Moving forward in circles: challenges and opportunities in modelling population cycles

Population cycling is a widespread phenomenon, observed across a multitude of taxa in both laboratory and natural conditions. Historically, the theory associated with population cycles was tightly linked to pairwise consumer–resource interactions and studied via deterministic models, but current empirical and theoretical research reveals a much richer basis for ecological cycles. Stochasticity and seasonality can modulate or create cyclic behaviour in non-intuitive ways, the high-dimensionality in ecological systems can profoundly influence cycling, and so can demographic structure and eco-evolutionary dynamics. An inclusive theory for population cycles, ranging from ecosystem-level to demographic modelling, grounded in observational or experimental data, is therefore necessary to better understand observed cyclical patterns. In turn, by gaining better insight into the drivers of population cycles, we can begin to understand the causes of cycle gain and loss, how biodiversity interacts with population cycling, and how to effectively manage wildly fluctuating populations, all of which are growing domains of ecological research

A nonsmooth two-sex population model

This paper considers a two-dimensional logistic model to study populations with two genders. The growth behavior of a population is guided by two coupled ordinary differential equations given by a non-differentiable vector field whose parameters are the secondary sex ratio (the ratio of males to females at time of birth), inter-, intra- and outer-gender competitions, fertility and mortality rates and a mating function. For the case where there is no inter-gender competition and the mortality rates are negligible with respect to the density-dependent mortality, using geometrical techniques, we analyze the singularities and the basin of attraction of the system, determining the relationships between the parameters for which the system presents an equilibrium point. In particular, we describe conditions on the secondary sex ratio and discuss the role of the average number of female sexual partners of each male for the conservation of a two-sex species.Comment: 18 pages, 6 figures. Section 2, in which the model is presented, was rewritten to better explain the elements of the proposed model. The description of parameter "r" was correcte

A Guide to Global Population Projections

Interdisciplinary studies that draw on long-term, global population projections often make limited use of projection results, due at least in part to the historically opaque nature of the projection process. We present a guide to such projections aimed at researchers and educators who would benefit from putting them to greater use. Drawing on new practices and new thinking on uncertainty, methodology, and the likely future courses of fertility and life expectancy, we discuss who makes projections and how, and the key assumptions upon which they are based. We also compare methodology and recent results from prominent institutions and provide a guide to other sources of demographic information, pointers to projection results, and an entry point to key literature in the field.forecasting, population projections, projection methodology, uncertainty

Critical Review of the Literature on Marine Mammal Population Modelling

A comprehensive literature review and modeling effort have been conducted in order to determine which vital rates are most important to determining the growth and sustainability of marine mammal populations. Also addressed are the impacts of life-history, ecological, and genetic variation on vital rates and population sustainability and how much each vital parameter can change before a change in population trend would be expected. Additionally, the influence of ecological energetics and foraging strategies on vital rates and their limits of sustainable change are examined, and the nature of how an increase in sound in the marine environment might influence marine mammal behavior, and thus life functions, vital rates and population sustainability is explored. An analysis of the elasticity and sensitivity of marine mammal population models suggests that: 1) Most whale populations appear to be most sensitive to changes in adult female survival and least sensitive to calf survival. 2) Most whale populations appear to be secondarily sensitive to changes in juvenile survival and growth. 3) Most whale populations, with the exception of North Atlantic right whales (Eubalaena glacialis), appear to be insensitive to changes in fecundity at any age. 4) Adult female whales may be sensitive to changes in foraging success that limit their ability to acquire sufficient body stores of energy to sustain gestation, parturition, and lactation. 5) These results are similar to those arising from studies of non-mammalian marine predators as well as terrestrial vertebrates with similar life history characteristics. A risk assessment of the potential impacts of ocean noise on marine mammal populations based on modeling marine mammal populations suggests that: 1) Any increase in anthropogenic noise in the marine environment that reduces adult female survival, for whatever reason, is to be avoided, 2) It may be impossible to detect the impact of a change in a population vital rate on population growth because such a change may be less than the confidence interval around the estimates of the rate of growth of most marine mammal populations. 3) Sensitivity and elasticity analyses of marine mammal population models predict linear changes in marine mammal population growth rates caused by linear changes in vital rates, and do not indicate thresholds within which vital rates can change without altering population growth rates. Future research efforts should focus on the following: 1) The relationship between noise in the marine environment and adult female and juvenile survival. 2) To increase the precision and decrease the uncertainty of marine mammal population and vital rate estimates. 3) Improving the concept of potential biological removal (PBR) to reflect cumulative mortality impacts and to incorporate the effects of noise. 4) Increasing knowledge of marine mammal activity budgets seasonally and in different parts of their habitats. 5) To more fully elucidate the roles of marine mammals in their ecosystems, and their importance as sentinels of ecosystem health. 6) To exhaustively utilize existing data and models because of the cost and difficulty of gathering more data

Climate change, phenological shifts, eco-evolutionary responses and population viability: toward a unifying predictive approach

