Prospectus, March 27, 1973

PC TO HOST WORKSHOP; \u27Clean\u27; Be a Bridgie!; Gang Night; Here and there with Parkland volunteers; Cruisin\u27 \u2773; True happenings; Letters To The Editor; A challenge; Candidate for PC board of trustees; IRS job openings; The genuine free Prospectus gasoline anti-ripoff charts; Candidates For Day Senator; Parkland Board Summary; PC bowling team roll-off today; 383 students on winter honors list; Community service fund guidelines completed; Prof Spectus; Number, please?; PC 9th in national indoor contest; Bicycles Bicyles Bicycles; Roller skating party; Magazines As Media; Hereditary Linked To Mental Illness; New, flexible baccalaureate program; Medical fields applicationhttps://spark.parkland.edu/prospectus_1973/1009/thumbnail.jp

Prospectus, April 25, 1973

NEW STUGO REPRESENTATIVES; 4-day nutrition workshop; Student\u27s views sought; Broken Hearts; Junior college visitation day; Student to give report to Academy; May elected chairman of nurse ass\u27n; Day Senator: Brenda Kendricks; Day Senator: Earnest Hite; Day Senator: Ken Segan; Convocations: Bill Tigrak; United Farm Workers organize boycotts; To the Editor; Brenda and Leroy; Judging teams; Festival; haiku; poem; incentive; Women welcome!; AAUW Scholarship awarded; Bridge tourney; bullet; Magical Mystery Tour: A quickie visit to Parkland\u27s new campus; What would you like to know about the new campus?; Prof Spectus; \u27How dare you presume I\u27m straight?\u27 Notes of a lesbian; PC bowlers romp to victory in 1st central Illinois tourney; From above an athlete\u27s feet; What\u27s decent to eat?; Baseballers win three of four games; Track team has high hopes; Changes in PC athletics; Thinclads take third; Wrestlinghttps://spark.parkland.edu/prospectus_1973/1008/thumbnail.jp

Prospectus, May 10, 1973

STUDENT GOVERNMENT ELECTIONS; Frank P. Hansbrough for presidency; Brenda Kendricks for presidency; Sangamon State rep to visit U. of I.; GE to hire more minorities; Tom Hamilton for the treasury; Larry J. Cotton for the V. presidency; BSA Scholarship; Mark Mumm for the V. Presidency; Karen Coleman for the treasury; U. of I. to discuss PC; Cruisin\u27 \u2773; Trye happenings; Open letter to Dan Walker; you kiss her when she snatches your head...; Movie Review: Lady Sings the Blues; Ceremonies in Dark Old Men; Violent crimes up; From above an athlete\u27s feet: Spring is baseball season, Rain ain\u27t all that bad, PC wins at Kansas Relays, PC runs at Vincennes; La Hora De Los Hornoshttps://spark.parkland.edu/prospectus_1973/1007/thumbnail.jp

Matrix models and sensitivity analysis of populations classified by age and stage : a vec-permutation matrix approach

© The Author(s), 2011. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Theoretical Ecology 5 (2012): 403-417, doi:10.1007/s12080-011-0132-2.Matrix population models in which individuals are classified by both age and stage can be constructed using the vec-permutation matrix. The resulting age-stage models can be used to derive the age-specific consequences of a stage-specific life history or to describe populations in which the vital rates respond to both age and stage. I derive a general formula for the sensitivity of any output (scalar, vector, or matrix-valued) of the model, to any vector of parameters, using matrix calculus. The matrices describing age-stage dynamics are almost always reducible; I present results giving conditions under which population growth is ergodic from any initial condition. As an example, I analyze a published stage-specific model of Scotch broom (Cytisus scoparius), an invasive perennial shrub. Sensitivity analysis of the population growth rate finds that the selection gradients on adult survival do not always decrease with age but may increase over a range of ages. This may have implications for the evolution of senescence in stage-classified populations. I also derive and analyze the joint distribution of age and stage at death and present a sensitivity analysis of this distribution and of the marginal distribution of age at death.This research was supported by National Science Foundation Grant DEB-0816514 and by a Research Award from the Alexander von Humboldt Foundation

