It occurs for a variety of models and for a broad selection of parameter values. These results suggest that the clustering phenomenon is robust and is likely to be observed in nature. Since there are necessarily an integer number of clusters, clustering would lead to periodic-like behaviour with periods that are nearly integer divisors of the period of the cell cycle. Related experiments have shown conclusively that cell cycle clustering occurs in some oscillating yeast cultures.     

Estimating population trends using population viability analyses for the conservation ofCapra pyrenaica

Large herbivore populations can suffer important oscillations with considerable effects on ecosystem functions and services, yet our capacity to predict population fate is limited and conditional upon the availability of data. This study investigated the interannual variation in the growth rate of populations ofCapra pyrenaica Schinz, 1838, and its extinction risk by comparing the dynamics of populations that were stable for more than two decades (Gredos and Tortosa-Beceite), populations that had increased recently (Tejeda-Almijara), and populations that were in decline (Cazorla-Segura) or extinct (the Pyrenees population; hereafter, bucardo). To estimate quasi-extinction threshold assessments (50% of population extinct in this study), which have implications for the conservation of the species, we used empirical data and the predictions derived from several theoretical models. The results indicate that when variance of log population growth rate reaches a specific threshold, the probability of quasi-extinction increased drastically. ForC. pyrenaica, we recommend keeping population variance < 0.05, which will reduce the likelihood that the irruptive oscillations caused by environmental and demographic stochasticity will put the population at risk. Models to predict the dynamics ofC. pyrenaica populations should incorporate temporal stochasticity because, in this study, it strongly increased the likelihood that a population declined.     

Developmental trap or demographic bonanza? Opposing consequences of earlier phenology in a changing climate for a multivoltine butterfly

A rapidly changing climate has the potential to interfere with the timing of environmental cues that ectothermic organisms rely on to initiate and regulate life history events. Short‐lived ectotherms that exhibit plasticity in their life history could increase the number of generations per year under warming climate. If many individuals successfully complete an additional generation, the population experiences an additional opportunity to grow, and a warming climate could lead to a demographic bonanza. However, these plastic responses could become maladaptive in temperate regions, where a warmer climate could trigger a developmental pathway that cannot be completed within the growing season, referred to as a developmental trap. Here we incorporated detailed demography into commonly used photothermal models to evaluate these demographic consequences of phenological shifts due to a warming climate on the formerly widespread, multivoltine butterfly (Pieris oleracea). Using species‐specific temperature‐ and photoperiod‐sensitive vital rates, we estimated the number of generations per year and population growth rate over the set of climate conditions experienced during the past 38 years. We predicted that populations in the southern portion of its range have added a fourth generation in recent years, resulting in higher annual population growth rates (demographic bonanzas). We predicted that populations in the Northeast United States have experienced developmental traps, where increases in the thermal window initially caused mortality of the final generation and reduced growth rates. These populations may recover if more growing degree days are added to the year. Our framework for incorporating detailed demography into commonly used photothermal models demonstrates the importance of using both demography and phenology to predict consequences of phenological shifts.     

Does climate variability influence the demography of wild primates? Evidence from long‐term life‐history data in seven species

Earth's rapidly changing climate creates a growing need to understand how demographic processes in natural populations are affected by climate variability, particularly among organisms threatened by extinction. Long‐term, large‐scale, and cross‐taxon studies of vital rate variation in relation to climate variability can be particularly valuable because they can reveal environmental drivers that affect multiple species over extensive regions. Few such data exist for animals with slow life histories, particularly in the tropics, where climate variation over large‐scale space is asynchronous. As our closest relatives, nonhuman primates are especially valuable as a resource to understand the roles of climate variability and climate change in human evolutionary history. Here, we provide the first comprehensive investigation of vital rate variation in relation to climate variability among wild primates. We ask whether primates are sensitive to global changes that are universal (e.g., higher temperature, large‐scale climate oscillations) or whether they are more sensitive to global change effects that are local (e.g., more rain in some places), which would complicate predictions of how primates in general will respond to climate change. To address these questions, we use a database of long‐term life‐history data for natural populations of seven primate species that have been studied for 29–52 years to investigate associations between vital rate variation, local climate variability, and global climate oscillations. Associations between vital rates and climate variability varied among species and depended on the time windows considered, highlighting the importance of temporal scale in detection of such effects. We found strong climate signals in the fertility rates of three species. However, survival, which has a greater impact on population growth, was little affected by climate variability. Thus, we found evidence for demographic buffering of life histories, but also evidence of mechanisms by which climate change could affect the fates of wild primates.     

