Ungulate population dynamics and optimization models

Optimal harvesting strategies for an ungulate population are estimated using stochastic dynamic programming. Data on the Llano Basin white-tailed deer (Odocoileus virginianus) population were used to construct a 2-variable population dynamics model. The model provided the basis for estimating optimal harvesting strategies as a feedback function of the current values of the state variables (prefawning older deer and juveniles). Optimal harvest strategies were insensitive to assumptions about the probability distributions of the stochastic variable (rainfall). The response of the population components to harvesting and the returns obtained from applying optimal strategies were explored through simulation. Mean annual harvest is about 15% of the population. Simplified harvesting strategies based on age-ratios as well as a simplified version based on optimal strategies—but assuming persisting equilibrium juvenile deer density—were compared to optimal strategies through examining values of information. Simplified harvesting strategies lead to a lower harvest over a 50-year simulation period.     

Transient dynamics and the destabilizing effects of prey heterogeneity

The presence of prey heterogeneity and weakly interacting prey species is frequently viewed as a stabilizer of predator-prey dynamics, countering the destabilizing effects of enrichment and reducing the amplitude of population cycles. However, prior model explorations have largely focused on long-term, dynamic attractors rather than transient dynamics. Recent theoretical work shows that the presence of prey that are defended from predation can have strongly divergent effects on dynamics depending on time scale: prey heterogeneity can counteract the destabilizing effects of enrichment on predator-prey dynamics at long time scales but strongly destabilize systems during transient phases by creating long periods of low predator/prey abundance and increasing extinction probability (an effect that is amplified with increasing enrichment). We tested these general predictions using a planktonic system composed of a zooplankton predator and multiple algal prey. We first parameterized a model of our system to generate predictions and tested these experimentally. Our results qualitatively supported several model predictions. During transient phases, presence of defended algal prey increased predator extinctions at low and high enrichment levels compared to systems with only a single edible prey. This destabilizing effect was moderated at higher dilution rates, as predicted by our model. When examining dynamics beyond initial oscillations, presence of the defended prey increased predator-prey temporal variability at high nutrient enrichment but had no effect at low nutrient levels. Our results highlight the importance of considering transient dynamics when assessing the role of stabilizing factors on the dynamics of food webs.     

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.     

Chihuahuan Desert kangaroo rats: nonlinear effects of population dynamics, competition, and rainfall

Using long-term data on two kangaroo rats in the Chihuahuan Desert of North America, we fitted logistic models including the exogenous effects of seasonal rainfall patterns. Our aim was to test the effects of intraspecific interactions and seasonal rainfall in explaining and predicting the numerical fluctuations of these two kangaroo rats. We found that logistic models fit both data sets quite well; Dipodomys merriami showed lower maximum per capita growth rates than Dipodomys ordii, and in both cases logistic models were nonlinear. Summer rainfall appears to be the most important exogenous effect for both rodent populations; models including this variable were able to predict independent data better than models including winter rainfall. D. merriami was also negatively affected by another kangaroo rat (Dipodomys spectabilis), consistent with previous experimental evidence. We hypothesized that summer rainfall influences the carrying capacity of the environment by affecting seed availability and the intensity of intraspecific competition.     

Analysis of competition models in periodic medium

We propose special models (the so-called D-systems) with periodic delta-functions being used as the growth velocities of the populations. This allows to build, in a practically explicit form, corresponding Poincare mapping and to reveal a series of “paradoxical” phenomena and selection criteria in the dynamics of the competitors. For the analysis of non-autonomous models, new general principle of inheritance of a series of local properties by the global Poincare shift mapping is worked up. Specifically, key heritable properties are determined for non-autonomous competition models. The selection criterion for competitive selection, based on the concept of the universal allowance constant, is derived in this work.     

Migration effects in a stochastic multipopulation model for African bee population dynamics

The rate of northern migration of the Africanized honey bee (AHB) in the United States has recently slowed dramatically. This paper investigates the impact of migration on the equilibrium size distributions of a particular stochastic multipopulation model, namely a coupled logistic power law model. The bivariate equilibrium size distribution of the model is derived and illustrated with parameter values used to describe AHB population dynamics. In the model, the difference between the equilibrium sizes of the two populations is a measure of the effect of migration. The distribution of this difference may be approximated by a normal distribution. The mean and variance parameters for the normal are predicted accurately by a second-order regression model based on the migration rate and the maximum size of the first population. The methodology is general, and should be useful in studying the migration effect in many other applications with one-way migration.     

