Integral projection models for finite populations in a stochastic environment

Continuous types of population structure occur when continuous variables such as body size or habitat quality affect the vital parameters of individuals. These structures can give rise to complex population dynamics and interact with environmental conditions. Here we present a model for continuously structured populations with finite size, including both demographic and environmental stochasticity in the dynamics. Using recent methods developed for discrete age-structured models we derive the demographic and environmental variance of the population growth as functions of a continuous state variable. These two parameters, together with the expected population growth rate, are used to define a one-dimensional diffusion approximation of the population dynamics. Thus, a substantial reduction in complexity is achieved as the dynamics of the complex structured model can be described by only three population parameters. We provide methods for numerical calculation of the model parameters and demonstrate the accuracy of the diffusion approximation by computer simulation of specific examples. The general modeling framework makes it possible to analyze and predict future dynamics and extinction risk of populations with various types of structure, and to explore consequences of changes in demography caused by, e.g., climate change or different management decisions. Our results are especially relevant for small populations that are often of conservation concern.     

Emergence cues of a mayfly in a high-altitude stream ecosystem: potential response to climate change.

To understand the consequences of human accelerated environmental change, it is important to document the effects on natural populations of an increasing frequency of extreme climatic events. In stream ecosystems, recent climate change has resulted in extreme variation in both thermal and hydrological regimes. From 2001 to 2004, a severe drought in western United States corresponded with earlier emergence of the adult stage of the high-altitude stream mayfly, Baetis bicaudatus. Using a long-term database from a western Colorado stream, the peak emergence date of this mayfly population was predicted by both the magnitude and date of peak stream flow, and by the mean daily water temperature, suggesting that Baetis may respond to declining stream flow or increasing water temperature as proximate cues for early metamorphosis. However, in a one-year survey of multiple streams from the same drainage basin, only water temperature predicted spatial variation in the onset of emergence of this mayfly. To decouple the effects of temperature and flow, we separately manipulated these factors in flow-through microcosms and measured the timing of B. bicaudatus metamorphosis to the adult stage. Mayflies emerged sooner in a warmed-water treatment than an ambient-water treatment; but reducing flow did not accelerate the onset of mayfly emergence. Nonetheless, using warming temperatures to cue metamorphosis enables mayflies to time their emergence during the descending limb of the hydrograph when oviposition sites (protruding rocks) are becoming available. We speculate that large-scale climate changes involving warming and stream drying could cause significant shifts in the timing of mayfly metamorphosis, thereby having negative effects on populations that play an important role in stream ecosystems.     

Spatial variation in population dynamics in a colonial ascidian (Botryllus schlosseri)

Recent interest in the dynamics of marine invertebrate populations has focused largely on taxa with an open population structure. However, in many colonial taxa with limited larval dispersal, settlers may be locally derived. Consequently, dynamics may vary among sites that are separated by relatively short distances. This study explored spatial variation in temporal dynamics of colonial ascidians (Botryllus schlosseri Pallas) inhabiting five sites distributed along a ≈ 17-km temperature and phytoplankton gradient in the Damariscotta River estuary, Maine, USA. Settlement and population densities and sexual reproductive status were assayed throughout the summer seasons of 1996 and 1997. Sexual reproduction and larval settlement commenced earlier in the summer in up-river populations, which subsequently underwent a seasonal population explosion that was much smalier in down-river populations. Two peaks in settlement density up-river (in early July and early September) suggest that colonies there may have completed two sexual generations, in contrast to a single generation at down-river sites. Similar spatial variation is expected among populations of other taxa with limited larval dispersal when they are distributed across environmental gradients. Published online: 18 September 2002     

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.     

