Frequency-dependent two-sex models : a new approach to sex ratio evolution with multiple maternal conditions

© The Author(s), 2016. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Ecology and Evolution 6 (2016): 6855–6879, doi:10.1002/ece3.2202.Mothers that experience different individual or environmental conditions may produce different proportions of male to female offspring. The Trivers-Willard hypothesis, for instance, suggests that mothers with different qualities (size, health, etc.) will use different sex ratios if maternal quality differentially affects sex-specific reproductive success. Condition-dependent, or facultative, sex ratio strategies like these allow multiple sex ratios to coexist within a population. They also create complex population structure due to the presence of multiple maternal conditions. As a result, modeling facultative sex ratio evolution requires not only sex ratio strategies with multiple components, but also two-sex population models with explicit stage structure. To this end, we combine nonlinear, frequency-dependent matrix models and multidimensional adaptive dynamics to create a new framework for studying sex ratio evolution. We illustrate the applications of this framework with two case studies where the sex ratios depend one of two possible maternal conditions (age or quality). In these cases, we identify evolutionarily singular sex ratio strategies, find instances where one maternal condition produces exclusively male or female offspring, and show that sex ratio biases depend on the relative reproductive value ratios for each sex.National Science Foundation Graduate Research Fellowship Grant Number: 1122374; National Science Foundation Grant Numbers: DEB1145017, DEB1257545; European Research Council Grant Number: 322989; Woods Hole Oceanographic Institution Academic Programs Offic

Calculating second derivatives of population growth rates for ecology and evolution

© The Author(s), 2014. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Methods in Ecology and Evolution 5 (2014): 473–482, doi:10.1111/2041-210X.12179.Second derivatives of the population growth rate measure the curvature of its response to demographic, physiological or environmental parameters. The second derivatives quantify the response of sensitivity results to perturbations, provide a classification of types of selection and provide one way to calculate sensitivities of the stochastic growth rate. Using matrix calculus, we derive the second derivatives of three population growth rate measures: the discrete-time growth rate λ, the continuous-time growth rate r = log λ and the net reproductive rate R0, which measures per-generation growth. We present a suite of formulae for the second derivatives of each growth rate and show how to compute these derivatives with respect to projection matrix entries and to lower-level parameters affecting those matrix entries. We also illustrate several ecological and evolutionary applications for these second derivative calculations with a case study for the tropical herb Calathea ovandensis.This work was supported by a National Science Foundation Graduate Research Fellowship under Grant 1122374, by NSF Grants DEB-1145017 and DEB1257545, and by Advanced Grant 322989 from the European Research Council

Evolutionary demography of structured two-sex populations and sex ratios

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution September 2015Males and females may differ in stage-specific survival, maturation, fertility, or mating availability. These demographic differences, in turn, affect population growth rates, equilibrium structure, and evolutionary trajectories. Models considering only a single sex cannot capture these effects, motivating the use of demographic two-sex models for sexually reproducing populations. I developed a new two-sex modeling framework that incorporates population structure and multiple life cycle processes through transition rate matrices. These models can be applied to a variety of life histories to address both ecological and evolutionary questions. Here, I apply the model to the effects of sex-biased harvest on populations with various mating systems. Demographic considerations also affect evolutionary projections. I derived matrix calculus expressions for key evolutionary quantities in my two-sex models, including the invasion fitness, selection gradient, and second derivatives of growth rates (which have many applications, including the classification of evolutionary singular strategies). I used these quantities to analyze the evolution of the primary sex ratio, under various sex- and stage-specific offspring costs and maternal conditions. Demographic two-sex models lend insight into complex, and sometimes counterintuitive, results that are not captured by models lacking population structure. These findings highlight the importance of demographic structure in ecology and evolution.This work was supported by a National Science Foundation Graduate Research Fellowship under Grant 1122374, NSF Grants DEB1145017 and DEB1257545 (to H. Caswell), Advanced Grant 322989 from the European Research Council (to H. Caswell), and theWoods Hole Oceanographic Institution Academic Programs Office

