On synchronization in semelparous populations

Synchronization, i.e., convergence towards a dynamical state where the whole population is in one age class, is a characteristic feature of some population models with semelparity. We prove some rigorous results on this, for a simple class of nonlinear one- population models with age structure and semelparity: (i) the survival probabilities are assumed constant, and (ii) only the last age class is reproducing (semelparity), with fecundity decreasing with total population. For this model we prove: (a) The synchronized, or Single Year Class (SYC), dynamical state is always attracting. (b) The coexistence equilibrium is often unstable; we state and prove simple results on this. (c) We describe dynamical states with some, but not all, age classes populated, which we call Multiple Year Class (MYC) patterns, and we prove results extending (a) and (b) into these patterns.Acknowledgement Boris Kruglikov contributed the nonlinear part of the formulation as well as the proof of Theorem 1. The authors are grateful for critical and constructive comments by N. Davydova and O. Diekmann. E.M. is also grateful for discussions with Marius Overholt concerning problems of proving Theorem 2.     

On the estimation of robustness and filtering ability of dynamic biochemical networks under process delays, internal parametric perturbations and external disturbances

Inherently, biochemical regulatory networks suffer from process delays, internal parametrical perturbations as well as external disturbances. Robustness is the property to maintain the functions of intracellular biochemical regulatory networks despite these perturbations. In this study, system and signal processing theories are employed for measurement of robust stability and filtering ability of linear and nonlinear time-delay biochemical regulatory networks. First, based on Lyapunov stability theory, the robust stability of biochemical network is measured for the tolerance of additional process delays and additive internal parameter fluctuations. Then the filtering ability of attenuating additive external disturbances is estimated for time-delay biochemical regulatory networks. In order to overcome the difficulty of solving the Hamilton Jacobi inequality (HJI), the global linearization technique is employed to simplify the measurement procedure by a simple linear matrix inequality (LMI) method. Finally, an example is given in silico to illustrate how to measure the robust stability and filtering ability of a nonlinear time-delay perturbative biochemical network. This robust stability and filtering ability measurement for biochemical network has potential application to synthetic biology, gene therapy and drug design.     

Age-specific, density-dependent and environment-based mortality of a short-lived perennial herb

Density-independent and density-dependent processes affect plant mortality. Although less well understood, age-specific mortality can also play an important role in plant mortality. The goal of this study was to analyse several factors accounting for mortality in the Mediterranean short-lived perennial herb Lobularia maritima. We followed three cohorts of plants (from emergence to death) during 4 years in field conditions. We collected data on plant mortality of the effect of biotic agents (moth larvae and mycoplasma-like organisms, MLOs) and environmental variables. We also estimated density-dependent relationships affecting the fate of seedlings and adults. Results show that cohorts differed in their survival curves and ageing significantly increased mortality risk. Seedling mortality was density-dependent whereas adult mortality was not affected by density. MLO infection led to higher plant mortality whereas moth larvae attack did not affect plant mortality. In general, seedlings and adult plants experienced the highest mortality events in summer. We found, however, weak relationships between weather records and plant mortality. Age and size structures were not correlated. Overall, this study provides a comprehensive review of age-specific, density-dependent and density-independent factors that account for mortality of L. maritima plants throughout their life cycle in field conditions, highlighting the fact that age is an important factor in determining plant population dynamics.     

Optimal resource allocation to seeds and vegetative propagules under density-dependent regulation in Syneilesis palmata (Compositae)

Syneilesis palmata reproduces by both seeds and vegetative propagules (short rhizomes). The latter result in the production of new plants that are larger in size and hence have a higher survival probability and a higher growth rate than seeds. A previous study predicted that the optimal reproductive strategy, in terms of maximizing population growth rate (a fitness measure under no density regulations), was pure vegetative reproduction. However, high resource investment to vegetative propagules can cause local crowding resulting in reduced demographic performances of the plants, because the vegetative propagules of Syneilesis are produced close to one another. We examined, in this situation, the impact of allocating a certain proportion of reproductive resource to seeds with relatively greater capacity for dispersal. We simulated dynamics of hypothetical Syneilesis populations with various reproductive resource allocation balances (from pure seed to pure vegetative reproduction), using a density-dependent matrix model. In the model, it was assumed that plants from vegetative propagules experienced density-dependent reduction in their survival probabilities, but this was not the case for plants originating from seeds. Each allocation strategy was evaluated based on an equilibrium population density, a fitness measure under density-dependent regulations. The optimal reproductive strategy predicted was pure vegetative reproduction. Unrealistic conditions were required for seed reproduction to be favoured, such as the production of seeds one hundred times the normal number per unit resource investment. However, the conditions were fairly relaxed compared with those required in the model where no density effects were incorporated. This indicates that escape from local crowding is likely to be one of the roles of seed production in Syneilesis.     

