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I present a dynamic bioenergetic model that couples individual energetics and population dynamics to predict current lizard ranges and those following climate warming. The model predictions are uniquely based on first principles of morphology, life history, and thermal physiology. I apply the model to five populations of a widespread North American lizard,Sceloporus undulatus, to examine how geographic variation in traits and life histories influences ranges. This geographic variation reflects the potential for species to adapt to environmental change. I then consider the range dynamics of the closely relatedSceloporus graciosus. Comparing predicted ranges and actual current ranges reveals how dispersal limitations, species interactions, and habitat requirements influence the occupied portions of thermally suitable ranges. The dynamic model predicts individualistic responses to a uniform 3°C warming but a northward shift in the northern range boundary for all populations and species. In contrast to standard correlative climate envelope models, the extent of the predicted northward shift depends on organism traits and life histories. The results highlight the limitations of correlative models and the need for more dynamic models of species’ ranges.

OBJECTIVE Few methods are available for analyzing populations with changing rates. Here hyperstable models are presented and substantially extended to facilitate such analyses. METHODS Hyperstable models, where a known birth trajectory yields a consistent set of age-specific birth rates, are set out in both discrete and continuous form. Mathematical analysis is used to find new relationships between model functions for a range of birth trajectories. RESULTS Hyperstable population projection matrices can create bridges that project any given initial population to any given ending population. New, explicit relationships are found between period and cohort births for exponential, polynomial, and sinusoidal birth trajectories. In quadratic and cubic models, the number of cohort births equals the number of period births a generation later, with a modest adjustment. In sinusoidal models, cohort births equal the number of period births a generation later, modified by a factor related to cycle length. CONTRIBUTION Because of their adaptability, structure, and internal relationships, hyperstable birth models afford a valuable platform for analyzing populations with changing fertility. The new relationships found provide insight into dynamic models and period-cohort connections and offer useful applications to analysts.

State-space estimation methods are increasingly used in ecology to estimate productivity and abundance of natural populations while accounting for variability in both population dynamics and measurement processes. However, functional forms for population dynamics and density dependence often will not match the true biological process, and this may degrade the performance of state-space methods. We therefore developed a Bayesian semiparametric state-space model, which uses a Gaussian process (GP) to approximate the population growth function. This offers two benefits for population modeling. First, it allows data to update a specified \"prior\" on the population growth function, while reverting to this prior when data are uninformative. Second, it allows variability in population dynamics to be decomposed into random errors around the population growth function (\"process error\") and errors due to the mismatch between the specified prior and estimated growth function (\"model error\"). We used simulation modeling to illustrate the utility of GP methods in state-space population dynamics models. Results confirmed that the GP model performs similarly to a conventional state-space model when either (1) the prior matches the true process or (2) data are relatively uninformative. However, GP methods improve estimates of the population growth function when the function is misspecified. Results also demonstrated that the estimated magnitude of \"model error\" can be used to distinguish cases of model misspecification. We conclude with a discussion of the prospects for GP methods in other state-space models, including age and length-structured, meta-analytic, and individual-movement models.

Many wildlife monitoring programmes collect annual data on population abundance. The resulting abundance estimates fluctuate over time partly because of true population change and partly because of observation error. These two components of variation can be separated by fitting the estimates to a population dynamics model within a Bayesian state-space modelling framework. By constraining the population trajectory to be biologically realistic, more precise estimates can be obtained. Independent biological knowledge can be incorporated through choice of model structure and by specifying informative prior distributions on demographic parameters. We illustrate the approach using a 31-year point transect study of the Hawai’i ’ākepa (Loxops coccineus). We fitted five models, each making different assumptions about how population change, recruitment and/or adult survival varied over time. Overall, the ’ākepa geometric mean growth rate was 1.02, indicating an increasing population over the 31-year time series, although there were periods of slow decline potentially associated with low recruitment and more rapid recovery associated with pulses of high recruitment. Abundance estimates derived from the population models were substantially more precise than the ‘raw’ point transect estimates: 95% credible interval (CrI) was on average 51.7% (s.d. = 14.1%) narrower.

We propose a coupled system of delay-algebraic equations to describe tick attaching and host grooming behaviors in the tick-host interface, and use the model to understand how this tick-host interaction impacts the tick population dynamics. We consider two critical state variables, the loads of feeding ticks on host and the engorged ticks on the ground for ticks in a particular development stage (nymphal stage) and show that the model as a coupled system of delay differential equation and an algebraic (integral) equation may have rich structures of equilibrium states, leading to multi-stability. We perform asymptotic analyses and use the implicit function theorem to characterize the stability of these equilibrium states, and show that bi-stability and quadri-stability occur naturally in several combinations of tick attaching and host grooming behaviours. In particular, we show that in the case when host grooming is triggered by the tick biting, the system will have three stable equilibrium states including the extinction state, and two unstable equilibrium states. In addition, the two nontrivial stable equilibrium states correspond to a low attachment rate and a large number of feeding ticks, and a high attachment rate and a small number of feeding ticks, respectively.

