Density-dependent vital rates and their population dynamic consequences

We explore a set of simple, nonlinear, two-stage models that allow us to compare the effects of density dependence on population dynamics among different kinds of life cycles. We characterize the behavior of these models in terms of their equilibria, bifurcations, and nonlinear dynamics, for a wide range of parameters. Our analyses lead to several generalizations about the effects of life history and density dependence on population dynamics. Among these are: (1) iteroparous life histories are more likely to be stable than semelparous life histories; (2) an increase in juvenile survivorship tends to be stabilizing; (3) density-dependent adult survival cannot control population growth when reproductive output is high; (4) density-dependent reproduction is more likely to cause chaotic dynamics than density dependence in other vital rates; and (5) changes in development rate have only small effects on bifurcation patterns. Received: 12 April 1999 / Published online: 3 August 2000     

Multiple attractors in stage-structured population models with birth pulses

In most models of population dynamics, increases in population due to birth are assumed to be time-independent, but many species reproduce only during a single period of the year. A single species stage-structured model with density-dependent maturation rate and birth pulse is formulated. Using the discrete dynamical system determined by its Poincaré map, we report a detailed study of the various dynamics, including (a) existence and stability of nonnegative equilibria, (b) nonunique dynamics, meaning that several attractors coexist, (c) basins of attraction (defined as the set of the initial conditions leading to a certain type of attractor), (d) supertransients, and (e) chaotic attractors. The occurrence of these complex dynamic behaviour is related to the fact that minor changes in parameter or initial values can strikingly change the dynamic behaviours of system. Further, it is shown that periodic birth pulse, in effect, provides a natural period or cyclicity that allows multiple oscillatory solutions in the continuous dynamical systems.     

Sex in space: population dynamic consequences

Sex, so important in the reproduction of bigametic species, is nonetheless often ignored in explorations of the dynamics of populations. Using a growth model of dispersal-coupled populations we can keep track of fluctuations in numbers of females and males. The sexes may differ from each other in their ability to disperse and their sensitivity to population density. As a further complication, the breeding system is either monogamous or polygamous. We use the harmonic mean birth function to account for sex-ratio-dependent population growth in a Moran–Ricker population renewal process. Incorporating the spatial dimension stabilizes the dynamics of populations with monogamy as the breeding system, but does not stabilize the population dynamics of polygamous species. Most notably, in populations coupled with dispersal, where the sexes differ in their dispersal ability there are rarely stable and equal sex ratios. Rather, a two-point cycle, four-point cycle and eventually complex behaviour of sex-ratio dynamics will emerge with increasing birth rates. Monogamy often leads to less noisy sex-ratio dynamics than polygamy. In our model, the sex-ratio dynamics of coupled populations differ from those of an isolated population system, where a stable 50:50 sex ratio is achievable with equal density-dependence costs for females and males. When sexes match in their dispersal ability, population dynamics and sex-ratio dynamics of coupled populations collapse to those of isolated populations.     

Density-dependent dispersal and spatial population dynamics

The synchronization of the dynamics of spatially subdivided populations is of both fundamental and applied interest in population biology. Based on theoretical studies, dispersal movements have been inferred to be one of the most general causes of population synchrony, yet no empirical study has mapped distance-dependent estimates of movement rates on the actual pattern of synchrony in species that are known to exhibit population synchrony. Northern vole and lemming species are particularly well-known for their spatially synchronized population dynamics. Here, we use results from an experimental study to demonstrate that tundra vole dispersal movements did not act to synchronize population dynamics in fragmented habitats. In contrast to the constant dispersal rate assumed in earlier theoretical studies, the tundra vole, and many other species, exhibit negative density-dependent dispersal. Simulations of a simple mathematical model, parametrized on the basis of our experimental data, verify the empirical results, namely that the observed negative density-dependent dispersal did not have a significant synchronizing effect.     