Epidemiological effects of seasonal oscillations in birth rates

Seasonal oscillations in birth rates are ubiquitous in human populations. These oscillations might play an important role in infectious disease dynamics because they induce seasonal variation in the number of susceptible individuals that enter populations. We incorporate seasonality of birth rate into the standard, deterministic susceptible-infectious-recovered (SIR) and susceptible-exposed-infectious-recovered (SEIR) epidemic models and identify parameter regions in which birth seasonality can be expected to have observable epidemiological effects. The SIR and SEIR models yield similar results if the infectious period in the SIR model is compared with the "infected period" (the sum of the latent and infectious periods) in the SEIR model. For extremely transmissible pathogens, large amplitude birth seasonality can induce resonant oscillations in disease incidence, bifurcations to stable multi-year epidemic cycles, and hysteresis. Typical childhood infectious diseases are not sufficiently transmissible for their asymptotic dynamics to be likely to exhibit such behaviour. However, we show that fold and period-doubling bifurcations generically occur within regions of parameter space where transients are phase-locked onto cycles resembling the limit cycles beyond the bifurcations, and that these phase-locking regions extend to arbitrarily small amplitude of seasonality of birth rates. Consequently, significant epidemiological effects of birth seasonality may occur in practice in the form of transient dynamics that are sustained by demographic stochasticity.     

Population responses to perturbations: the importance of trait-based analysis illustrated through a microcosm experiment

Environmental change continually perturbs populations from a stable state, leading to transient dynamics that can last multiple generations. Several long-term studies have reported changes in trait distributions along with demographic response to environmental change. Here we conducted an experimental study on soil mites and investigated the interaction between demography and an individual trait over a period of nonstationary dynamics. By following individual fates and body sizes at each life-history stage, we investigated how body size and population density influenced demographic rates. By comparing the ability of two alternative approaches, a matrix projection model and an integral projection model, we investigated whether consideration of trait-based demography enhances our ability to predict transient dynamics. By utilizing a prospective perturbation analysis, we addressed which stage-specific demographic or trait-transition rate had the greatest influence on population dynamics. Both body size and population density had important effects on most rates; however, these effects differed substantially among life-history stages. Considering the observed trait-demography relationships resulted in better predictions of a population's response to perturbations, which highlights the role of phenotypic plasticity in transient dynamics. Although the perturbation analyses provided comparable predictions of stage-specific elasticities between the matrix and integral projection models, the order of importance of the life-history stages differed between the two analyses. In conclusion, we demonstrate how a trait-based demographic approach provides further insight into transient population dynamics.     

Feedback control of a competitive mixed-culture system

Three feedback strategies for the on-line control of cell densities in a mixed-culture system have been examined. A competitive mixed-culture system of Candida utilis and Corynebacterium glutamicum grown on glucose as the limiting carbon source was modeled using Monod growth kinetics. First-order time constants were added to simulate transient growth effects. Multivariable feedback control of cell densities by manipulation of substrate feed and dilution rate was investigated. Feedback strategies directed to minimizing control interactions were found to be superior to classical feedback. Transients in the growth-rate response produced oscillations in cell density and required retuning of control constants. The relative time constants of the two species were important, with the largest oscillations resulting when the faster growing organism had the faster time constant.     

Simply the best: the transition of savanna saplings to trees

Tree cover in savannas is determined as much by disturbances from fire and herbivory as by rainfall and soil resources. Fire especially acts to limit tree cover via a demographic bottleneck, limiting the recruitment of tree saplings to adults. Because sapling growth rates determine rates of sapling to tree recruitment, predicting changes in tree cover requires data on sapling growth rates, commonly expressed as population means. Here, we discuss the variability in sapling growth rates in Acacia populations in a savanna in Hluhluwe iMfolozi Park in South Africa. Saplings growing at mean rates under typical fire regimes in African savannas would likely never escape the fire‐trap to become adults. Only the fastest growing saplings could grow above the flame zone between fires. We suggest that maximum growth rates are more ecologically relevant than mean growth rates in natural populations and experiments. Maximum growth rates are better than mean growth rates as predictors of sapling release within species, as shown here, and probably of which species are likely ‘winners’ in savanna tree communities.     

