The interplay of sex ratio, male success and density-independent mortality affects population dynamics

Environmental constraints can limit a population to a certain size, which is usually called the carrying capacity of a habitat. Besides to this ‘external’ factor, which is mainly determined by the limitation of resources, we investigate here another set of population-intrinsic factors that can limit a population size significantly below the maximum sustainable size. Firstly, density-independent mortality is a prominent factor in all organisms that show age-related and/or accidental death. Secondly, in sexually reproducing organisms the sex ratio and the success of pairing is important for finding reproductive partners. Using a simple model, we demonstrate how sex ratio, mating success and gender-specific mortality can strongly affect the speed of population growth and the maximum population size. In addition, we demonstrate that density-independent mortality, which is often neglected in population models, adds a very important feature to the system: it strongly enhances the negative influence of unbiased sex ratios and inefficient pairing to the maximum sustainable population size. A decrease of the maximum population size significantly affects a population's survival chance in inter-specific competition. Thus, we conclude that the inclusion of density-independent mortality is crucial, especially for models of species that reproduce sexually. We show that density-independent mortality, together with biased sex ratios, can significantly lower the abilities of a population to survive in conditions of strong inter-specific competition and due to the Allee effect. We emphasize that population models should incorporate the sex ratio, male success and density-independent mortality to make plausible predictions of the population dynamics in a gender-structured population. We show that the population size is limited by these intrinsic factors. This is of high ecological significance, because it means that there will always be resources available in any habitat that allows other species (e.g., invaders) to use these resources and settle successfully, if they are sufficiently adapted.     

A survival-analysis-based simulation model for Russian wheat aphid population dynamics

A simulation model for Russian wheat aphid (RWA), Diuraphis noxia (Mordvilko), populations is built by integrating survival-analysis-based development and survivor functions and the same-shape reproduction distribution model in the framework of Leslie [Leslie, P.H., 1945. On the use of matrices in certain population mathematics. Biometrika 33, 183–212] matrix structure. Survival analysis is utilized to model both the development and survival of RWA populations, and the Cox (1972) proportional hazards model is fitted with the data sets from our laboratory observation of 1800 RWA individuals under 25 factorial combinations of five temperature regimes and five barley plant-growth stages. Rather than using simple age-specific survivor rates as in the traditional Leslie matrix, the survivor functions based on survival analysis describe age-specific, temperature and plant stage-dependent RWA survival probabilities. Similarly, a probability model from survival analysis to estimate the probability that an individual will reach mature adult stage is utilized to describe the development process; this makes the transition from nymphal stage to mature adult stage dependent on RWA age as well as temperature and plant-growth stage.Inspired by the same-shape distribution and rate-summation approach for modeling insect development, a similar approach for modeling insect reproduction under variable temperature is developed. This new same-shape reproduction distribution model incorporates individual variation in reproduction capability, as well as the effects of RWA age, temperature and plant-growth stage. Consequently, the same-shape reproduction distribution model replaces the simple age-specific fecundities in Leslie matrix model. To the best of our knowledge, this work is the first to introduce survival analysis to simulation modeling in entomology and ecology and also the first to integrate our newly developed same-shape reproduction distribution model into application.     

Modelling crayfish population dynamics using catch data: A size-structured model

In this study we explore a rather unique time series (1979–2002) of catch data of the crayfish Astacus astacus in Lake Steinsfjorden (SE Norway) in combination with temperature data and data on Canadian pondweed Elodea canadensis coverage. In 1977, E. canadensis was for the first time observed in the lake. Over the following years, the plant established dense covers over large parts of the shallow areas, excluding the crayfish from these areas and causing a sudden drop in population size. A size-structured model with bi-stability including a range of observed stage-specific life-cycle attributes (e.g. growth, fecundity, fertility, sex-ratio), population specific parameters and density-dependant (shelters, cannibalism, unspecified predators, competition between individuals, catch, number of traps) as well as density independent factors (temperature and Elodea coverage) were constructed to evaluate the various drivers for the population dynamics, and as a predictive tool for assessing the effects of future changes. Our model revealed that the decline primarily was due to density-dependant effect of the Elodea expansion with reduced number of hides and thus increased risk for predation and cannibalism, but also that temperature played an important role related to recruitment. The model should be relevant for crayfish stock management in general, and by demonstrating the major role of temperature, it is also relevant for predicting population responses under a changing climate. The model should also be applicable to other crustaceans and species with discrete growth and late maturation.     