Vertical migration strategies with respect to advection and stratification in a semi-enclosed lough: a comparison of mero- and holozooplankton

Patterns of zooplankton vertical movement are often difficult to interpret because of multiple, complex and confounding environmental factors. Behavioural adaptations to these environmental variables are compared within and between the holo- and meroplankton constituents of a community. We used a nested design to analyse patterns at several scales in time; (semi-diel, diel, spring-neap tidal cycle and season) and two in space; (depth and site). To reduce complexity and aid interpretation we studied a semi-isolated community in a semi-enclosed, seasonally stratified sea lough (Lough Hyne Marine Nature Reserve, Ireland). In this, the main environmental gradient was water flow rate (or water residence time) caused by tidal currents. Vertical profiles of abundance showed that populations of the most abundant species of holo- and meroplankton in the lough have considerable behavioural plasticity, enabling them to switch between sedentary and migratory behaviour and patterns of migration. Some species migrate vertically in synchrony with diel cycles and others in response to semi-diel tidal currents; a few do both, but the majority did neither. It is suggested that water column structure and hydrographic discontinuities caused by flow rate and pycnocline dynamics are responsible for the variable patterns of vertical migration and distribution.Communicated by J.P. Thorpe, Port Erin     

A hydrologically driven model of swamp water mosquito population dynamics

We develop a swamp water mosquito population model that is forced solely by environmental variability. Measured temperature and land surface wetness conditions are used to simulate Anopheles walkeri population dynamics in a northern New Jersey habitat. Land surface wetness conditions, which represent oviposition habitat availability, are derived from simulations using a dynamic hydrology model. Using only these two density-independent effects, population model simulations of biting Anoph. walkeri correlate significantly with light trap collections. These results suggest that prediction of mosquito populations and the diseases they transmit could be better constrained by inclusion of environmental variability.     

Importance of Habitat Quality and Landscape Connectivity for the Persistence of Endangered Natterjack Toads

Abstract: The natterjack toad (Bufo calamita) is endangered in several parts of its distribution, including Belgium, where it occurs mainly in artificial habitats. We parameterized a general model for natterjack population viability analysis (PVA) and tested its sensitivity to changes in the values of basic parameters. Then we assessed the relative efficiency of various conservation measures in 2 situations: a small isolated population and a system of 4 populations connected by rare dispersal movements. We based the population viability analysis on a stage‐structured model of natterjack population dynamics. We parameterized the model in the RAMAS GIS platform with vital rates obtained from our own field experience and from published studies. Simulated natterjack populations were highly sensitive to habitat quality (particularly pond drying), to dispersal from surrounding local populations, and to a lesser extent to values of fecundity and survival of terrestrial stages. Population trajectories were nearly insensitive to initial abundances, carrying capacities, and the frequency of extreme climatic conditions. The simulations showed that in habitats with highly ephemeral ponds, where premetamorphosis mortality was high, natterjack populations nearly always had a very high extinction risk. We also illustrated how low dispersal rates (<1 dispersing individual/generation) efficiently rescued declining local populations. Such source‐sink dynamics demonstrate that the identification and management of source populations should be a high priority.     

Why are metapopulations so rare?

Roughly 40 years after its introduction, the metapopulation concept is central to population ecology. The notion that local populations and their dynamics may be coupled by dispersal is without any doubt of great importance for our understanding of population-level processes. A metapopulation describes a set of subpopulations linked by (rare) dispersal events in a dynamic equilibrium of extinctions and recolonizations. In the large body of literature that has accumulated, the term "metapopulation" is often used in a very broad sense; most of the time it simply implies spatial heterogeneity. A number of reviews have recently addressed this problem and have pointed out that, despite the large and still growing popularity of the metapopulation concept, there are only very few empirical examples that conform with the strict classical metapopulation (CM) definition. In order to understand this discrepancy between theory and observation, we use an individual-based modeling approach that allows us to pinpoint the environmental conditions and the life-history attributes required for the emergence of a CM structure. We find that CM dynamics are restricted to a specific parameter range at the border between spatially structured but completely occupied and globally extinct populations. Considering general life-history attributes, our simulations suggest that CMs are more likely to occur in arthropod species than in (large) vertebrates. Since the specific type of spatial population structure determines conservation concepts, our findings have important implications for conservation biology. Our model suggests that most spatially structured populations are panmictic, patchy, or of mainland-island type, which makes efforts spent on increasing connectivity (e.g., corridors) questionable. If one does observe a true CM structure, this means that the focal metapopulation is on the brink of extinction and that drastic conservation measures are needed.     

