First Passage Times of Long Transient Dynamics in Ecology.

Long transient dynamics in ecological models are characterized by extended periods in one state or regime before an eventual, and often abrupt, transition. One mechanism leading to long transient dynamics is the presence of ghost attractors, states where system dynamics slow down and the system lingers before eventually transitioning to the true attractor. This transition results solely from system dynamics rather than external factors. This paper investigates the dynamics of a classical herbivore-grazer model with the potential for ghost attractors or alternative stable states. We propose an intuitive threshold for first passage time analysis applicable to both bistable and ghost attractor regimes. By formulating the first passage time problem as a backward Kolmogorov equation, we examine how the mean first passage time changes as parameters are varied from the ghost attractor regime to the bistable one, through a saddle-node bifurcation. Our results reveal that the mean and variance of first passage times vary smoothly across the bifurcation threshold, eliminating the deterministic distinction between ghost attractors and bistable regimes. This work suggests that first passage time analysis can be an informative way to classify the length of a long transient. A better understanding of the duration of long transients may contribute to greater ecological understanding and more effective environmental management.

Strategy maps: Generalised giving-up densities for optimal foraging.

Finding a common currency for benefits and hazards is a major challenge in optimal foraging theory, often requiring complex computational methods. We present a new analytic approach that builds on the Marginal Value Theorem and giving-up densities while incorporating the nonlinear effect of predation risk. We map the space of all possible environments into strategy regions, each corresponding to a discrete optimal strategy. This provides a generalised quantitative measure of the trade-off between foraging rewards and hazards. This extends a classic optimal diet choice rule-of-thumb to incorporate the hazard of waiting for better resources to appear. We compare the dynamics of optimal decision-making for three foraging life-history strategies: One in which fitness accrues instantly, and two with delays before fitness benefit is accrued. Foragers with delayed-benefit strategies are more sensitive to predation risk than resource quality, as they stand to lose more fitness from a predation event than instant-accrual foragers.

Uncertainty quantification for ecological models with random parameters.

There is often considerable uncertainty in parameters in ecological models. This uncertainty can be incorporated into models by treating parameters as random variables with distributions, rather than fixed quantities. Recent advances in uncertainty quantification methods, such as polynomial chaos approaches, allow for the analysis of models with random parameters. We introduce these methods with a motivating case study of sea ice algal blooms in heterogeneous environments. We compare Monte Carlo methods with polynomial chaos techniques to help understand the dynamics of an algal bloom model with random parameters. Modelling key parameters in the algal bloom model as random variables changes the timing, intensity and overall productivity of the modelled bloom. The computational efficiency of polynomial chaos methods provides a promising avenue for the broader inclusion of parametric uncertainty in ecological models, leading to improved model predictions and synthesis between models and data.

The Effects of Using a Clinical Prediction Rule to Prioritize Diagnostic Testing on Transmission and Hospital Burden: A Modeling Example of Early Severe Acute Respiratory Syndrome Coronavirus 2.

BACKGROUND: Prompt identification of infections is critical for slowing the spread of infectious diseases. However, diagnostic testing shortages are common in emerging diseases, low resource settings, and during outbreaks. This forces difficult decisions regarding who receives a test, often without knowing the implications of those decisions on population-level transmission dynamics. Clinical prediction rules (CPRs) are commonly used tools to guide clinical decisions. METHODS: Using early severe acute respiratory syndrome coronavirus disease 2 (SARS-CoV-2) as an example, we used data from electronic health records to develop a parsimonious 5-variable CPR to identify those who are most likely to test positive. To consider the implications of gains in daily case detection at the population level, we incorporated testing using the CPR into a compartmentalized model of SARS-CoV-2. RESULTS: We found that applying this CPR (area under the curve, 0.69; 95% confidence interval, .68-.70) to prioritize testing increased the proportion of those testing positive in settings of limited testing capacity. We found that prioritized testing led to a delayed and lowered infection peak (ie, "flattens the curve"), with the greatest impact at lower values of the effective reproductive number (such as with concurrent community mitigation efforts), and when higher proportions of infectious persons seek testing. In addition, prioritized testing resulted in reductions in overall infections as well as hospital and intensive care unit burden. CONCLUSION: We highlight the population-level benefits of evidence-based allocation of limited diagnostic capacity.SummaryWhen the demand for diagnostic tests exceeds capacity, the use of a clinical prediction rule to prioritize diagnostic testing can have meaningful impact on population-level outcomes, including delaying and lowering the infection peak, and reducing healthcare burden.

Contribution of late-litter juveniles to the population dynamics of snowshoe hares.