Hundreds of species are shifting their ranges in response to recent climate warming. To predict how continued climate warming will affect the potential, or “bioclimatic range,” of a skipper butterfly, we present a population‐dynamic model of range shift in which population growth is a function of temperature. We estimate the parameters of this model using previously published data forAtalopedes campestris. Summer and winter temperatures affect population growth rate independently in this species and therefore interact as potential range‐limiting factors. Our model predicts a two‐phase response to climate change; one range‐limiting factor gradually becomes dominant, even if warming occurs steadily along a thermally linear landscape. Whether the range shift accelerates or decelerates and whether the number of generations per year at the range edge increases or decreases depend on whether summer or winter warms faster. To estimate the uncertainty in our predictions of range shift, we use a parametric bootstrap of biological parameter values. Our results show that even modest amounts of data yield predictions with reasonably small confidence intervals, indicating that ecophysiological models can be useful in predicting range changes. Nevertheless, the confidence intervals are sensitive to regional differences in the underlying thermal landscape and the warming scenario.

In this paper, we aim to investigate the influence of delay on the global attractivity of a tick population dynamics model incorporating two distinctive time-varying delays. By exploiting some differential inequality techniques and with the aid of the fluctuation lemma, we first prove the persistence and positiveness for all solutions of the addressed equation. Consequently, a delay-dependent criterion is derived to assure the global attractivity of the positive equilibrium point. And lastly, some numerical simulations are presented to verify that the obtained results improve and complement some existing ones.

Wastewater-based epidemiology is a useful approach to estimate population-level exposure to a wide range of substances (e.g., drugs, chemicals, biological agents) by wastewater analysis. An important uncertainty in population normalized loads generated is related to the size and variability of the actual population served by wastewater treatment plants (WWTPs). Here, we built a population model using location-based services (LBS) data to estimate dynamic consumption of illicit drugs. First, the LBS data from Tencent Location Big Data and resident population were used to train a linear population model for estimating population (r2 = 0.92). Then, the spatiotemporal accuracy of the population model was validated. In terms of temporal accuracy, we compared the model-based population with the time-aligned ammonia nitrogen (NH4-N) population within the WWTP of SEG, showing a mean squared error of < 10%. In terms of spatial accuracy, we estimated the model-based population of 42 WWTPs in Dalian and compared it with the NH4-N and design population, indicating good consistency overall (5% less than NH4-N and 4% less than design). Furthermore, methamphetamine consumption and prevalence based on the model were calculated with an average of 111 mg/day/1000 inhabitants and 0.24%, respectively, and dynamically displayed on a visualization system for real-time monitoring. Our study provided a dynamic and accurate population for estimating the population-level use of illicit drugs, much improving the temporal and spatial trend analysis of drug use. Furthermore, accurate information on drug use could be used to assess population health risks in a community.

The fractional exponential function is considered. General expansions in fractional powers are used to solve fractional population dynamics problems. Laguerretype exponentials are also considered, and an application to Laguerre-type fractional logistic equation is shown.

Diabetes mellitus (DM) is rising worldwide, exacerbated by aging populations. We estimated and predicted the diabetes burden and mortality due to undiagnosed diabetes together with screening program efficacy and reporting completeness in Thailand, in the context of demographic changes. An age and sex structured dynamic model including demographic and diagnostic processes was constructed. The model was validated using a Bayesian Markov Chain Monte Carlo (MCMC) approach. The prevalence of DM was predicted to increase from 6.5% (95% credible interval: 6.3–6.7%) in 2015 to 10.69% (10.4–11.0%) in 2035, with the largest increase (72%) among 60 years or older. Out of the total DM cases in 2015, the percentage of undiagnosed DM cases was 18.2% (17.4–18.9%), with males higher than females (p-value < 0.01). The highest group with undiagnosed DM was those aged less than 39 years old, 74.2% (73.7–74.7%). The mortality of undiagnosed DM was ten-fold greater than the mortality of those with diagnosed DM. The estimated coverage of diabetes positive screening programs was ten-fold greater for elderly compared to young. The positive screening rate among females was estimated to be significantly higher than those in males. Of the diagnoses, 87.4% (87.0–87.8%) were reported. Targeting screening programs and good reporting systems will be essential to reduce the burden of disease.