When stable-stage equilibrium is unlikely: integrating transient population dynamics improves asymptotic methods

Background and Aims Evaluation of population projection matrices (PPMs) that are focused on asymptotically based properties of populations is a commonly used approach to evaluate projected dynamics of managed populations. Recently, a set of tools for evaluating the properties of transient dynamics has been expanded to evaluate PPMs and to consider the dynamics of populations prior to attaining the stable-stage distribution, a state that may never be achieved in disturbed or otherwise ephemeral habitats or persistently small populations. This study re-evaluates data for a tropical orchid and examines the value of including such analyses in an integrative approach.Methods Six small populations of Lepanthes rubripetala were used as a model system and the R software package popdemo was used to produce estimates of the indices for the asymptotic growth rate (lambda), sensitivities, reactivity, first-time step attenuation, maximum amplification, maximum attenuation, maximal inertia and maximal attenuation. The response in lambda to perturbations of demographic parameters using transfer functions and multiple perturbations on growth, stasis and fecundity were also determined. The results were compared with previously published asymptotic indices.Key Results It was found that combining asymptotic and transient dynamics expands the understanding of possible population changes. Comparison of the predicted density from reactivity and first-time step attenuation with the observed change in population size in two orchid populations showed that the observed density was within the predicted range. However, transfer function analysis suggests that the traditional approach of measuring perturbation of growth rates and persistence (inertia) may be misleading and is likely to result in erroneous management decisions.Conclusions Based on the results, an integrative approach is recommended using traditional PPMs (asymptotic processes) with an evaluation of the diversity of dynamics that may arise when populations are not at a stable-stage distribution (transient processes). This method is preferable for designing rapid and efficient interventions after disturbances, and for developing strategies to establish new populations.     

Phylogeography and ecological niche modelling in Eugenia uniflora (Myrtaceae) suggest distinct vegetational responses to climate change between the southern and the northern Atlantic Forest

In this study, we evaluate phylogeographic patterns and predictions of ecological niche modelling (ENM) for Eugenia uniflora (Myrtaceae), a widely distributed taxon in the Atlantic forest domain, to understand the effect of past climatic oscillations on the demographic history of this species. An analysis of phylogeographic population structure and demography was conducted on E. uniflora from 46 localities in natural environments across the distribution range of the species based on three plastid markers. ENM was also performed to predict suitable environments and areas of dramatic decrease in future suitability for the species under distinct representative concentration pathways (RCPs). Eugenia uniflora exhibited higher haplotype and nucleotide diversity in the southern part of its distribution than in the northern part. Two divergent lineages were revealed in the phylogenetic analysis of haplotypes, with an estimated divergence at c. 4.9 Mya. The populations in the northern and central regions of the range probably experienced population growth, whereas populations in the southern region are marked by historical demographic stability. ENM results indicate that the distribution of E. uniflora was fragmented in cool periods and was broader and more connected during warm periods during Pleistocene. The results suggest distinct evolutionary histories in southern to northern populations, indicating region‐specific responses to changes.     

Effective size of fluctuating populations with two sexes and overlapping generations

We derive formulas that can be applied to estimate the effective population size N(e) for organisms with two sexes reproducing once a year and having constant adult mean vital rates independent of age. Temporal fluctuations in population size are generated by demographic and environmental stochasticity. For populations with even sex ratio at birth, no deterministic population growth and identical mean vital rates for both sexes, the key parameter determining N(e) is simply the mean value of the demographic variance for males and females considered separately. In this case Crow and Kimura's generalization of Wright's formula for N(e) with two sexes, in terms of the effective population sizes for each sex, is applicable even for fluctuating populations with different stochasticity in vital rates for males and females. If the mean vital rates are different for the sexes then a simple linear combination of the demographic variances determines N(e), further extending Wright's formula. For long-lived species an expression is derived for N(e) involving the generation times for both sexes. In the general case with nonzero population growth and uneven sex ratio of newborns, we use the model to investigate numerically the effects of different population parameters on N(e). We also estimate the ratio of effective to actual population size in six populations of house sparrows on islands off the coast of northern Norway. This ratio showed large interisland variation because of demographic differences among the populations. Finally, we calculate how N(e) in a growing house sparrow population will change over time.     

Ionic and osmotic disruptions of the lily pollen tube oscillator: testing proposed models

Two mechanisms have been proposed as the primary control of oscillating tip growth in Lilium longiflorum Thunb. pollen tubes: changes in cell wall strength (Holdaway-Clarke et al. 1997) or alternatively, changes in turgor pressure (Messerli et al. 2000). Here we have modified the ionic and osmotic concentrations of the growth medium to test predictions derived from both models. Raising the [Ca2+]o tenfold above normal reduced the amplitude of the [Ca2+]i oscillations and growth oscillations while it raised the basal [Ca2+]i and growth rate such that the average growth rate did not change. Raising the [H+] of the growth medium tenfold reversibly decreased and sometimes eliminated the [Ca2+]i and growth oscillations without changing the average growth rate. Lowering the [H+] tenfold led to irregular frequency and amplitude [Ca2+]i oscillations, reduced the average growth rate of tubes and led to cell bursting in 33% of tubes. Addition of 50 mM H+ buffer, MES, to prevent pH changes in the cell wall increased the period, amplitude and duration of both [Ca2+]i and growth oscillations. Changing the [K+]o did not markedly effect [Ca2+]i oscillations. Reducing the osmolarity of the medium led to transient large-amplitude [Ca2+]i and growth oscillations while reducing large-amplitude oscillations over long periods. In many different conditions under which growth still occurs, lily pollen tubes maintain growth oscillations, albeit with modified frequency, amplitude and duration. We conclude that modifications to both proposed models are necessary to explain oscillating growth in this system.     