Characterizing cumulative impacts using a brook trout population dynamics model

An individuals-based modelling framework is used to characterize the nature of exploitation and toxaphene stressors acting simultaneously on a population of brook trout (Salvelinus fontinalis) in terms of age 0 + and adult abundance, survivorship and population size-structure. A no-stressor control case was estimated against which exploitation-only, toxaphene-only and cumulative exploitation and toxaphene stressor cases were compared to determine the extent and significance of impacts. Single stressor case results were used to predict cumulative impacts by assuming additivity and predictions compared to modelled cumulative stressor results. Comparisons indicated the inadequacy of assuming additivity in predicting cumulative impacts. A factorial experimental design was used to estimate the size and significance of interactive effects. Effects are substantial and underscore the necessity of interpreting probable impacts of increases in a single stressor in conjunction with knowledge of other stressors acting on a population. A positive functional relationship between variability in population abundance and stress was estimated and is suggested as a potentially useful means of characterizing risks posed to populations by increases in, or additions to, population stressors. Multiple stressors were also demonstrated to effectively eliminate the significance of density-dependent mortality processes in determining age 0 + and adult abundance. Taken together, results indicate the inappropriateness of attempting to predict additional perturbation impacts without considering the sum of population stressors and their associated interactions.     

A model of nematode dynamics in the Westerschelde Estuary

We developed a time dynamic model to investigate the temporal dynamics of nematode community in the brackish zone of the Westerschelde Estuary. The biomass of four nematode feeding groups observed from March 1991 to February 1992 is used to calibrate the model. Using environmental data as the input, the model predicts the temporal modification and interrelation of four nematode feeding groups. Nematodes achieve a dominant position in the community because of their lower loss rate (in respiration, excretion and natural death). Predators which are deposit-feeding macrobenthos control the variations of dominant nematodes, such as omnivores and non-selective deposit feeders. Food availability causes modification only for rare nematodes such as epigrowth feeders and selective deposit feeders. Temperature is a factor affecting both predation death and a loss including respiration, excretion and natural death. Overall, the modification of nematode community by food availability is much lower than by predator. The macrobenthos in the Westerschelde Estuary decrease from upstream to the estuarine mouth. The stability and standing stock of nematode population follow the opposite gradient of their predators. They increase from upstream to the estuarine mouth.     

A finite element method to solve a population dynamics stage-structured model of intertidal barnacles

Many marine organisms are fixed or highly sedentary as adults but the adult population may be strongly dependent on the oceanic transport of planktonic larvae. In order to assess interactions between oceanographic and biological processes that determine the population dynamics of marine organisms with a sessile adult phase restricted to the coastline and a planktonic larval phase, we present a stage-structured finite element model for the barnacle Balanus glandula that inhabits the rocky intertidal zone of central California, USA.     

大亚湾裸甲藻种群动态及其关键调控因子

2008年1—12月对大亚湾养殖海域裸甲藻种群动态和主要环境因子进行了周年调查。结果表明,大亚湾海域裸甲藻类群以直径约为16～22μm的小型裸甲藻（Gymnodinium sp.）为主,另外米氏凯伦藻（Karenia mikimotoi）、链状裸甲藻（Gymnodnium catenatum）和血红哈卡藻（Akashiwo sanguinea）也有少量出现。裸甲藻种群密度呈现出明显的季节性变化特征：5月出现裸甲藻密度高峰,全年最大密度达到903 cells.mL-1,秋冬季节密度最小。不同站位裸甲藻密度也具有明显的空间分布差异,养殖及近岸海域密度普遍高于外海对照区。相关性分析结果表明,裸甲藻密度的关键调控因子包括温度、化学需氧量（COD）、可溶性有机氮（DON）和尿素浓度。裸甲藻高密度、高频率出现的温度范围在24～26℃,DON和尿素的质量浓度范围分别为N 156.38～187μg·L-1和N 17.4～38.9μg·L-1。在温度适宜的条件下,尿素等有机氮含量的增加可能成为裸甲藻赤潮的触发因子。     

Modelling of spatio-temporal population dynamics of earthworms under wetland conditions—An integrated approach

Both the effects of earthworms on soils and the effects of soil conditions on earthworms have been studied with the help of experiments and modelling. This paper provides a model architecture allowing coupling both effects to a dynamic interaction in changing environmental conditions. We chose for a spatio-temporally explicit model and focussed on wetland conditions. Soil temperature and humidity have been modelled by means of finite volumes and were used to determine the spatial habitat suitability. The life cycles of earthworms have been modelled by Leslie matrices where soil humidity, soil temperature and population densities have been used to parametrize survival and transition probabilities. Earthworm dispersion has been described by a cellular automaton of the domain providing spatial population densities for both the life cycle submodel and the soil conditions submodel.     

