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Population models developed for Gammarus take into account species phenology . Today, virtual population analysis (VPA) refers to a family of methods that.
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The sensitivity analysis of periodic matrix models. Chapman, F. Handbook of Birds of Eastern North America. Applet on, New York. Cushing, J. Nonlinear matrix models and population dynamics. Natural Resource Modeling 2: — DeAngelis, D.

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Svoboda, S. Christensen, and D.

Virtual Population Analysis - A Practical Manual for Stock Assessment

Stability and return times of Leslie matrices with density-dependent survival: Applications to fish populations. Ecological Modelling 8: — Dennis, B. Desharnais, J. Cushing, and R. Nonlinear demographic dynamics: Mathematical models, statistical methods, and biological experiments. Ecological Monographs — Getz, W. Princeton University Press, Princeton, N. Goodman, L. On the reconciliation of mathematical theories of population growth. Journal of the Royal Statistical Society A — Guckenheimer, J.

Oster, and A. The dynamics of density dependent population models.

What is Population Pharmacokinetic (popPK) Analysis?

Journal of Mathematical Biology 4: — Hale, J. Dynamics and Bifurcations. Springer-Verlag, New York. Hartshorn, G. A matrix model of tree population dynamics. Golley and E. Medina, eds. Horn, R. Matrix Analysis. Cambridge University Press. Keyfitz, N. Reconciliation of population models: Matrix, integral equation and partial fraction. Journal of the Royal Statistical Society A 61— Introduction to the mathematics of population. Addison-Wesley, Reading, Mass. While popPK methods can, and often are, applied to rich data, the real value of popPK lies in its ability to analyze clinical data collected in a setting where rich data are not practical, such as in Phase 2 and 3 trials.

PopPK tends to use rather complex mathematical and compartmental methods to reach conclusions. Because of the technical constraints of popPK model development and optimization, popPK approaches often take considerably longer than NCA methods. By integrating covariate information e. Understanding PK variability is vitally important because drug safety and effectiveness can vary with changes in PK. Using the information provided by the popPK model, appropriate dosages can be selected for a given population or subgroup.

Population PK modeling and simulation can help drive decision making at all stages of drug development model-based drug development. Applications of popPK models include:. They provide an integrated assessment of PK and explain variability in PK due to covariates.

Pack: Matrix Population Model construction and analysis pack

Understanding variability in PK is important to guide optimal dosing in subpopulations and to support critical drug development decisions. Because of the growing emphasis placed on popPK analyses by regulatory authorities, not to mention the wealth of information that these analyses provide, it is more important than ever to consider how popPK fits into your own drug development program.

Consider the following questions: Do you need to make quick but informed dosing decisions based upon interim PK data e. Do you want detailed, subject-level PK profiles and calculated mean PK parameters within a single study? Accurate statistical models with manageable financial costs and field efforts are needed for hunted populations and using age-at-harvest data may be the most practical foundation for these models.

Several rigorous statistical approaches that use age-at-harvest and other data to accurately estimate populations have recently been developed, but these are often dependent on a accurate prior knowledge about demographic parameters of the population, b auxiliary data, and c initial population size. We developed a two-stage state-space Bayesian model for a black bear Ursus americanus population with age-at-harvest data, but little demographic data and no auxiliary data available, to create a statewide population estimate and test the sensitivity of the model to bias in the prior distributions of parameters and initial population size.

Single species population model - stability and bifurcation

The posterior abundance estimate from our model was similar to an independent capture-recapture estimate from tetracycline sampling and the population trend was similar to the catch-per-unit-effort for the state. Our model was also robust to bias in the prior distributions for all parameters, including initial population size, except for reporting rate.

Integrated Population Models | American Ornithological Society Journals | Oxford Academic

Our state-space model created a precise estimate of the black bear population in Wisconsin based on age-at-harvest data and potentially improves on previous models by using little demographic data, no auxiliary data, and not being sensitive to initial population size. Population estimates are essential for making decisions about management and conservation of many species 1 , 2 , but often are difficult or expensive to obtain across large geographical scales 2 , 3.