The effect of summer drought on the predictability of local extinctions in a butterfly metapopulation

The ecological impacts of extreme climatic events on population dynamics and community composition are profound and predominantly negative. Using extensive data of an ecological model system, we tested whether predictions from ecological models remain robust when environmental conditions are outside the bounds of observation. We observed a 10-fold demographic decline of the Glanville fritillary butterfly (Melitaea cinxia) metapopulation on the Åland islands, Finland in the summer of 2018 and used climatic and satellite data to demonstrate that this year was an anomaly with low climatic water balance values and low vegetation productivity indices across Åland. Population growth rates were strongly associated with spatiotemporal variation in climatic water balance. Covariates shown previously to affect the extinction probability of local populations in this metapopulation were less informative when populations were exposed to severe drought during the summer months. Our results highlight the unpredictable responses of natural populations to extreme climatic events.     

Reproductive synchrony in a habitat-forming kelp and its relationship with environmental conditions

Key biological processes such as the timing and synchrony of reproduction, are sensitive to fluctuations in the environment, as well as alterations in the physiology and behaviour of individuals and the ecology of populations. The main aim of this study was to identify patterns in reproductive timing and relationships with prevailing environmental conditions, for the major habitat-forming alga in temperate Australia, Ecklonia radiata (C. Agardh) J. Agardh. We observed strong synchronous patterns of zoospore production across spatial scales from hundreds of metres to tens of kilometres, with populations of E. radiata reproducing from mid-summer to the end of autumn. High zoospore densities were positively related to sea temperature and E. radiata released zoospores in temperatures well above previously documented thermal tolerance limits for other Laminariales. Reproductive timing was also negatively related to seasonal increase in wave exposure. We conclude that E. radiata undergoes synchronous reproduction which can be linked to its annual growth cycle and natural environmental fluctuations, to promote growth and survival of recruits.     

Evaluating the Effects of Anthropogenic Stressors on Source‐Sink Dynamics in Pond‐Breeding Amphibians

Although interwetland dispersal is thought to play an important role in regional persistence of pond‐breeding amphibians, few researchers have modeled amphibian metapopulation or source‐sink dynamics. Results of recent modeling studies suggest anthropogenic stressors, such as pollution, can negatively affect density and population viability of amphibians breeding in isolated wetlands. Presumably population declines also result in reduced dispersal to surrounding (often uncontaminated) habitats, potentially affecting dynamics of nearby populations. We used our data on the effects of mercury (Hg) on the American toad ( Bufo americanus) as a case study in modeling the effects of anthropogenic stressors on landscape‐scale amphibian dynamics. We created a structured metapopulation model to investigate regional dynamics of American toads and to evaluate the degree to which detrimental effects of Hg contamination on individual populations can disrupt interpopulation dynamics. Dispersal from typical American toad populations supported nearby populations that would otherwise have been extirpated over long time scales. Through support of such sink populations, dispersal between wetland‐associated subpopulations substantially increased overall productivity of wetland networks, but this effect declined with increasing interwetland distance and decreasing wetland size. Contamination with Hg substantially reduced productivity of wetland‐associated subpopulations and impaired the ability of populations to support nearby sinks within relevant spatial scales. Our results add to the understanding of regional dynamics of pond‐breeding amphibians, the wide‐reaching negative effects of environmental contaminants, and the potential for restoration or remediation of degraded habitats. Evaluación de los Efectos de Estresantes Antropogénicos sobre la Dinámica Fuente‐Vertedero en Anfibios que se Reproducen en Charcas     

Ecotoxicology and population dynamics: Using DEBtox models in a Leslie modeling approach