The invisible niche: Weakly density-dependent mortality and the coexistence of species

Weakly density-dependent effects, characterized by fractional scaling exponents close to one, are rarely studied in the ecological literature. Here, we consider the effect of an additional weakly density-dependent term on a simple competition model. Our investigation reveals that weak density-dependence opens up an “invisible niche”. This niche does not constitute a new mechanism for coexistence, but is a previously unexplored consequence of known mechanisms. In the invisible niche a weaker competitor can survive at very low density. Coexistence thus requires large habitat size. Such niches, if found in nature, would have a direct impact on species-area laws and species-abundance curves and should therefore receive more attention.     

Effect of the early-life nutritional environment on fecundity and fertility of mammals

The early-life developmental environment is instrumental in shaping our overall adult health and well-being. Early-life diet and endocrine exposure may independently, or in concert with our genetic constitution, induce a pathophysiological process that amplifies with age and leads to premature morbidity and mortality. Recently, this has become known as ‘programming’ but is akin to ‘maternal effects’ described for many years in the biological sciences and is defined as any influence that acts during critical developmental windows to induce long-term changes in the organisms'' phenotype. To date, such delayed maternal effects have largely been characterized in terms of susceptibility to cardiovascular or metabolic disease. Here, we review evidence from experimental animal species, non-human primates and man for an effect of the early-life nutritional environment on adult fecundity and fertility. In addition, using a database of pedigree sheep, we also specifically test the hypothesis that being born small for gestational age with or without post-natal growth acceleration directly programmes fertility. We conclude that there is a lack of compelling evidence to suggest pre-natal undernutrition may directly reduce adult fecundity and fertility, but may exert some effects secondarily via an increased incidence of ‘metabolic syndrome’. Possible effects of being born relatively large on subsequent fecundity and fertility warrant further investigation.     

Entropy and convergence in dynamics and demography

Demographic dynamics is formally equivalent to the dynamics of a Markov chain, as is true of some nonlinear dynamical systems. Convergence to demographic equilibrium can be studied in terms of convergence in the Markov chain. Tuljapurkar (1982) showed that population entropy (Kolmogorov-Sinai entropy) provides information on the rate of this convergence. This paper begins by considering finite state Markov chains, providing elementary proofs of the relationship between convergence rate and entropy, and discusses in detail the uses and limitations of entropy as a convergence measure; these results also apply to Markovian dynamical systems. Next, new qualitative and quantitative arguments are used to discuss the demographic meaning of entropy. An exact relationship is established giving population entropy in terms of the eigenvalues of the Leslie matrix characteristic equation. Finally, the significance of imprimitive and periodic limits is discussed in relation to population entropy.     

Temporal changes in the strength of density-dependent mortality and growth in intertidal barnacles

1. In demographically open marine systems, the extent to which density-dependent processes in the benthic adult phase are required for population persistence is unclear. At one extreme, represented by the recruitment limitation hypothesis, larval supply may be insufficient for the total population size to reach a carrying capacity and density-independent mortality predominates. At the opposite extreme, populations are saturated and density-dependent mortality is sufficiently strong to reshape patterns established at settlement. 2. We examined temporal variation in the way density-independent and density-dependent mortality interact in a typical sessile marine benthic invertebrate, the acorn barnacle Semibalanus balanoides (L.), over a 2-year period. 3. Recruitment was manipulated at two high recruitment sites in north Wales, UK to produce recruit densities covering the range naturally found in this species. Following manipulation, fixed quadrats were monitored using digital photography and temporal changes in mortality and growth rate were examined. 4. Over a 2-year period there was a clear, spatially consistent, over-compensatory relationship between the density of recruits and adult abundance indicating strong density-dependent mortality. The strength of density dependence intensified with increasing recruitment. 5. Density-dependent mortality did not operate consistently over the study period. It only operated in the early part of the benthic phase, but the pattern of adult abundance generated was maintained throughout the whole 2-year period. Thus, early life-history processes dictated adult population abundance and dynamics. 6. Examination of the natural recruitment regime in the area of study indicated that both positive and negative effects of recruitment will occur over scales varying from kilometres to metres.     

一类两种群均有收获率捕食系统的细焦点与极限环

研究一类具有HollingⅡ类功能反应且两种群均为非常数收获率的捕食系统,其中食饵种群具有非线性密度制约.利用微分方程定性与稳定性理论及分支理论,得到系统平衡点的性态及极限环存在与否的充分条件,利用Hopf分支理论得到存到多个极限环的充分条件.     