Migratory divides and their consequences for dispersal, population size and parasite-host interactions

Populations of migratory birds differ in their direction of migration with neighbouring populations often migrating in divergent directions separated by migratory divides. A total of 26% of 103 passerine bird species in Europe had migratory divides that were located disproportionately often along a longitudinal gradient in Central Europe, consistent with the assumption of a Quaternary glacial origin of such divides in the Iberian and Balkan peninsulas followed by recolonization. Given that studies have shown significant genetic differentiation and reduced gene flow across migratory divides, we hypothesized that an absence of migratory divides would result in elevated rates of gene flow and hence a reduced level of local adaptation. In a comparative study, species with migratory divides had larger population sizes and population densities and longer dispersal distances than species without migratory divides. Species with migratory divides tended to be habitat generalists. Bird species with migratory divides had higher richness of blood parasites and higher growth rates of Staphylococcus on their eggs during the incubation period. There was weaker cell-mediated immunity in adults and stronger cell lysis in species with migratory divides. These findings may suggest that migratory divides constitute barriers to dispersal with consequences for ecology and evolution of distributions, population sizes, habitats and parasite-host interactions. They also suggest that migratory divides may play a role in local adaptation in host-parasite interactions.     

Density-dependent dispersal and spatial distribution of a population

Many models have been proposed to suggest that animal dispersal enhances stability of an ecological system. However, little attention has been paid on the property of a boundary and on the size of a region. In this paper, we will consider the models proposed by Gurney & Nisbet (1975), from those points of view. We will show that, if a population is dispersing in a highly density-dependent manner, a stationary distribution which does not depend on boundary conditions is established in a finite region by interactions between the population and a heterogeneous environment. We will also show that, even when a population is confined in a habitat with a limited size a population dispersing density-dependently can establish a stationary distribution, whereas a population dispersing randomly either goes to extinction or grows explosively.     

Worms and germs: the population dynamic consequences of microparasite-macroparasite co-infection

Hosts are typically simultaneously co-infected by a variety of microparasites (e.g. viruses and bacteria) and macroparasites (e.g. parasitic helminths). However, the population dynamical consequences of such co-infections and the implications for the effectiveness of imposed control programmes have yet to be fully realised. Mathematical models may provide an important framework for exploring such issues and have proved invaluable in helping to understand the factors affecting the epidemiology of single parasitic infections. Here the first population dynamic model of microparasite-macroparasite co-infection is presented and used to explore how co-infection alters the predictions of the existing single-species models. It is shown that incorporating an additional parasite species into existing models can greatly stabilise them, due to the combined density-dependent impacts on the host population, but co-infection can also restrict the region of parameter space where each species could persist alone. Overall it is concluded that the dynamic feedback between host, microparasite and macroparasite means that it is difficult to appreciate the factors affecting parasite persistence and predict the effectiveness of control by just studying one component in isolation.     

A note on dynamics of population with history-dependent birth rate

A model for the dynamics of a single-species population whose birth rate depends on densities of previous generations is introduced. A difference equation formulation is proposed and the solutions classified for the various parameter values. Data from an experimental population of mice growing in limited space is cited and compared with the model predictions.     

Approximations and their consequences for dynamic modelling of signal transduction pathways

Signal transduction is the process by which the cell converts one kind of signal or stimulus into another. This involves a sequence of biochemical reactions, carried out by proteins. The dynamic response of complex cell signalling networks can be modelled and simulated in the framework of chemical kinetics. The mathematical formulation of chemical kinetics results in a system of coupled differential equations. Simplifications can arise through assumptions and approximations. The paper provides a critical discussion of frequently employed approximations in dynamic modelling of signal transduction pathways. We discuss the requirements for conservation laws, steady state approximations, and the neglect of components. We show how these approximations simplify the mathematical treatment of biochemical networks but we also demonstrate differences between the complete system and its approximations with respect to the transient and steady state behavior.     

Density-dependent migration and human population structure in historical Massachusetts

Studies of population structure often focus on the effects of population size and migration rates on genetic variation. Few studies, however, have investigated the relationship between these two factors. The purpose of this paper is to determine the extent to which migration (and gene flow) is density-dependent (that is, affected by population size) for populations in historical Massachusetts. Data from 4,859 marriage records were analyzed from four populations in north-central Massachusetts during the time period 1741 to 1849. These data were placed into 29 samples defined in terms of population and time cohort. Within each cohort the overall exogamy rate was computed along with three estimates of gene flow based on marital migration: local migration (k), long-distance migration (m), and effective migration rate (me). Three samples show unusually low rates that reflect the history of settlement. Regression analyses were used with the remaining samples, and they show nonlinear density-dependent migration that is unrelated to temporal trends. Migration is highest in samples with small population sizes (less than 800) and large population sizes (greater than 1,600). Migration is lowest in medium-sized populations. Two processes are suggested to explain this curvilinear relationship of migration and population size. In small populations, the lack of suitable potential mates and/or availability of settled land leads to an increase in migration into the population. As population size increases, this migration decreases. After populations reach a certain size, migration increases again, most likely reflecting the economic pull of larger populations. These patterns could act to enhance, or counter, genetic drift, depending on the direction of density dependence.     