Although the ecological risks of toxic chemicals are usually assessed on the basis of individual responses, such as survival, reproduction or growth, ecotoxicologists are now attempting to assess the impact of environmental pollution on the dynamics of naturally exposed populations. The main issue is how to infer the likely impact on the population of the toxic effects observed at the individual level. Dynamic energy budget in toxicology (DEBtox) is the most user-friendly software currently available to analyze the experimental data obtained in toxicity tests performed on individuals. Because toxic effects are diverse and because the sensitivity of individuals varies considerably depending on life-cycle stage, Leslie models offer a convenient way of predicting toxicant effects on population dynamics.In the present study, we first show how parameter inputs, estimated from individual data using DEBtox, can be coupled using a Leslie matrix population model. Then, using experimental data obtained with Chironomus riparius, we show how the effects of a pesticide (methiocarb) on the population growth rate of a laboratory population can be estimated. Lastly, we perform a complex sensitivity analysis to pinpoint critical age classes within the population for the purposes of the field management of populations.     

Population dynamics of natural colonies of <Emphasis Type="Italic">Aurelia</Emphasis> sp. scyphistomae in Tasmania,Australia

The aim of this study was to identify potential environmental controls of the asexual phases of reproduction by measuring the rates of asexual reproduction (budding and strobilation) and mortality in naturally occurring populations of Aurelia sp. scyphistomae at different spatial and temporal scales. The percentage cover, density of colonies of Aurelia sp. scyphistomae, and density of the population of two naturally occurring colonies of Aurelia sp. scyphistomae were examined over 2 years in southern Tasmania. Artificial substrates were also deployed to investigate colony dynamics when density dependent effects were reduced. Clear spatial and temporal differences in the population dynamics of the colonies were observed. Density dependent effects controlled budding and recruitment of new scyphistomae to the substrate when populations were dense and space limiting. In contrast, environmental controls of budding and strobilation were more apparent in a colony with significantly greater area of bare substrate and hence room for expansion. Water temperature and rainfall (as a proxy for salinity) were linked to changes in population size. Annual and seasonal differences in population dynamics were not observed in a colony limited by space but were apparent in a colony where space was not limited. When space was removed as a limiting factor by deploying artificial substrates, a seasonal environmental effect on the rate of growth of the colony was observed. These studies suggest that the growth, survival and reproduction of the sessile colonial phase of Aurelia sp. is regulated by a combination of density dependent factors and environmental conditions, which are consequently important to the formation of jellyfish blooms.     

A new hypothesis concerning the nature of small pelagic fish clusters: An individual-based modelling study of Sardinella aurita dynamics off West Africa

Coastal populations of small pelagic fish display nested aggregation levels. Above the level of the school structure, clusters are observed the nature of which has not been definitively determined. We hypothesized that these clusters corresponded to a materialisation of the microcohorts originating from successive spawnings of fish populations in their vital domain.A candidate individual-based model was developed to investigate this hypothesis. This model is based on pattern-oriented modelling of a concrete documented case: the dynamics of the round sardinella (Sardinella aurita) population living off the West African coasts and subject to environmental fluctuations caused by seasonal upwelling. The simulated agents were round sardinella microcohorts situated and moving in a discretised physical environment. The combined effects of environmental forcing (temperature, wind, retention) and inner biological dynamics (reproduction, growth and mortality, competition) condition the dynamics of this population.The modelled behaviour generated realistic dynamic patterns (population distribution, spawning zones, periods and plasticity, biomass fluctuations), which were obtained simultaneously and successfully compared with observations. The steady-state number of microcohorts obtained after simulation convergence was similar to the number of clusters observed in situ in this area for this population.The realism and diversity of the patterns simultaneously simulated suggested the cluster-microcohort equivalence hypothesis as a candidate framework accounting for the origin of the clusters observed in situ. Within this preliminary exploration, we discuss the consistency of the hypothesis and the accuracy of the model. If the correspondence between clusters and microcohorts proves to be real, it may be transient and progressively modified by other environmental factors. If stable over time, as simulated in the model, the number of observed clusters should be related to the number of spawning events in the species’ lifetime.     