On the latent state estimation of nonlinear population dynamics using Bayesian and non-Bayesian state-space models

Nonlinear state-space models have been increasingly applied to study population dynamics and data assimilation in environmental sciences. State-space models can account for process error and measurement error simultaneously to correct for the bias in the estimates of system state and model parameters. However, few studies have compared the performance of different nonlinear state-space models for reconstructing the state of population dynamics from noisy time series. This study compared the performance of the extended Kalman filter (EKF), unscented Kalman filter (UKF) and Bayesian nonlinear state-space models (BNSSM) through simulations. Synthetic population time series were generated using the theta logistic model with known parameters, and normally distributed process and measurement errors were introduced using the Monte Carlo simulations. At higher levels of nonlinearity, the UKF and BNSSM had lower root mean square error (RMSE) than the EKF. The BNSSM performed reliably across all levels of nonlinearity, whereas increased levels of nonlinearity resulted in higher RMSE of the EKF. The Metropolis–Hastings algorithm within the Gibbs algorithm was used to fit the theta logistic model to synthetic time series to estimate model parameters. The estimated posterior distribution of the parameter θ indicated that the 95% credible intervals included the true values of θ (=0.5 and 1.5), but did not include 1.0 and 0.0. Future studies need to incorporate the adaptive Metropolis algorithm to estimate unknown model parameters for broad applications of Bayesian nonlinear state-space models in ecological studies.     

Nonlinear effects of climate and density in the dynamics of a fluctuating population of reindeer

Nonlinear and irregular population dynamics may arise as a result of phase dependence and coexistence of multiple attractors. Here we explore effects of climate and density in the dynamics of a highly fluctuating population of wild reindeer (Rangifer tarandus platyrhynchus) on Svalbard observed over a period of 29 years. Time series analyses revealed that density dependence and the effects of local climate (measured as the degree of ablation [melting] of snow during winter) on numbers were both highly nonlinear: direct negative density dependence was found when the population was growing (Rt > 0) and during phases of the North Atlantic Oscillation (NAO) characterized by winters with generally high (1979-1995) and low (1996-2007) indices, respectively. A growth-phase-dependent model explained the dynamics of the population best and revealed the influence of density-independent processes on numbers that a linear autoregressive model missed altogether. In particular, the abundance of reindeer was enhanced by ablation during phases of growth (Rt > 0), an observation that contrasts with the view that periods of mild weather in winter are normally deleterious for reindeer owing to icing of the snowpack. Analyses of vital rates corroborated the nonlinearity described in the population time series and showed that both starvation mortality in winter and fecundity were nonlinearly related to fluctuations in density and the level of ablation. The erratic pattern of growth of the population of reindeer in Adventdalen seems, therefore, to result from a combination of the effects of nonlinear density dependence, strong density-dependent mortality, and variable density independence related to ablation in winter.     

Local population dynamics of an invasive tree species with a complex life-history cycle: A stochastic matrix model

Biological invasions are widely accepted as having a major impact on ecosystem functioning worldwide, giving urgency to a better understanding of the factors that control their spread. Modelling tools have been developed for this purpose but are often discrete-space, discrete-time spatial-mechanistic models that adopt a computer simulation approach and resist mathematical analysis. We constructed a simple demographic matrix model to explore the local population dynamics of an invasive species with a complex life history and whose invasive success depends on resource availability, which occurs stochastically. As a case study we focused on the American black cherry (Prunus serotina Ehrh.), a gap-dependent tree able both to constitute a long-living seedling bank under unfavourable light conditions and to resprout vigorously once cut-down, which is invading European temperate forests. The model used was a stage-classified matrix population model (i.e., Lefkovitch matrix), integrating environmental stochasticity. Stochastic matrix projection analysis was combined with elasticity analysis and stochastic simulations to search for the species’ ‘Achille heel’. As expected, the population growth rate (i.e., Lyapunov exponent), which measures the risk of P. serotina invasion at the stand scale, increased with light frequency. There was a critical value above which the population of P. serotina explodes and below which it locally goes extinct. The resprouting capacity usually speed up the invasion but appeared to play a minor role. The mean duration of stand invasion was measured and important life stage transitions that mostly contribute to the local stochastic growth rate were identified. Some relevant management implications are discussed and the interest of such models for the understanding of demographic characteristics of invasive species is stressed.     

Interactive effects of prey and p,p'-DDE on burrowing owl population dynamics.