A process-based population dynamics model to explore target and non-target impacts of a biological control agent

The risks and benefits associated with efforts to control invasive alien species using classical biological control are being subjected to increasing scrutiny. A process-based population dynamics model was developed to explore the interactions between a folivorous biological control agent, Cleopus japonicus, and its plant host Buddleja davidii. The model revealed that climate could have a significant impact upon the interactions between B. davidii and C. japonicus. At the coolest sites, the impact of C. japonicus on B. davidii was slowed, but it was still eventually capable of controlling populations of B. davidii. At the warmer sites where both B. davidii and C. japonicus grew faster, B. davidii succumbed rapidly to weevil damage. We hypothesise that barring an encounter with a natural enemy, C. japonicus will eventually be able to provide sustained control B. davidii throughout the North Island of New Zealand. The model scenarios illustrate the potential for the C. japonicus population to attain high densities rapidly, and to defoliate patches of B. davidii, creating the potential for spill-over feeding on non-target plants. The potential magnitude of this threat will depend partly on the climate suitability for C. japonicus, the pattern by which it migrates in response to a reduction in the available leaf resource, and the suitability of non-target plants as hosts. In all migration scenarios considered, the pattern of population growth and resource consumption by C. japonicus was exponential, with a strong tendency toward complete utilisation of resource patches more quickly at the warmer compared to colder sites. In addition to providing some useful hypotheses about the effects of climate on the biological control system, and the non-target risks, it also provides some insight into the mechanisms by which climate affects the system.     

Modeling the brown bear population in Slovenia: A tool in the conservation management of a threatened species

In this paper, we address three aspects of the brown bear population in Slovenia: its size (and its evolution over time), its spatial expansion out of the core area, and its potential habitat based on natural habitat suitability. Data collected through measurement/observation of the bear population and from the literature are used. A model is developed for each aspect. The results are estimates of population size, a picture of the spatial expansion of the population and maps of its optimal and maximal potential habitat (based on natural suitability). Overall, the brown bear population has been increasing since the establishment of a core protective area and has been expanding outside this area. The habitat suitability maps show that there is room for further expansion. Based on habitat suitability and bear population density, as well as human activity and current damage reports, we recommend that the Alps should be temporarily kept free of the bears, until the necessary mitigation measures regarding human–bear conflicts are carried out. On the other hand it is of crucial importance to adapt human activities and improve bear management in the optimal habitat, with which the goals of successful conservation of the species might be achieved.     

Individual based model of slug population and spatial dynamics

The slug, Deroceras reticulatum, is one of the most important pests of agricultural and horticultural crops in UK and Europe. In this paper, a spatially explicit individual based model (IbM) is developed to study the dynamics of a population of D. reticulatum. The IbM establishes a virtual field within which slug spatial dynamics and changes in abundance were simulated. The strong dependence of slug behaviour on environmental conditions is built into the model, which is based upon previous work on the environmental dependence of slug population dynamics. The simulation results show that the IbM described well changes in the slug population. The IbM proved capable of describing slug populations over 3.5 years, including the presence, magnitude and duration of D. reticulatum population crashes within this period. Moreover, the model was capable of reproducing slug population dynamics at two sites, with distinct weather and some 100 km apart, with minor changes in initialisation values but no change in model structure and parameter values. A study of field heterogeneity, which might simulate various field designs, indicated the importance of spatial structuring to slug population dynamics and the utility of the IbM for simulating a range of potential spatial management treatments for slug control to maximise crop yield. This IbM system performs well and is currently being used as part of an integrated approach to predict slug population dynamics and control in the UK.     

A simple population theory for mutualism by the use of lattice gas model

The population dynamics of species interactions provides valuable information for life sciences. Lotka-Volterra equations (LVEs) are known to be the most popular model, and they are mainly applied to the systems of predation and competition. However, LVEs often fail to catch the population dynamics of mutualism; the population sizes of species increase infinitely under certain condition (divergence problem). Furthermore, LVEs never predicts the Allee effect in the systems of obligate mutualism. Instead of LVEs, several models have been presented for mutualism; unfortunately, they are rather complicated. It is, therefore, necessary to introduce a simpler theory for mutualism. In the present paper, we apply the lattice gas model which corresponds to the mean-field theory of the usual lattice model. The derived equations are cubic and contain only essential features for mutualism. In the case of obligate mutualism, the dynamics exhibits the Allee effect, and it is almost the same as in the male-female systems. In our model, the population sizes never increase infinitely, because our model contains not only intra- but also interspecific competitions. If the density of one species increases disproportionately in respect of its mutual partners, then this might imply downward pressure on the population abundance of the mutual partner species and such feedback would eventually act as a controlling influence on the population abundance of either species. We discuss several assumptions in our model; in particular, if both species can occupy in each cell simultaneously, then the interspecific competition disappears.     