Living close, doing differently: small-scale asynchrony in demography of two species of seabirds

Studies on spatiotemporal pattern of population abundance predict that close populations should exhibit a high level of synchrony, reflected in a parallel time variation of at least one demographic parameter. We tested this prediction for two threatened species of Procellariiformes sharing similar life history traits: the European Storm Petrel (Hydrobates pelagicus) and the Balearic Shearwater (Puffinus mauretanicus). Within each species, we compared adult survival, proportion of transients (breeders that do not settle), and average productivity at two neighboring colonies. Physical and environmental features (e.g., food availability) of the breeding sites were similar. However, while Balearic Shearwater colonies were free of predators, aerial predators occurred especially in one colony of the European Storm Petrel. Despite this difference, we found similar results for the two species. A high proportion of transient birds was detected in only one colony of each species, ranging between 0.00-0.38 and 0.10-0.63 for the petrels and shearwaters, respectively. This seems to be an emergent feature of spatially structured populations of seabirds, unrelated to colony size or predator pressure, that can have important demographic consequences for local population dynamics and their synchrony. Local survival of resident birds was different at each colony, an unexpected result, especially for predator-free colonies of Balearic Shearwater. Productivity varied between the two colonies of European Storm Petrels, but not between the two colonies of Balearic Shearwaters. We demonstrated that within each species, several demographic parameters were colony specific and sufficiently different to generate short-term asynchronous dynamics. Our findings suggest that, in spatially structured populations, local factors, such as predation or small-scale habitat features, or population factors, such as individual quality or age structure, can generate unexpected asynchrony between neighboring populations.     

Effect of Vegetation Matrix on Animal Dispersal: Genetic Evidence from a Study of Endangered Skinks

Abstract:  Maintaining connectivity in fragmented landscapes is a key principle of biological conservation. Although corridors are a widely accepted approach to connecting populations, their merits are still debated, and they may be impractical in many situations. A focus on management of the vegetation matrix between populations has been advocated as an alternative way to deal with habitat fragmentation and has theoretical support. We combined microsatellite DNA and demographic data to provide an empirical account of how two forms of agricultural land use affect the connectivity of insular populations of an endangered skink in southern New Zealand. The grand skink ( Oligosoma grande ) lives in small populations (approximately 20 individuals) on rock outcrops separated from one another by 50–150 m of inhospitable matrix vegetation (either native tussock grassland or exotic pasture). Skinks typically dispersed short distances, and the nature of the matrix both quantitatively and qualitatively affected dispersal dynamics. Skink populations in pasture were significantly more genetically structured and had less genetic variation than similar populations in tussock, implying less dispersal between populations in pasture than tussock. Furthermore, although female-biased dispersal was a feature of populations in tussock, no sex bias was evident in pasture. In addition, Bayesian individual-based genetic assignment tests that incorporated prior mark-recapture information revealed that some populations produced many emigrants but received few immigrants, whereas other populations were relatively insular. Patterns of dispersal and response to matrix vegetation were complex, and the causes of these patterns deserve attention in future studies of habitat fragmentation. Managing the vegetation matrix may be a practical way to connect animal populations in some situations.     

Modeling the population dynamics of capybara Hydrochaeris hydrochaeris: a first step towards a management plan

Capybara (Hydrochaeris hydrochaeris) is the largest living rodent, widely distributed in South America, with a considerable potential as an economic resource. There are large populations in the region of Esteros del Ibera that could be exploited in a sustainable manner and contribute positively to the development of the region. Such exploitation requires to be done responsibly and following a specially designed management plan. In the particular case of wildlife management, a sustainable exploitation of a given species requires knowledge of its dynamics, its density in the area, and its vital rates, as well as understanding how the natural environment will respond to the proposed manipulation. It is also important to determine which environmental variables lead the population dynamics in each region. A mathematical model is a very convenient tool for analyzing possible strategies.This work presents a matrix population model structured in five stages. Sensitivity and elasticity analyses of the model provide an understanding of the effects of differentiated class-dependent survival and growth probabilities on the life cycle. A harvest term has been included in the model with the purpose of evaluating the sustainability of a given exploitation scenario or comparing different harvest strategies. The different strategies depend on the exploitation pattern, the exploitation intensity, and the season in which the harvest takes place.The purpose is to formulate a simple tool that can be understood by a manager without specific training. Hence, the software interface was specially designed for a user with elementary knowledge of vital parameters of the species.     