Determining the factors driving cyclic dynamics in species has been a primary focus of ecology. For snowshoe hares (Lepus americanus), explanations of their 10-year population cycles most commonly feature direct predation during the peak and decline, in combination with their curtailment in reproduction. Hares are thought to stop producing third and fourth litters during the cyclic decline and do not recover reproductive output for several years. The demographic effects of these reproductive changes depend on the consistency of this pattern across cycles, and the relative contribution to population change of late-litter versus early litter juveniles. We used monitoring data on snowshoe hares in Yukon, Canada, to examine the contribution of late-litter juveniles to the demography of their cycles, by assigning litter group for individuals caught in autumn based on body size and capture date. We found that fourth-litter juveniles occur consistently during the increase phase of each cycle, but are rare and have low over-winter survival (0.05) suggesting that population increase is unlikely to be caused by their occurrence. The proportion of third-litter juveniles captured in the autumn remains relatively constant across cycle phases, while over-winter survival rates varies particularly for earlier-litter juveniles (0.14-0.39). Juvenile survival from all litters is higher during the population increase and peak, relative to the low and decline. Overall, these results suggest that the transition from low phase to population growth may stem in large part from changes in juvenile survival as opposed to increased reproductive output through the presence of a 4th litter.

Modeling optimal responses and fitness consequences in a changing Arctic.

Animals must balance a series of costs and benefits while trying to maximize their fitness. For example, an individual may need to choose how much energy to allocate to reproduction versus growth, or how much time to spend on vigilance versus foraging. Their decisions depend on complex interactions between environmental conditions, behavioral plasticity, reproductive biology, and energetic demands. As animals respond to novel environmental conditions caused by climate change, the optimal decisions may shift. Stochastic dynamic programming provides a flexible modeling framework with which to explore these trade-offs, but this method has not yet been used to study possible changes in optimal trade-offs caused by climate change. We created a stochastic dynamic programming model capturing trade-off decisions required by an individual adult female polar bear (Ursus maritimus) as well as the fitness consequences of her decisions. We predicted optimal foraging decisions throughout her lifetime as well as the energetic thresholds below which it is optimal for her to abandon a reproductive attempt. To explore the effects of climate change, we shortened the spring feeding period by up to 3 weeks, which led to predictions of riskier foraging behavior and higher reproductive thresholds. The resulting changes in fitness may be interpreted as a best-case scenario, where bears adapt instantaneously and optimally to new environmental conditions. If the spring feeding period was reduced by 1 week, her expected fitness declined by 15%, and if reduced by 3 weeks, expected fitness declined by 68%. This demonstrates an effective way to explore a species' optimal response to a changing landscape of costs and benefits and highlights the fact that small annual effects can result in large cumulative changes in expected lifetime fitness.

Ringed seal demography in a changing climate.

Climate change is affecting species' distributions and abundances worldwide. Baseline population estimates, against which future observations may be compared, are necessary if we are to detect ecological change. Arctic sea ice ecosystems are changing rapidly and we lack baseline population estimates for many ice-associated species. Provided we can detect them, changes in Arctic marine ecosystems may be signaled by changes in indicator species such as ringed seals (Pusa hispida). Ringed seal monitoring has provided estimates of survival and fertility rates, but these have not been used for population-level inference. Using matrix population models, we synthesized existing demographic parameters to obtain estimates of historical ringed seal population growth and structure in Amundsen Gulf and Prince Albert Sound, Canada. We then formalized existing hypotheses about the effects of emerging environmental stressors (i.e., earlier spring ice breakup and reduced snow depth) on ringed seal pup survival. Coupling the demographic model to ice and snow forecasts available from the Coupled Model Intercomparison Project resulted in projections of ringed seal population size and structure up to the year 2100. These projections showed median declines in population size ranging from 50% to 99%. Corresponding to these projected declines were substantial changes in population structure, with increasing proportions of ringed seal pups and adults and declining proportions of juveniles. We explored if currently collected, harvest-based data could be used to detect the projected changes in population stage structure. Our model suggests that at a present sample size of 100 seals per year, the projected changes in stage structure would only be reliably detected by mid-century, even for the most extreme climate models. This modeling process revealed inconsistencies in existing estimates of ringed seal demographic rates. Mathematical population models such as these can contribute both to understanding past population trends as well as predicting future ones, both of which are necessary if we are to detect and interpret future observations.

Evidence of intraspecific prey switching: stage-structured predation of polar bears on ringed seals.

Prey switching is a phenomenon in which a predator disproportionately consumes the most abundant prey type, and switches to preferentially consume another prey type if the first becomes relatively rare. This concept may be expanded outside of its usual usage describing switching between prey species (interspecific), to describe switching between prey stages within a given species (intraspecific). Polar bears (Ursus maritimus) are thought to seek out naive ringed seal (Pusa hispida) pups in the spring, but how that may change in years with low seal productivity is unknown. We addressed two main questions: If polar bears typically select for ringed seals' pups, how does this change in years with reduced ringed-seal productivity? How does polar bear predation during years with low ringed-seal productivity impact the ringed seal population? We created a matrix population model for ringed seals to get an estimate of each stage's availability to polar bears in the spring. These estimates of availability were combined with existing studies on the ages of seals consumed by polar bears in years of both high and low ringed seal productivity. Our results suggest that polar bears typically strongly select for ringed seal pups, but switch to disproportionately select older ringed seals in years with low pup availability. The effects of this on ringed seal population growth appear negligible. Non-intuitive results on the effect of prey switching on the prey population emphasize the importance of considering environmental sequences rather than individual years.