Sensitivity analysis of periodic matrix population models

Author Posting. © The Author(s), 2012. This is the author's version of the work. It is posted here by permission of Elsevier B.V. for personal use, not for redistribution. The definitive version was published in Theoretical Population Biology 82 (2012): 329-339, doi:10.1016/j.tpb.2012.03.008.Periodic matrix models are frequently used to describe cyclic temporal variation (seasonal or interannual) and to account for the operation of multiple processes (e.g., demography and dispersal) within a single projection interval. In either case, the models take the form of peri- odic matrix products. The perturbation analysis of periodic models must trace the e ects of parameter changes, at each phase of the cycle, on output variables that are calculated over the entire cycle. Here, we apply matrix calculus to obtain the sensitivity and elasticity of scalar-, vector-, or matrix-valued output variables. We apply the method to linear models for periodic environments (including seasonal harvest models), to vec-permutation models in which individ- uals are classi ed by multiple criteria, and to nonlinear models including both immediate and delayed density dependence. The results can be used to evaluate management strategies and to study selection gradients in periodic environments.This research was supported by NSF Grant DEB-0816514, by a Research Award from the Alexander von Humboldt Foundation, and by WHOI Academic Programs Funds

Beyond R0 : demographic models for variability of lifetime reproductive output

© The Author(s), 2011. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in PLoS One 6 (2011): e20809, doi:10.1371/journal.pone.0020809.The net reproductive rate measures the expected lifetime reproductive output of an individual, and plays an important role in demography, ecology, evolution, and epidemiology. Well-established methods exist to calculate it from age- or stage-classified demographic data. As an expectation, provides no information on variability; empirical measurements of lifetime reproduction universally show high levels of variability, and often positive skewness among individuals. This is often interpreted as evidence of heterogeneity, and thus of an opportunity for natural selection. However, variability provides evidence of heterogeneity only if it exceeds the level of variability to be expected in a cohort of identical individuals all experiencing the same vital rates. Such comparisons require a way to calculate the statistics of lifetime reproduction from demographic data. Here, a new approach is presented, using the theory of Markov chains with rewards, obtaining all the moments of the distribution of lifetime reproduction. The approach applies to age- or stage-classified models, to constant, periodic, or stochastic environments, and to any kind of reproductive schedule. As examples, I analyze data from six empirical studies, of a variety of animal and plant taxa (nematodes, polychaetes, humans, and several species of perennial plants).Supported by National Science Foundation Grant DEB-0816514 and by a Research Award from the Alexander von Humboldt Foundation

Demography when history matters: construction and analysis of second-order matrix population models

History matters when individual prior conditions contain important information about the fate of individuals. We present a general framework for demographic models which incorporates the effects of history on population dynamics. The framework incorporates prior condition into the i-state variable and includes an algorithm for constructing the population projection matrix from information on current state dynamics as a function of prior condition. Three biologically motivated classes of prior condition are included: prior stages, linear functions of current and prior stages, and equivalence classes of prior stages. Taking advantage of the matrix formulation of the model, we show how to calculate sensitivity and elasticity of any demographic outcome. Prior condition effects are a source of inter-individual variation in vital rates, i.e., individual heterogeneity. As an example, we construct and analyze a second-order model of Lathyrus vernus, a long-lived herb. We present population growth rate, the stable population distribution, the reproductive value vector, and the elasticity of λ to changes in the second-order transition rates. We quantify the contribution of prior conditions to the total heterogeneity in the stable population of Lathyrus using the entropy of the stable distribution

Stochasticity, heterogeneity, and variance in longevity in human populations

Inter-individual variance in longevity (or any other demographic outcome) may arise from heterogeneity or from individual stochasticity. Heterogeneity refers to differences among individuals in the demographic rates experienced at a given age or stage. Stochasticity refers to variation due to the random outcome of demographic rates applied to individuals with the same properties. The variance due to individual stochasticity can be calculated from a Markov chain description of the life cycle. The variance due to heterogeneity can be calculated from a multistate model that incorporates the heterogeneity. We show how to use this approach to decompose the variance in longevity into contributions from stochasticity and heterogeneous frailty for male and female cohorts from Sweden (1751-1899), France (1816-1903), and Italy (1872-1899), and also for a selection of period data for the same countries. Heterogeneity in mortality is described by the gamma-Gompertz-Makeham model, in which a gamma distributed "frailty'' modifies a baseline Gompertz-Makeham mortality schedule. Model parameters were estimated by maximum likelihood for a range of starting ages. The estimates were used to construct an age×frailty-classified matrix model, from which we compute the variance of longevity and its components due to heterogeneous frailty and to individual stochasticity. The estimated fraction of the variance in longevity due to heterogeneous frailty (averaged over time) is less than 10% for all countries and for both sexes. These results suggest that most of the variance in human longevity arises from stochasticity, rather than from heterogeneous frailty