This is particularly true of mammalian carnivores 4 , 5 , which are cryptic and difficult to count directly 6 , 7 , 8. Consequently, carnivore managers often base their population estimates on extrapolations from small data sets and adjust harvest quotas based on subjective opinion from the public and experts 9. The importance and challenges of estimating wildlife populations has led to many different estimation methods 2 , 10 , and more are developed each decade e. For hunted populations, models using age-at-harvest data are often most practical, especially when working with a population across large scales when other methods of collecting data are difficult 2 , Several rigorous statistical approaches, including both frequentist and Bayesian statistics, have recently been developed that use age-at-harvest and integrate auxiliary data usually other harvest or demographic data to accurately estimate populations 3 , 11 , 12 , To date there has not been a model developed that creates accurate estimates without integrating auxiliary data, which makes it necessary for large field projects to collect demographic data.

Bayesian state-space models may be able to accomplish this, as one of their main strengths is that they appropriately use regularization to share information across space and time in the model 11 , and may efficiently use all available data compared to other modeling approaches Bayesian models can improve upon deterministic methods by being less reliant on prior information and allowing variation in parameters over time. Deterministic methods can sometimes be limited in accuracy 11 , 14 , because they rely on assumptions that demographic parameters are stable over time e. The Bayesian state-space modelling approach allows the modeler to transparently provide biologically supported information and constraints on parameters as priors, but the models use these as a starting point and the posterior values are not dependent on the prior values provided.


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Bayesian state-space models are also similar to stochastic population models, in that they reduce potential bias by allowing the demographic parameters to vary over time 3 , Bayesian state-space models also allow for a range of information in parameters, from completely informative parameters similar to a deterministic accounting model to uninformative parameters similar to frequentist approaches, formalizing a process to transparently accommodate expert opinion when estimating wildlife populations. Drawbacks of Bayesian models is that they can be more complex and difficult to comprehend and more computationally intensive to implement than simpler models.

Their implementation, however, could result in better decision-making about populations and harvest quotas, and lead to more effective monitoring and management, particularly for cryptic species. Black bears Ursus americanus are a K-selected e. Black bears are a widely distributed species across North America, with many populations expanding in recent years In Wisconsin, black bears are a widespread game animal whose population and harvest have increased over the last few decadess 22 , 23 Fig.

Most black bears in Wisconsin are found in the northern half of the state, but the population has been expanding southward in recent years.


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This is mainly due to the inability of the deterministic model to account for variation in harvest and population demographics over time and because the model incorrectly assumes a linear relationship between independent bear abundance estimates from bait stations and population abundance Independent population estimates have allowed the WDNR to more accurately assess the black bear population in the state 22 , but these are expensive and often conducted years apart.

Consequently, there is a need to update the population models in Wisconsin, as well as in many other states and jurisdictions. The number of harvested black bears in Wisconsin from —, with no bear harvest in The number of harvested bears in each county is noted by a different color. K-selected species, including black bears, are susceptible to over-harvest 25 , and management agencies need to carefully track populations when setting harvest quotas and goals. Bayesian state-space models may be ideal for estimating wildlife populations 13 , but have been used less frequently by wildlife managers to date but see 11 , Our goal was to create and evaluate a Bayesian state-space model using age-at-harvest data to estimate the statewide abundance of black bears in Wisconsin.

Our study focused on the black bear population for the entire state of Wisconsin Fig. Most of the bear population is in the northern half of Wisconsin hunting zones A, B, and D , and each zone has unique quotas and hunting regulations Over the course of our study the bear season began on the first Wednesday after Labor Day and was open for 35 days.

Our methods were carried out in accordance with approved guidelines from the WDNR and University of Wisconsin, because we only performed analyses of harvest data did not include any experimental protocols or handling of animals. The data used for analyses in this manuscript are available within the manuscript and associated supplementary material. Study area of Wisconsin in gray, and quasi-study area of the northern mixed forest ecotone.

We used the quasi-study area to restrict the scope of the literature review of black bear studies to develop appropriate prior distributions for demographic parameters. The figure was created with ArcGIS We used reasonably informative prior distributions for the model parameters. Because information from Wisconsin for such prior distributions was sparse, we relied on studies from surrounding areas.

To limit potential bias due to variation between Wisconsin and other study areas e.