We used population models to explore the effects of the organochlorine contaminant p,p'-DDE and fluctuations in vole availability on the population dynamics of Burrowing Owls (Athene cunicularia). Previous work indicated an interaction between low biomass of voles in the diet and moderate levels of p,p'-DDE in Burrowing Owl eggs that led to reproductive impairment. We constructed periodic and stochastic matrix models that incorporated three vole population states observed in the field: average, peak, and crash years. We modeled varying frequencies of vole crash years and a range of impairment of owl demographic rates in vole crash years. Vole availability had a greater impact on owl population growth rate than did reproductive impairment if vole populations peaked and crashed frequently. However, this difference disappeared as the frequency of vole crash years declined to once per decade. Fecundity, the demographic rate most affected by p,p'-DDE, had less impact on population growth rate than adult or juvenile survival. A life table response experiment of time-invariant matrices for average, peak, and crash vole conditions showed that low population growth under vole crash conditions was due to low adult and juvenile survival rates, whereas the extremely high population growth under vole peak conditions was due to increased fecundity. Our results suggest that even simple models can provide useful insights into complex ecological interactions. This is particularly valuable when temporal or spatial scales preclude manipulative experimental work in the field or laboratory.     

Human trampling as short-term disturbance on intertidal mudflats: effects on macrofauna biodiversity and population dynamics of bivalves

The effect of physical disturbance in the form of trampling on the benthic environment of an intertidal mudflat was investigated. Intense trampling was created as unintended side-effect by benthic ecologists during field experiments in spring and summer 2005, when a mid-shore area of 25 × 25 m was visited twice per month by on average five researchers for a period of 8 months. At the putatively-impacted location (I) (25 × 25 m) and two nearby control locations (Cs) (25 × 25 m each), three sites (4 × 4 m) were randomly selected and at each site, three plots (50 × 50 cm) were sampled after 18 and 40 days from the end of the disturbance. Multivariate and univariate asymmetrical analyses tested for changes in the macrofaunal assemblage, biomass of microphytobenthos and various sediment properties (grain-size, water content, NH₄ and NO₃ concentrations in the pore water) between the two control locations (Cs) and the putatively-impacted location (I). There were no detectable changes in the sediment properties and microphytobenthos biomass, but variability at small scale was observed. Microphytobenthos and NH₄ were correlated at I to the number of footprints, as estimated by the percentage cover of physical depressions. This indicated that trampling could have an impact at small scales, but more investigation is needed. Trampling, instead, clearly modified the abundance and population dynamics of the clam Macoma balthica (L.) and the cockle Cerastoderma edule (L.). There was a negative impact on adults of both species, probably because footsteps directly killed or buried the animals, provoking asphyxia. Conversely, trampling indirectly enhanced recruitment rate of M. balthica, while small-sized C. edule did not react to the trampling. It was likely that small animals could recover more quickly because trampling occurred during the growing season and there was a continuous supply of larvae and juveniles. In addition, trampling might have weakened negative adult-juvenile interactions between adult cockles and juvenile M. balthica, thus facilitating the recruitment. Our findings indicated that human trampling is a relevant source of disturbance for the conservation and management of mudflats. During the growing season recovery can be fast, but in the long-term it might lead towards the dominance of M. balthica to the cost of C. edule, thereby affecting ecosystem functioning.     

Enchytraeid population dynamics: Resource limitation and size-dependent mortality

Enchytraeids are regarded as keystone soil organisms in forest ecosystems. Their abundance and biomass fluctuate widely. Predicting the consequences of anthropogenic disturbances requires an understanding of the mechanisms underlying enchytraeid population dynamics. Here I develop a simple model, which predicts that the type of dynamics is controlled by resource input rate. If fungal resource input is a discrete event once a year, an exponential growth phase is followed by starvation and sharp decline of enchytraeid abundance. Model simulations with three different forcing functions were compared to field data. Initial parameter values were obtained from various independent sources, and parameters were estimated by minimizing the residual sum of squares. The best fitting model with resource addition once a year explained 39% of the variation in enchytraeid biomass over an 8-year study period. Further, variation in rainfall explained 59% of the variation in R² of the exponential phase models, which is also an index of the stability of population size-structure. The results emphasize the importance of resource limitation for enchytraeid population dynamics and support the hypothesis that the mortality during the decline phase is size-dependent.     