Zooplankton population model coupled to a biogeochemical model of the North Western Mediterranean Sea ecosystem

A stage structured population (SSP) model based on Fennel's [Fennel, W., 2001. Modelling copepods with links to circulation models. Journal of Plankton Research, 23, 1217–1232] equations is applied to Centropages typicus (Kröyer), a dominant copepod species of the North Western Mediterranean Sea (NWMS) and a prey of small pelagic fish. The model considers five groups of stages and development rates are represented by a mechanistic formulation depending on individual specific growth in each stage. Individual growth is calculated from the individual energy budget depending on food availability and temperature.     

The influences of climate and hydrology on population dynamics of waterbirds in the lower Murrumbidgee River floodplains in Southeast Australia: Implications for environmental water management

Restoration of waterbird diversity and abundance is a key objective of river system management in Australia. Therefore, understanding the effects of climatic and hydrological variables on waterbird population dynamics is fundamental for successful river restoration programs. We investigated the population dynamics of waterbirds (total abundance) and seven functional waterbird groups in the floodplains of lower Murrumbidgee River. We found a general declining abundance trend from 1983 to 2007, except for the deep water foragers. We modelled the relative contribution of the climatic and hydrological factors to waterbird population decrease using the generalized additive model (GAM) framework after identifying the negative binomial distribution. Most of the seven functional groups were positively related to both annual rainfall and water usage, defined as the total water volume intercepted by the river reach, and the models indicated that rainfall was slightly more important. Temperature also played a role in waterbird abundance: the maximum summer temperature negatively influenced the abundance of dabbling ducks, shoreline foragers and fish eaters, while the minimum winter temperature positively affected the abundance of dabbling ducks and shoreline foragers. Overall, our results support the practice of providing environmental water for sustaining waterbird populations. However, environmental water provision is likely to be most effective when timed to coincide with antecedent rainfall.     

A Voronoi diagram based population model for social species of wildlife

A population model is presented that accounts for spatial structure within habitat patches. It is designed for social species of wildlife that form social group home ranges that are much smaller than patch size. The model represents social group home ranges by Voronoi regions that tessellate a patch to form a Voronoi diagram. Neighbouring social groups are linked with habitat-confined shortest paths and form a dispersal network. The model simulates population dynamics and makes use of Voronoi diagrams and dispersal networks as a spatial component. It then produces density maps as outputs. These are maps that show predicted animal densities across the patches of a landscape. A construction procedure for the particular Voronoi diagram type used by the model is described. As a test case, the model is run for the squirrel glider (Petaurus norfolcensis), a small arboreal marsupial native to Australia. A time series of density maps are produced that show squirrel glider density changing across a landscape through time.     

Development and validation of an individual based Daphnia magna population model: The influence of crowding on population dynamics

An individual-based model was developed to predict the population dynamics of Daphnia magna at laboratory conditions from individual life-history traits observed in experiments with different feeding conditions. Within the model, each daphnid passes its individual life cycle including feeding on algae, aging, growing, developing and – when maturity is reached – reproducing. The modelled life cycle is driven by the amount of ingested algae and the density of the Daphnia population. At low algae densities the population dynamics is mainly driven by food supply, when the densities of algae are high, the limiting factor is “crowding” (a density-dependent mechanism due to chemical substances released by the organisms or physical contact, but independent of food competition).     

Potential shift of bacterial community structure and corrosion-related bacteria in drinking water distribution pipeline driven by water source switching

• Bacterial release from aged pipe sections under extreme conditions was quantified. • Released bacterial community structure exhibited large variation after transition. • Risks from transition reduced significantly with cleaner source. As a result of pollution in the present water sources, cities have been forced to utilize cleaner water sources. There are few reports regarding the potential shift of bacterial community structure driven by water source switching, especially that of corrosion-related bacteria. Three types of finished water were used for simulation, the polluted source water from the Qiantang and Dongtiaoxi Rivers (China) was replaced by cleaner water from Qiandao Lake (China). Here, we discussed the transition effects through three simulated reactors. The bacterial characteristics were identified using the high-throughput sequencing and heterotrophic plate count method. It was observed that the level of culturable bacteria declined by 2–3 orders of magnitude after water source switching. The bacterial community released from the pipeline reactor was significantly different under different finished water, and it exhibited large variation at the genus level. Porphyrobacter (58.2%) and Phreatobacter (14.5%) clearly replaced Novosphingobium, Aquabacterium, and Cupriavidus as new dominant genera in system A, which could be attributed to the lower carbon and nitrogen content of the new water source. Although corrosion-inhibiting bacteria decreased after switching, they still maintained dominant in three reactors (6.6%, 15.9%, and 19.7%). Furthermore, potential opportunistic pathogens such as Sphingomonas were detected. Our study shows that after transition to a high quality water source, the total culturable bacteria released was in a downtrend, which leads to a great reduction in the risk of bacterial leakage in the produced drinking water.     