Density-dependent growth rate in an age-structured population: a field study on stream-dwelling brown trout Salmo trutta

A field experiment during autumn, winter and spring was performed in a small stream on the west coast of Sweden, aiming to examine the direct and indirect consequences of density-dependent intercohort competition in brown trout Salmo trutta . Individual growth rate, recapture rate and site fidelity were used as response variables in the young-of-the-year (YOY) age class, experiencing two different treatments: presence or absence of yearlings and over-yearlings (age ≥ 1+ year individuals). YOY individuals in stream sections with reduced density of age ≥ 1+ year individuals grew significantly faster than individuals experiencing natural cohort structure. In the latter, growth rate was negatively correlated with density and biomass of age ≥ 1+ year individuals, which may induce indirect effects on year-class strength through, for example, reduced fecundity and survival. Movement of YOY individuals and turnover rate ( i.e. proportion of untagged individuals) were used to demonstrate potential effects of intercohort competition on site fidelity. While YOY movement was remarkably restricted (83% recaptured within 50 m from the release points), turnover rate was higher in sections with reduced density of age ≥1+ year individuals, suggesting that reduced density of age ≥1+ year individuals may have released favourable microhabitats.     

湖北石首散养麋鹿种群的调控机制:密度制约下种群产仔率下降

为了探讨散养麋鹿(Elaphurus davidianus)种群密度制约的调控机制,1993–2013年,我们以湖北石首麋鹿国家级自然保护区围栏内的散养麋鹿种群为研究对象,采用分区直接计数法统计麋鹿种群数量,计算种群增长率、死亡率、存活率和产仔率等参数,对麋鹿种群的发展是否受到密度制约影响以及作用于哪些种群参数进行了研究。结果表明:石首麋鹿保护区散养麋鹿种群的发展过程可分为5个阶段,分别为稳定增长阶段(1993–1997年)、快速增长阶段(1998–2006年)、缓慢增长阶段(2007–2009年)、迅速下降阶段(2010年)和种群恢复阶段(2011–2013年)。1993–1997年,种群增长率为16.60±3.10(%),而死亡率为4.34±0.93(%);1998–2006年,种群增长率增加为28.98±3.62(%),死亡率为4.35±2.31(%);2007–2009年,种群的增长率下降为7.36±1.64(%),而死亡率增加为6.32±2.85(%);2010年种群暴发传染性疾病,数量急剧下降;2011–2013年,种群增长率增加为10.95±4.04(%),而死亡率下降为5.70±2.03(%)。Pearson相关性检验结果显示:种群密度与增长率呈极显著负相关(r=–0.612,P=0.0050.01),与产仔率也呈极显著的负相关(r=–0.902,P=0.0000.01),与死亡率的相关性不显著(r=0.425,P=0.0620.05)。独立样本t检验结果显示,2010年之前(1993–2009年)和之后(2011–2013年)的成、幼体存活率分别为95.40±1.56(%)、95.79±1.80(%)和96.67±0.92(%)、94.04±2.20(%),两者差异不显著(成体:t=–0.503,df=8,P=0.6280.05;幼体:t=0.558,df=8,P=0.5920.05),这说明密度制约因素未对石首麋鹿保护区散放麋鹿种群的存活率产生明显影响。从2003年起,种群受到密度制约机制的调控,主要表现为产仔率下降,同时也受到了洪水、疾病和人类干扰等环境因素的影响。针对目前石首麋鹿保护区散养麋鹿种群面临的密度制约和环境容纳量等问题,我们提出了应对策略。     

Homoplasy and mutation model at microsatellite loci and their consequences for population genetics analysis