Spatial scaling of avian population dynamics: population abundance, growth rate, and variability

Synchrony in population fluctuations has been identified as an important component of population dynamics. In a previous study, we determined that local-scale (<15-km) spatial synchrony of bird populations in New England was correlated with synchronous fluctuations in lepidopteran larvae abundance and with the North Atlantic Oscillation. Here we address five questions that extend the scope of our earlier study using North American Breeding Bird Survey data. First, do bird populations in eastern North America exhibit spatial synchrony in abundances at scales beyond those we have documented previously? Second, does spatial synchrony depend on what population metric is analyzed (e.g., abundance, growth rate, or variability)? Third, is there geographic concordance in where species exhibit synchrony? Fourth, for those species that exhibit significant geographic concordance, are there landscape and habitat variables that contribute to the observed patterns? Fifth, is spatial synchrony affected by a species' life history traits? Significant spatial synchrony was common and its magnitude was dependent on the population metric analyzed. Twenty-four of 29 species examined exhibited significant synchrony in population abundance: mean local autocorrelation (rho)= 0.15; mean spatial extent (mean distance where rho=0) = 420.7 km. Five of the 29 species exhibited significant synchrony in annual population growth rate (mean local autocorrelation = 0.06, mean distance = 457.8 km). Ten of the 29 species exhibited significant synchrony in population abundance variability (mean local autocorrelation = 0.49, mean distance = 413.8 km). Analyses of landscape structure indicated that habitat variables were infrequent contributors to spatial synchrony. Likewise, we detected no effects of life history traits on synchrony in population abundance or growth rate. However, short-distance migrants exhibited more spatially extensive synchrony in population variability than either year-round residents or long-distance migrants. The dissimilarity of the spatial extent of synchrony across species suggests that most populations are not regulated at similar spatial scales. The spatial scale of the population synchrony patterns we describe is likely larger than the actual scale of population regulation, and in turn, the scale of population regulation is undoubtedly larger than the scale of individual ecological requirements.     

Linking edge effects and patch size effects: Importance of matrix nest predators

The edge effect is usually considered to be the proximate cause of area sensitivity in forest birds. We tested if birds nesting in large patches are less vulnerable to the edge effect using a simple model that assumes an increase in patch size reduces the probability of a matrix predator moving to the core areas of forest and that larger perimeter/area ratios result in a higher number of matrix predators per unit of area. The probability of a nest being successful decreased asymptotically with an increase in either the patch penetration distance of predators or predator density, but those effects were reduced when patch size was increased. Large patches have a lower probability of being affected by an Allee effect and they can function as sink habitats only if penetration distance and predator density are largely increased. However, the transition from an Allee effect to a sink condition occurs with a small increase in penetration distance and predator density. Since birds nesting in large patches are less vulnerable to an increase in matrix predator populations, persistence of bird populations may be possible by increasing the size of habitat patches that can act as source populations.     

Assessing the effects of disease and bleaching on Florida Keys corals by fitting population models to data

Coral diseases have increased in frequency over the past few decades and have important influences on the structure and composition of coral reef communities. However, there is limited information on the etiologies of many coral diseases, and pathways through which coral diseases are acquired and transmitted are still in question. Furthermore, it is difficult to assess the impacts of disease on coral populations because outbreaks often co-occur with temperature-induced bleaching and anthropogenic stressors. We developed spatially explicit population models of coral disease and bleaching dynamics to quantify the impact of six common diseases on Florida Keys corals, including aspergillosis, dark spots, white band, white plague, white patch, and Caribbean yellow band. Models were fit to an 8-year data set of coral abundance, disease prevalence, and bleaching prevalence. Model selection was used to assess alternative pathways for disease transmission, and the influence of environmental stressors, including sea temperature and human population density, on disease prevalence and coral mortality. Classic disease transmission from contagious to susceptible colonies provided the best-fit model only for aspergillosis. For other diseases, external disease forcing, such as through a vector or directly from pathogens in the environment, provided the best fit to observed data. Estimates of disease reproductive ratio values (R₀) were less than one for each disease, indicating coral colonies were below densities required for diseases to become established through contagious spread alone. Incidences of white band and white patch disease were associated with greater susceptibility or slower recovery of bleached colonies, and no disease outbreaks were associated with periods of elevated sea temperatures alone. Projections of best-fit models indicated that, atleast during the period of this study, disease and bleaching did not have substantial impacts on populations and impaired rates of population growth appeared to be attributable to other stressors. By applying epidemiological models to field data, our study gives qualitative insights into the dynamics of coral diseases, relative stressor impacts, and directions for future research.     

Transient dynamics of pelagic producer-grazer systems in a gradient of nutrients and mixing depths