The debate on emission targets of greenhouse gasses designed to limit global climate change has to take into account the ecological consequences. One of the clearest ecological consequences is shifts in phenology. Linking these shifts to changes in population viability under various greenhouse gasses emission scenarios requires a unifying framework. We propose a box-in-a-box modeling approach that couples population models to phenological change. This approach unifies population modeling with both ecological responses to climate change as well as evolutionary processes. We advocate a mechanistic embedded correlative approach, where the link from genes to population is established using a periodic matrix population model. This periodic model has several major advantages: (1) it can include complex seasonal behaviors allowing an easy link with phenological shifts; (2) it provides the structure of the population at each phase, including the distribution of genotypes and phenotypes, allowing a link with evolutionary processes; and (3) it can incorporate the effect of climate at different time periods. We believe that the way climatologists have approached the problem, using atmosphere–ocean coupled circulation models in which components are gradually included and linked to each other, can provide a valuable example to ecologists. We hope that ecologists will take up this challenge and that our preliminary modeling framework will stimulate research toward a unifying predictive model of the ecological consequences of climate change

Northern bobwhite brood ecology and population dynamics in southwest Missouri

Northern bobwhite (Colinus virginianus) have experienced widespread, long-term population declines. Bobwhite populations in Missouri have declined 2.7% annually between 1966 and 2015, and 3.5% annually between 2005 and 2015, for a cumulative loss of 80% since 1966. Maintaining healthy populations requires a better understanding of how population growth and vital rates across seasons are affected by habitat and land management practices. We examined bobwhite brood ecology and population dynamics in southwest Missouri. My dissertation objectives were to: (1) Examine the influence of cover type, management, and weather on juvenile bobwhite body condition; (2) Estimate bobwhite juvenile survival from hatch as a function of herbaceous cover, habitat management practices, woody vegetation structure, and landscape patterns; (3) Determine population-level bobwhite brood resource selection patterns for managed grasslands and agricultural habitat; and (4) Estimate site-specific bobwhite fecundity, seasonal age- and sex-specific survival, and the relative contributions of these vital rates to trends in abundance. Among our five study sites, Wade and June Shelton Memorial Conservation Area, Stony Point Prairie Conservation Area, and Wah'Kon-Tah Prairie are native grasslands ranging in size from 320 to 3030 acres. These sites were considered extensively managed, with fire, grazing, mowing and haying implemented to maintain continuous tracts of native grasslands. By contrast, Robert E. Talbot and Shawnee Trail conservation areas (3635–4361 acres) are intensively managed sites. In addition to grassland habitats, both of these areas incorporated small units of agriculture, food plots, and woody vegetation strips for wildlife use. We used radio telemetry and brood capture data to evaluate the influence of habitat management on juvenile body condition, survival, and brood habitat selection patterns. Brood attending adults were tracked daily from nest hatch to brood capture at approximately 3-weeks old. On capture, juveniles were fitted with transmitters and observed through the life of the bird or the life of the transmitter. Habitat was characterized using maps of herbaceous cover (native- mixed- and cool-season grasslands, and agricultural cover), management activities (prescribed burning, conservation grazing, mowing/haying), and woody vegetation structure (shrub and tree cover). To evaluate environmental influencers on bobwhite juvenile body condition, we captured 216 individuals from 33 broods >16-days old across our study sites in 2017 and 2018. We used the residuals from a linear regression of tarsus length and body mass as an index of body condition in a generalized linear mixed model evaluating effects of season, weather, and habitat. We found some support for improved body condition early in the breeding season, under warmer average temperatures, and in native grasslands that were burned and grazed in the previous two years. We estimated bobwhite juvenile survival based on observations of 705 individuals from 75 broods for a total of 14,904 exposure days. This included 493 individuals observed from hatch to capture and 212 radio-tagged individuals. We estimated 28.6% 114-day period survival for juvenile bobwhite 2016–2018. Survival was highest on native grasslands burned and grazed at least once in the previous two years and survival increased with local shrub cover. Local agricultural cover also improved survival, however landscape interactions suggest survival is low in small units of cultivated crops surrounded by grasslands or woody vegetation. We evaluated patterns in brood resource selection and the effects of those choices on brood survival using integrated step selection analysis. We quantified resource selection behavior of 101 bobwhite broods by comparing each of 2,788 chosen daily steps to 10 random available steps not taken. Consistent with our body condition and survival results, native grasslands that were burned and grazed at least once in the previous two years had the highest relative probability of use. Selection for idle native grasslands increased with age. We also found selection influenced brood success; broods that succeeded were more likely to choose available habitats with more shrub cover, while failed broods avoided available habitats with more shrub cover. Successful broods also selected areas farther from trees than failed broods. To quantify full annual cycle population dynamics in an integrated population model, we tracked 766 juveniles and 618 adults during the breeding season, we tracked 772 juveniles and 349 adults during the non-breeding season, we monitored success of 276 nests incubated among 576 adults, and conducted whistle counts in May 2016–2018. Talbot Conservation Area had the lowest population growth rate ([lambda]TAL = 0.31, 95% CRI: 0.03, 0.65), due to low fecundity and summer adult survival. Shelton Memorial Conservation Area had low estimated breeding season juvenile survival, non-breeding season survival, and the second lowest population growth rate ([lambda]SLT = 0.37, 95% CRI: 0.00, 0.74), possibly due to its small area (320 acres) and low bobwhite density. Stony Point Prairie had high fecundity and adult breeding season survival probabilities, but the lowest non-breeding season survival among all sites, which depressed population growth ([lambda]STP = 0.51 95% CRI: 0.08, 0.85). Extensive native grasslands had consistently higher fecundity and adult summer survival probabilities than intensively managed conservation areas. Wah'Kon-Tah Prairie, our largest extensively managed site, had the highest population growth rate ([lambda]WKT = 0.55, 95% CRI: 0.13, 0.94). We found declining population trends on all conservation areas. Non-breeding season survival from 1 November to 30 April was most strongly correlated with abundance, followed by juvenile breeding season survival. Greater, less variable non-breeding season survival is required to achieve population stability. Further evaluation of intra-annual environmental influencers and the relationship between habitat area and population viability would better inform bobwhite management approaches. Important next steps in this research include examining finer temporal scales that separately evaluate breeding, winter, and transitional periods in the annual cycle. Additionally, effects of weather and climate on population viability will be important considerations as Missouri experiences warmer temperatures and potentially extreme changes in precipitation patterns. Finally, this study generated valuable data that can be used to simulate regional population trends and projections across the surrounding landscape.Includes bibliographical reference