Homoplasy has recently attracted the attention of population geneticists, as a consequence of the popularity of highly variable stepwise mutating markers such as microsatellites. Microsatellite alleles generally refer to DNA fragments of different size (electromorphs). Electromorphs are identical in state (i.e. have identical size), but are not necessarily identical by descent due to convergent mutation(s). Homoplasy occurring at microsatellites is thus referred to as size homoplasy. Using new analytical developments and computer simulations, we first evaluate the effect of the mutation rate, the mutation model, the effective population size and the time of divergence between populations on size homoplasy at the within and between population levels. We then review the few experimental studies that used various molecular techniques to detect size homoplasious events at some microsatellite loci. The relationship between this molecularly accessible size homoplasy size and the actual amount of size homoplasy is not trivial, the former being considerably influenced by the molecular structure of microsatellite core sequences. In a third section, we show that homoplasy at microsatellite electromorphs does not represent a significant problem for many types of population genetics analyses realized by molecular ecologists, the large amount of variability at microsatellite loci often compensating for their homoplasious evolution. The situations where size homoplasy may be more problematic involve high mutation rates and large population sizes together with strong allele size constraints.     

Mothers' birth weight and survival of their offspring: population based study.

OBJECTIVE: To test the hypothesis that a baby''s survival is related to the mother''s birth weight. DESIGN: Population based dataset for two generations. SETTING: Population registry in Norway. SUBJECTS: All birth records for women born in Norway since 1967 were linked to births during 1981-94, thereby forming 105104 mother-offspring units. MAIN OUTCOME MEASURES: Perinatal mortality specific for weight for offspring in groups of maternal birth weight (with 500 g categories in both). RESULTS: A mother''s birth weight was strongly associated with the weight of her baby. Maternal birth weight was associated with perinatal survival of her baby only for mothers with birth weights under 2000 g. These mothers were more likely to lose a baby in the perinatal period (odds ratio 2.3, 95% confidence interval 1.4 to 3.7). Among mothers with a birth weight over 2000 g there was no overall association between mother''s weight and infant survival. There was, however, a strong interaction between mother''s birth weight, infant birth weight, and infant survival. Mortality among small babies was much higher for those whose mothers had been large at birth. For example, babies weighing 2500-2999 g had a threefold higher mortality if their mother''s birth weight had been high (> or = 4000 g) than if the mother had been small (2500-2999 g). CONCLUSION: Mothers who weighed less than 2000 g at birth have a higher risk of losing their own babies. For mothers who weighed > or = 2000 g their birth weight provides a benchmark for judging the growth of their offspring. Babies who are small relative to their mother''s birth weight are at increased risk of mortality.     

Effect of birth litter size, birth parity number, growth rate, backfat thickness and age at first mating of gilts on their reproductive performance as sows

The present study was performed to evaluate retrospectively the influence of birth litter size, birth parity number, performance test parameters (growth rate from birth to 100kg body weight and backfat thickness at 100kg body weight) and age at first mating (AFM) of gilts on their reproductive performance as sows. Traits analysed included remating rate in gilts (RRG), litter size, weaning-to-first-service interval (WSI), remating rate in sows and farrowing rate (FR). Data were collected from 11 Swedish Landrace (L) and 8 Swedish Yorkshire (Y) nucleus herds and included 20712 farrowing records from sow parities 1-5. Sows that farrowed for the first time during 1993-1997, having complete records of performance test and AFM, were followed up to investigate their subsequent reproductive performance until their last farrowing in 1999. Analysis of variance and multiple regression were applied to continuous data. Logistic regression was applied to categorical data. The analyses were based on the same animals and the records were split into six groups of females, i.e. gilts, primiparous sows, and sows in parities 2-5, respectively. Each additional piglet in the litter in which the gilt was born was associated with an increase of her own litter size of between 0.07 and 0.1 piglets per litter (P<0.001). Gilts born from sow parity 1 had a longer WSI as primiparous sows compared with gilts born from sow parity 4 (0.3 days; P<0.05) or parity 5 (0.4 days; P<0.01). Gilts with a higher growth rate of up to 100kg body weight had a larger litter size (all parities 1-5; P<0.05), shorter WSI (all parities 1-5; P<0.05) and higher FR (parities 2 and 5; P<0.05) than gilts with a lower growth rate. Gilts with a high backfat thickness at 100kg body weight had a shorter WSI as primiparous sows (P<0.001) compared with low backfat gilts, and 0.1 piglets per litter more as second parity sows (P<0.01). A 10 day increase in AFM resulted in an increase in litter size of about 0.1 piglet for primiparous sows (P<0.001) and a decrease (P<0.05) for sow parities 4 and 5.