Development of a coupled reservoir operation and water diversion model: Balancing human and environmental flow requirements

Maintaining a natural flow regime helps preserve the health of riverine ecosystems. Conventional studies on reservoir operations have focused mainly on identifying optimal operational schemes for satisfying human water demands. To systematically reflect the ecological effects of both natural and human-induced hydrologic alterations, water diversions downstream of the reservoirs should be considered as well. This research focused on a coupled reservoir operation and water diversion (CROWD) model, created through the integration of a reservoir operation model and a water diversion model. The proposed model considers both human and environmental flow requirements, and represents a compromise that balances ecological protection (preservation of the natural flow regime of a river) and human needs (reduced water shortages). In the reservoir operation model, the reservoir space is divided into three zones and different operating rules are developed for directing reservoir operation when water levels are in different zones; in the water diversion model, different water users are assigned different supply priorities with the instream flows no more than the minimum environmental flows having the highest priority; and the two models are coupled by the water mass balance between the two hydraulic facilities. The non-dominated-sorting genetic algorithm II (NSGA-II) was used to determine the parameters of the developed CROWD model and the model was applied to support the joint operational management of the Tanghe Reservoir and the Liaoyang Diversion in the Tang river basin, China. The resulting reservoir operation and water diversion schemes indicate that the CROWD model is useful for optimizing the operation of reservoirs and water diversion schemes. Moreover, it helps to analyze tradeoffs between human and environmental water needs, resulting in solutions that reduce the risk of water shortages and minimize ecological integrity disturbances.     

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.     

Stochastic population dynamics in populations of western terrestrial garter snakes with divergent life histories

Comparative evaluations of population dynamics in species with temporal and spatial variation in life-history traits are rare because they require long-term demographic time series from multiple populations. We present such an analysis using demographic data collected during the interval 1978-1996 for six populations of western terrestrial garter snakes (Thamnophis elegans) from two evolutionarily divergent ecotypes. Three replicate populations from a slow-living ecotype, found in mountain meadows of northeastern California, were characterized by individuals that develop slowly, mature late, reproduce infrequently with small reproductive effort, and live longer than individuals of three populations of a fast-living ecotype found at lakeshore locales. We constructed matrix population models for each of the populations based on 8-13 years of data per population and analyzed both deterministic dynamics based on mean annual vital rates and stochastic dynamics incorporating annual variation in vital rates. (1) Contributions of highly variable vital rates to fitness (lambda(s)) were buffered against the negative effects of stochastic variation, and this relationship was consistent with differences between the meadow (M-slow) and lakeshore (L-fast) ecotypes. (2) Annual variation in the proportion of gravid females had the greatest negative effect among all vital rates on lambda(s). The magnitude of variation in the proportion of gravid females and its effect on lambda(s) was greater in M-slow than L-fast populations. (3) Variation in the proportion of gravid females, in turn, depended on annual variation in prey availability, and its effect on lambda(s) was 4 23 times greater in M-slow than L-fast populations. In addition to differences in stochastic dynamics between ecotypes, we also found higher mean mortality rates across all age classes in the L-fast populations. Our results suggest that both deterministic and stochastic selective forces have affected the evolution of divergent life-history traits in the two ecotypes, which, in turn, affect population dynamics. M-slow populations have evolved life-history traits that buffer fitness against direct effects of variation in reproduction and that spread lifetime reproduction across a greater number of reproductive bouts. These results highlight the importance of long-term demographic and environmental monitoring and of incorporating temporal dynamics into empirical studies of life-history evolution.