Mammography Utilization in African American Women

Purpose: Breast cancer presents differently among women causing breast cancer health disparities with women of color disproportionally shouldering later-stage screening, incidence, and treatment, and greater mortality. This study assessed 10 predictors and rates of recent and long-term mammography utilization for women 43-79 years of age to better understand differences among age strata and races. This was the first study to use both the calculated Gail Risk scores (calculates absolute breast cancer risk over time intervals) from the 2010 National Health Interview Survey (NHIS) and a temporary homelessness variable in predicting mammography utilization using national-level data. Theoretical Framework: A modified Behavioral Model for Vulnerable Populations guided this study and provided a unique and well-established framework in evaluating vulnerable population domains and ethnicities. Methods: Secondary data analysis of 2010 NHIS data was completed, that included a Cancer Control Module (cancer control questions), which is incorporated into the NHIS every five years. Using logistic regression, N= 6,334; n=1,141 for African American (AA) was used to examine mammography utilization differences between and among age strata and races (AA, Non-Hispanic White, and Hispanic), with focus on younger AA women in their 40s. Wald F test statistics with two-sided p-values Results:AA had the highest (79.3%) of lowest risk Gail Risk scores, while Whites had the highest (30.7%) of highest risk Gail Risk scores. There was no statistically significant difference in Gail Risk scores by race on recent, Wald F(2, 299)=1.76, p=0.18, and long-term Wald F(2, 299)-0.58, p=0.56. Women in the 50-64 age strata had greater odds of both recent, Wald F(2, 299)=7.52, p Significance to Nursing: Risk assessment and mammography are vital prevention modalities in mitigating breast cancer health disparities. It is important for women to know their risk and for continued testing of predictor interactions to improve mammography knowledge and practice

Mathematical Modeling, Analysis and Simulation of COVID-19 Dynamics

COVID-19 is an infectious disease caused by the SAR-COV-2 virus. Globally, as of 21 February 2023, there have been 757,264,511 confirmed cases of COVID-19, including 6,850,594 deaths, reported to the World Health Organization (WHO). \cite{WHO} The disease dynamics have evolved considerably since the initial outbreak in Wuhan, China with multiple variants, diverse public health measures and shifting public perception. Various public health measures have been implemented in order to slow the spread of including; social distancing, masking and several vaccines have been developed and granted emergency use authorization to help quell the spread of COVID-19. \cite{vaxreview}Since the onset of the coronavirus pandemic, researchers have been formulating mathematical models to gain insight into the complex dynamics of disease.In this talk, a model is proposed to study Coronavirus Disease 2019 (COVID-19) with the effect of vaccination with waning immunity. We also consider how hospitalization and COVID-19 specific deaths effect the disease dynamics. Our deterministic model is formulated by a system of ordinary differential equations (ODEs) that is built upon the classical SEIR framework. The local and global dynamics of the disease are analyzed by using the deterministic model with a time dependent vaccination parameter, and the result indicates that the basic reproduction number $\mathcal{R}_0$ serves as a valid disease threshold. Globally the disease dies out if $\mathcal{R}_0 1$. The time dependent vaccination parameter was modeled after the historical vaccination trends. Our results indicate that both the exposed and infected classes as well as vaccination play an important role in shaping the epidemic dynamics of COVID-19.