The critical domain size of stochastic population models.

Identifying the critical domain size necessary for a population to persist is an important question in ecology. Both demographic and environmental stochasticity impact a population's ability to persist. Here we explore ways of including this variability. We study populations with distinct dispersal and sedentary stages, which have traditionally been modelled using a deterministic integrodifference equation (IDE) framework. Individual-based models (IBMs) are the most intuitive stochastic analogues to IDEs but yield few analytic insights. We explore two alternate approaches; one is a scaling up to the population level using the Central Limit Theorem, and the other a variation on both Galton-Watson branching processes and branching processes in random environments. These branching process models closely approximate the IBM and yield insight into the factors determining the critical domain size for a given population subject to stochasticity.

Approximating the Critical Domain Size of Integrodifference Equations.

Integrodifference (IDE) models can be used to determine the critical domain size required for persistence of populations with distinct dispersal and growth phases. Using this modelling framework, we develop a novel spatially implicit approximation to the proportion of individuals lost to unfavourable habitat outside of a finite domain of favourable habitat, which consistently outperforms the most common approximations. We explore how results using this approximation compare to the existing IDE results on the critical domain size for populations in a single patch of good habitat, in a network of patches, in the presence of advection, and in structured populations. We find that the approximation consistently provides results which are in close agreement with those of an IDE model except in the face of strong advective forces, with the advantage of requiring fewer numerical approximations while providing insights into the significance of disperser retention in determining the critical domain size of an IDE.

Modeling reductions in SARS-CoV-2 transmission and hospital burden achieved by prioritizing testing using a clinical prediction rule.

Prompt identification of cases is critical for slowing the spread of COVID-19. However, many areas have faced diagnostic testing shortages, requiring difficult decisions to be made regarding who receives a test, without knowing the implications of those decisions on population-level transmission dynamics. Clinical prediction rules (CPRs) are commonly used tools to guide clinical decisions. We used data from electronic health records to develop a parsimonious 5-variable CPR to identify those who are most likely to test positive, and found that its application to prioritize testing increases the proportion of those testing positive in settings of limited testing capacity. To consider the implications of these gains in daily case detection on the population level, we incorporated testing using the CPR into a compartmentalized disease transmission model. We found that prioritized testing led to a delayed and lowered infection peak (i.e. 'flattens the curve'), with the greatest impact at lower values of the effective reproductive number (such as with concurrent social distancing measures), and when higher proportions of infectious persons seek testing. Additionally, prioritized testing resulted in reductions in overall infections as well as hospital and intensive care unit (ICU) burden. In conclusion, we present a novel approach to evidence-based allocation of limited diagnostic capacity, to achieve public health goals for COVID-19.

Influence of sea ice dynamics on population energetics of Western Hudson Bay polar bears.

The Arctic marine ecosystem has experienced extensive changes in sea ice dynamics, with significant effects on ice-dependent species such as polar bears (Ursus maritimus). We used annual estimates of the numbers of bears onshore in the core summering area, age/sex structure and body condition data to estimate population energy density and storage energy in Western Hudson Bay polar bears from 1985 to 2018. We examined intra-population variation in energetic patterns, temporal energetic trends and the relationship between population energetics and sea ice conditions. Energy metrics for most demographic classes declined over time in relation to earlier sea ice breakup, most significantly for solitary adult females and subadult males, suggesting their greater vulnerability to nutritional stress than other age/sex classes. Temporal declines in population energy metrics were related to earlier breakup and longer lagged open-water periods, suggesting multi-year effects of sea ice decline. The length of the open-water period ranged from 102 to 166 days and increased significantly by 9.9 days/decade over the study period. Total population energy density and storage energy were significantly lower when sea ice breakup occurred earlier and the lagged open-water period was longer. At the earliest breakup and a lagged open-water period of 180 days, population energy density was predicted to be 33% lower than our minimum estimated energy density and population storage energy was predicted to be 40% lower than the minimum estimated storage energy. Consequently, over the study, the total population energy density declined by 53% (mean: 3668 ± 386 MJ kg-1/decade) and total population storage energy declined by 56% (mean: 435900 ± 46770 MJ/decade). This study provides insights into ecological mechanisms linking population responses to sea ice decline and highlights the significance of maintaining long-term research programs.