甘油生物歧化非线性动力系统的平衡点及其稳定性分析

针对甘油生物歧化为1,3-丙二醇过程的酶催化动力系统,利用符号化实根隔离法求解系统的平衡点,验证了系统的多稳态现象,利用微分方程稳定性理论,分析了平衡点的稳定性,并结合数值结果讨论了系统的多态现象．本文的结果可为微生物发酵甘油生产1,3-丙二醇的实验优化参数设计提供参考．     

高寒草甸生态系统牲畜种群结构和动态

本文用Leslie矩阵模型研究了高寒草甸生态系统牲畜种群结构及动态。模型考虑了更加精确的年龄组转移关系,出栏率是种群波动的主要因子。目前,牲畜种群结构不合理,种群数量不能保持平衡。     

具有状态反馈收获项的第Ⅲ类功能性反应模型的分支与极限环

研究了带有功能性反应捕食项的捕食与食饵模型在线性状态反馈收获的作用下所呈现的复杂性质,其中包括正平衡点的存在与唯一性、平衡点的渐近稳定性、产生分支的原因与极限坏的存在性等,研究结果表明：通过调整反馈项的系数,可以改变该系统正平衡点的稳定性,从而使系统或是稳定在正平衡点处,或是在正平衡点处产生周期运动,本文的结果为研究再生性资源管理中的复杂性问题奠定了理论基础。     

Interactions between density-dependent processes, population dynamics and control of an invasive plant species, Tripleurospermum perforatum (scentless chamomile)

Tripleurospermum perforatum is an invasive weedy species which exhibits strong over-compensating density dependence. Interactions between density-dependent survival, probability of flowering and fecundity were modelled and their impact on the population dynamics were examined. When only fecundity was density-dependent, the dynamics were similar to those observed in the model containing all three density-dependent terms. Density-dependent survival was a stabilizing process when acting in combination with density-dependent fecundity and probability of flowering; removing density-dependent survival from the model produced two-point cycles. The addition of a seed bank was also stabilizing. Simulations of control strategies at different life-history stages indicated that full control would be difficult due to the strong over-compensating density dependence, with severe reductions in fecundity and late season survival necessary in order to reduce equilibrium seed density and biomass.     

Anti-mosquito antibodies and their effects on feeding, fecundity and mortality of Aedes aegypti

Anti-mosquito antibodies, produced in mice inoculated with mosquito homogenates or exposed to mosquito bites, reacted with a variety of mosquito antigens including muscle, gut, fat body and nervous tissue; those in anti-mosquito bite sera reacted solely with salivary glands. Mosquitoes fed on restrained immunized mice showed a significant increase in mortality correlated to both the titre and specificity of the anti-mosquito antibodies ingested. No changes in their fecundity or feeding success were noted. Mosquitoes exposed to unrestrained immunized mice or mosquito-bitten mice, however, showed a significant reduction in feeding success, possibly reflecting enhanced host grooming.     

A comparison of restricted selection index and linear programming in sire selection

Summary The objective of restricted selection index is to enhance genetic change in one trait while restricting to zero change in a second trait. Linear programming is another, yet conceptually different, technique to maximize one function while enforcing limits on others. The objective of this research was to compare restricted selection index and linear programming in ability to maximize performance in one trait while limiting change in a second trait to zero. Results of a numerical study demonstrate that linear programming is a more effective method to limit correlated response than restricted selection index. On average, both methods limited response in a correlated trait to zero. However, the squared deviation of actual response in the restricted trait from zero was smaller with linear programming than with restricted selection index. Response to selection in the unrestricted trait is greater with restricted selection index than with linear programming.     

Optimization of biochemical systems by linear programming and general mass action model representations

A new method is proposed for the optimization of biochemical systems. The method, based on the separation of the stoichiometric and kinetic aspects of the system, follows the general approach used in the previously presented indirect optimization method (IOM) developed within biochemical systems theory. It is called GMA-IOM because it makes use of the generalized mass action (GMA) as the model system representation form. The GMA representation avoids flux aggregation and thus prevents possible stoichiometric errors. The optimization of a system is used to illustrate and compare the features, advantages and shortcomings of both versions of the IOM method as a general strategy for designing improved microbial strains of biotechnological interest. Special attention has been paid to practical problems for the actual implementation of the new proposed strategy, such as the total protein content of the engineered strain or the deviation from the original steady state and its influence on cell viability.     

Population dynamics and density-dependent seasonal mortality indices of the tick Rhipicephalus appendiculatus in eastern and southern Africa

Abstract. Eight sets of previously published data on the seasonal abundance of the tick Rhipicephalus appendiculatus in Burundi, Uganda, Tanzania and Zimbabwe are analysed to yield seasonal mortality indices. Correlations between these indices and abiotic (climatic) and biotic (tick density) variables suggest that it is the stage from females to larvae that is most sensitive to adverse abiotic conditions, specifically low moisture availability. Mortality at the other stages of the tick's life cycle is strongly density-dependent. The precise nature of this density-dependence suggests that it may be caused by acquired resistance to ticks by cattle. Robust correlations between satellite-derived vegetation indices, climatic factors and mortality indices suggest that detailed climatic data, often unavailable, may be replaced by satellite data, now widely available, for use in modelling tick populations.     

Evolution,games theory and polyhedra

The problem of finding an Evolutionary Stable Strategy (ESS) for an animal species is defined. It is shown how such strategies are a subset of the equilibrium solutions for a particular non-zero sum game. These equilibrium solutions are then shown to arise from the vertices of a particular convex polyhedron. A method of finding these equilibrium solutions through the vertices and then the ESS solutions is given. This is illustrated by a number of numerical examples taken from the literature. Finally an alternative approach based on solving a Linear Complementarity Problem is discussed.