Mechanisms of radiation in a bat group from the genus Pipistrellus inferred by phylogeography, demography and population genetics

Here, we present a study of the Pipistrellus pipistrellus species complex, a highly diversified bat group with a radiation centre in the Mediterranean biodiversity hotspot. The study sample comprised 583 animals from 118 localities representatively covering the bats' range in the western Palearctic. We used fast-evolving markers (the mitochondrial D-loop sequence and 11 nuclear microsatellites) to describe the phylogeography, demography and population structure of this model taxon and address details of its diversification. The overall pattern within this group includes a mosaic of phylogenetically basal, often morphologically distant, relatively small and mostly allopatric demes in the Mediterranean Basin, as well as two sympatric sibling species in the large continental part of the range. The southern populations exhibit constant size, whereas northern populations show a demographic trend of growth associated with range expansion during the Pleistocene climate oscillations. There is evidence of isolation by distance and female philopatry in P. pipistrellus sensu stricto. Although the northern populations are reproductively isolated, we detected introgression events among several Mediterranean lineages. This pattern implies incomplete establishment of reproductive isolating mechanisms in these populations as well as the existence of a past reinforcement stage in the continental siblings. The occurrence of reticulations in the radiation centre among morphologically and ecologically derived relict demes suggests that adaptive unequal gene exchange within hybridizing populations could play a role in speciation and adaptive radiation within this group.     

Modeling the synchronization of yeast respiratory oscillations

The budding yeast Saccharomyces cerevisiae exhibits autonomous oscillations when grown aerobically in continuous culture with ethanol as the primary carbon source. A single cell model that includes the sulfate assimilation and ethanol degradation pathways recently has been developed to study these respiratory oscillations. We utilize an extended version of this single cell model to construct large cell ensembles for investigation of a proposed synchronization mechanism involving hydrogen sulfide. Ensembles with as many as 10,000 cells are used to simulate population synchronization and to compute transient number distributions from asynchronous initial cell states. Random perturbations in intracellular kinetic parameters are introduced to study the synchronization of single cells with small variations in their unsynchronized oscillation periods. The cell population model is shown to be consistent with available experimental data and to provide insights into the regulatory mechanisms responsible for the synchronization of yeast metabolic oscillations.     

Morphologically-structured models of growing budding yeast populations

It has been well recognized that many key aspects of cell cycle regulation are encoded into the size distributions of growing budding yeast populations due to the tight coupling between cell growth and cell division present in this organism. Several attempts have been made to model the cell size distribution of growing yeast populations in order to obtain insight on the underlying control mechanisms, but most were based on the age structure of asymmetrically dividing populations. Here we propose a new framework that couples a morphologically-structured representation of the population with population balance theory to formulate a dynamic model for the size distribution of growing yeast populations. An advantage of the presented framework is that it allows derivation of simpler models that are directly identifiable from experiments. We show how such models can be derived from the general framework and demonstrate their utility in analyzing yeast population data. Finally, by employing a recently proposed numerical scheme, we proceed to integrate numerically the full distributed model to provide predictions of dynamics of the cell size structure of growing yeast populations.     

Population Dynamics of the Endangered, Long-Lived Perennial Species, Ligularia sibirica

Ligularia sibirica is a relict wetland perennial plant species of the Czech and Slovak Republic. Explaining variation in population growth rate and identifying the causes of that variation is important for effective protection of such an endangered species. Matrix models based on four years of data of 11 populations were used to identify the pattern of variation in the demographic vital rates of this species, and to examine the causes of the variation such as population size and habitat type. Further, the matrix model was used to determine the population growth rate, longevity and risk of extinction of each population and to identify the specific vital rates that most affect population growth rate. The results showed that population growth rates were significantly different between years and populations. Temporal variation was mostly due to variable survival of adult individuals, while spatial variation was mainly driven by fertility of one small currently expanding population. Further, most studied populations of L. sibirica are performing well and only those growing in nitrogen-rich habitats have a high extinction risk. The results also indicate that all populations have low adult mortality, long-lived individuals (61.3?years on average) and some populations also show features of remnant populations (i.e., the persistence of populations in severe conditions in spite of no reproduction). Our results imply that detailed demographic data are needed to understand the long-term prospects of these populations. These data may serve as an early warning system for this species long before an obvious decline occurs in the populations.