Phytoplankton-grazer dynamics are often characterized by long transients relative to the length of the growing season. Using a phytoplankton-grazer model parameterized for Daphnia pulex with either flexible or fixed algal carbon:nutrient stoichiometry, we explored how nutrient and light supply (the latter by varying depth of the mixed water column) affect the transient dynamics of the system starting from low densities. The system goes through an initial oscillation across nearly the entire light-nutrient supply space. With flexible (but not with fixed) algal stoichiometry, duration of the initial algal peak, timing and duration of the subsequent grazer peak, and timing of the algal minimum are consistently accelerated by nutrient enrichment but decelerated by light enrichment (decreasing mixing depth) over the range of intermediate to shallow mixing depths. These contrasting effects of nutrient vs. light enrichment are consequences of their opposing influences on food quality (algal nutrient content): algal productivity and food quality are positively related along a nutrient gradient but inversely related along a light gradient. Light enrichment therefore slows down grazer growth relative to algal growth, decelerating oscillatory dynamics; nutrient enrichment has opposite effects. We manipulated nutrient supply and mixing depth in a field enclosure experiment. The experimental results were qualitatively much more consistent with the flexible than with the fixed stoichiometry model. Nutrient enrichment increased Daphnia peak biomass, decreased algal minimum biomass, decreased the seston C:P ratio, and accelerated transient oscillatory dynamics. Light enrichment (decreasing mixing depth) produced the opposite patterns, except that Daphnia peak biomass increased monotonously with light enrichment, too. Thus, while the model predicts the possibility of the "paradox of energy enrichment" (a decrease in grazer biomass with light enrichment) at high light and low nutrient supply, this phenomenon did not occur in our experiment.     

Spatial selection and inheritance: applying evolutionary concepts to population dynamics in heterogeneous space

Organisms in highly suitable sites generally produce more offspring, and offspring can inherit this suitability by not dispersing far. This combination of spatial selection and spatial inheritance acts to bias the distribution of organisms toward suitable sites and thereby increase mean fitness (i.e., per capita population increase). Thus, population growth rates in heterogeneous space change over time by a process conceptually analogous to evolution by natural selection, opening avenues for theoretical cross-pollination between evolutionary biology and ecology. We operationally define spatial inheritance and spatial selective differential and then combine these two factors in a modification of the breeder's equation, derived from simple models of population growth in heterogeneous space. The modified breeder's equation yields a conservative criterion for persistence in hostile environments estimable from field measurements. We apply this framework for understanding gypsy moth population persistence amidst abundant predators and find that the predictions of the modified breeder's equation match initial changes in population growth rate in independent simulation output. The analogy between spatial dynamics and natural selection conceptually links ecology and evolution, provides a spatially implicit framework for modeling spatial population dynamics, and represents an important null model for studying habitat selection.     

Life history and population dynamics ofKinbergonuphis simoni (Polychaeta: Onuphidae)

The relationship between life-history characteristics and population dynamics were investigated in the onuphid polychaeteKinbergonuphis simoni (Santos, Day and Rice) between 1982 and 1987. The studied population is located in Upper Tampa Bay, Florida, USA. This worm attains sexual maturity at 5 to 10 mo of age, depending on temperature. Several consecutive broods are produced during a female's life time, with 7 to 26 young per brood. Adults die in June–July after the breeding season. Generations of breeding individuals do not overlap and the replacement of generations occurs in July–August. Only one extended breeding season is experienced per life time. Life span does not exceed 2 yr. Field population density in 1982 was high in fall and spring (2000 to 9000 individuals/m²), low in summer (1600 individuals/m²), and slightly depressed in winter (2500 to 4000 individuals/m²). Changes in population density may be explained by seasonal, temperature-controlled changes in instantaneous birth and death rates. Birth rates are high in fall and spring, while death rates are high in early summer. Death of juveniles contributes to the winter density decrease.     

Spatiotemporal variation in survival rates: implications for population dynamics of yellow-bellied marmots

Spatiotemporal variation in age-specific survival rates can profoundly influence population dynamics, but few studies of vertebrates have thoroughly investigated both spatial and temporal variability in age-specific survival rates. We used 28 years (1976-2003) of capture-mark-recapture (CMR) data from 17 locations to parameterize an age-structured Cormack-Jolly-Seber model, and investigated spatial and temporal variation in age-specific annual survival rates of yellow-bellied marmots (Marmota flaviventris). Survival rates varied both spatially and temporally, with survival of younger animals exhibiting the highest degree of variation. Juvenile survival rates varied from 0.52 +/- 0.05 to 0.78 +/- 0.10 among sites and from 0.15 +/- 0.14 to 0.89 +/- 0.06 over time. Adult survival rates varied from 0.62 +/- 0.09 to 0.80 +/- 0.03 among sites, but did not vary significantly over time. We used reverse-time CMR models to estimate the realized population growth rate (lamda), and to investigate the influence of the observed variation in age-specific survival rates on lamda. The realized growth rate of the population closely covaried with, and was significantly influenced by, spatiotemporal variation in juvenile survival rate. High variability in juvenile survival rates over space and time clearly influenced the dynamics of our study population and is also likely to be an important determinant of the spatiotemporal variation in the population dynamics of other mammals with similar life history characteristics.