Using a fisheries ecosystem model with a water quality model to explore trophic and habitat impacts on a fisheries stock: A case study of the blue crab population in the Chesapeake Bay

Recent calls for the development of ecosystem-based fisheries management compel the development of resource management tools and linkages between existing fisheries management tools and other resource tools to enable assessment and management of multiple impacts on fisheries resources. In this paper, we describe the use of the Chesapeake Bay Fisheries Ecosystem Model (CBFEM), developed using the Ecopath with Ecosim (EwE) software, and the Chesapeake Bay Water Quality Model (WQM) to demonstrate how linkages between available modeling tools can be used to inform ecosystem-based natural resource management. The CBFEM was developed to provide strategic ecosystem information in support of fisheries management. The WQM was developed to assess impacts on water quality. The CBFEM was indirectly coupled with the WQM to assess the effects of water quality and submerged aquatic vegetation (SAV) on blue crabs. The output from two WQM scenarios (1985-1994), a baseline scenario representing actual nutrient inputs and another with reduced inputs based on a tributary management strategy, was incorporated into the CBFEM. The results suggested that blue crab biomass could be enhanced under management strategies (reduced nutrient input) when the effective search rate of blue crab young-of-the-year's (YOY's) predators or the vulnerability of blue crab YOY to its predators was adjusted by SAV. Such model linkages are important for incorporating physical and biological components of ecosystems in order to explore ecosystem-based fisheries management options.     

Uncertainty analysis of transient population dynamics

Two types of demographic analyses, perturbation analysis and uncertainty analysis, can be conducted to gain insights about matrix population models and guide population management. Perturbation analysis studies how the perturbation of demographic parameters (survival, growth, and reproduction parameters) may affect the population projection, while uncertainty analysis evaluates how much uncertainty there is in population dynamic predictions and where the uncertainty comes from. Previously, both perturbation analysis and uncertainty analysis were conducted on the long-term population growth rate. However, the population may not reach its equilibrium state, especially when there is management by harvesting or hunting. Recently, there has been an increased interest in short-term transient dynamics, which can differ from asymptotic long-term dynamics. There are currently techniques to conduct perturbation analyses of short-term transient dynamics, but no techniques have been proposed for uncertainty analysis of such dynamics. In this study, we introduced an uncertainty analysis technique, the general Fourier Amplitude Sensitivity Test (FAST), to study uncertainties in transient population dynamics. The general FAST is able to identify the amount of uncertainty in transient dynamics and contributions by different demographic parameters. We applied the general FAST to a mountain goat (Oreamnos americanus) matrix population model to give a clear illustration of how uncertainty analysis can be conducted for transient dynamics arising from matrix population models.     

A simulation model to evaluate the impacts of invasive earthworms on soil carbon dynamics

Recent studies have reported that earthworm invasions alter native communities and impact nutrient cycling in terrestrial ecosystems. We developed a simulation model to evaluate the potential impacts of earthworm invasions on carbon dynamics, taking into consideration earthworm feeding strategies and priming effects on the microorganisms through their casting activities. Responses of carbon stocks (forest litter, soil organic matter, microbial biomass and earthworm populations) and carbon fluxes (litter decomposition, earthworm consumption, and microbial respiration) were used to evaluate an earthworm invasion of a forest ecosystem. Data from a northern temperate forest (Arnot Forest, New York) were adapted for model calibration and evaluation. Simulation results suggest that the impact and outcome of earthworm invasions are affected by pre-invasion resource availability (litter and soil organic matter), invasive earthworm assemblages (particularly feeding strategy), and invasion history (associated with earthworm population dynamics). The abovementioned factors may also determine invasion progress of earthworm species. The accuracy of the model could be improved by the addition of environmental modules (e.g., soil water regimes), precise parameters accounting for individual species attributes under different environmental conditions (e.g. utilization ability of different types of food resources), as well as earthworm population dynamics (size and structure) and interactions with predators and other invasive/indigenous species during the invasion progress. Such an earthworm invasion model could provide valuable evaluation of the complicated responses of carbon dynamics to earthworm invasions in a range of forest ecosystems, particularly under global change scenarios.