A seasonal, density-dependent model for the management of an invasive weed

Author Posting. © Ecological Society of America, 2013. This article is posted here by permission of Ecological Society of America for personal use, not for redistribution. The definitive version was published in Ecological Applications 23 (2013): 1893-1905, doi:10.1890/12-1712.1.The population effects of harvest depend on complex interactions between density dependence, seasonality, stage structure, and management timing. Here we present a periodic nonlinear matrix population model that incorporates seasonal density dependence with stage-selective and seasonally selective harvest. To this model, we apply newly developed perturbation analyses to determine how population densities respond to changes in harvest and demographic parameters. We use the model to examine the effects of popular control strategies and demographic perturbations on the invasive weed garlic mustard (Alliaria petiolata). We find that seasonality is a major factor in harvest outcomes, because population dynamics may depend significantly on both the season of management and the season of observation. Strategies that reduce densities in one season can drive increases in another, with strategies giving positive sensitivities of density in the target seasons leading to compensatory effects that invasive species managers should avoid. Conversely, demographic parameters to which density is very elastic (e.g., seeding survival, second-year rosette spring survival, and the flowering to fruiting adult transition for maximum summer densities) may indicate promising management targets.This work was supported by the National Science Foundation (grant DEB-0816514), the National Research Initiative of the USDA Cooperative State Research, Education and Extension Service (grant 05-2290), the Alexander von Humboldt Foundation, and the Academic Programs Office at WHOI

On the bioeconomics of marine reserves when dispersal evolves

Author Posting. © The Author(s), 2015. This is the author's version of the work. It is posted here by permission of John Wiley & Sons for personal use, not for redistribution. The definitive version was published in Natural Resource Modeling 28 (2015): 456-474, doi:10.1111/nrm.12075.Marine reserves are an increasingly used and potentially contentious tool in fisheries management. Depending upon the way that individuals move, no-take marine reserves can be necessary for maximizing equilibrium rent in some simple mathematical models. The implementation of no-take marine reserves often generates a redistribution of fishing effort in space. This redistribution of effort, in turn, produces sharp spatial gradients in mortality rates for the targeted stock. Using a two-patch model, we show that the existence of such gradients is a sufficient condition for the evolution of an evolutionarily stable conditional dispersal strategy. Thus, the dispersal strategy of the fish depends upon the harvesting strategy of the manager and vice versa. We find that an evolutionarily stable optimal harvesting strategy (ESOHS)—one which maximizes equilibrium rent given that fish disperse in an evolutionarily stable manner– - never includes a no-take marine reserve. This strategy is economically unstable in the short run because a manager can generate more rent by disregarding the possibility of dispersal evolution. Simulations of a stochastic evolutionary process suggest that such a short-run, myopic strategy performs poorly compared to the ESOHS over the long run, however, as it generates rent that is lower on average and higher in variability.This material is based upon work supported by funding from: The Woods Hole Oceanographic Institution's Investment in Science Fund to MGN; The Recruitment Program of Global Experts to YL; The University of Tennessee Center for Business and Economics Research to SL; and the U.S. National Science Foundation (NSF) through grants OCE-1031256, DEB-1257545, and DEB-1145017 to MGN, CNH-0707961 to GEH, DMS-1411476 to YL; and NSF Graduate Research Fellowships under Grant No. 1122374 to EAM and ES

Meconium pseudocyst secondary to ileum volvulus perforation without peritoneal calcification: a case report

<p>Abstract</p> <p>Introduction</p> <p>A case of giant meconium pseudocyst secondary to ileum volvulus perforation is presented. Conventional radiographic features of meconium peritonitis with secondary meconium pseudocyst formation are well described. Our case is unusual in comparison to other cases reported in the literature and needs to be reported because the meconium pseudocyst presented without the typical ultrasound features (calcifications, polyhydramnios and ascites) and was initially identified as an abdominal mass.</p> <p>Case presentation</p> <p>We describe the case of a 29-year-old Caucasian woman in her third trimester of pregnancy, in which an abdominal mass was detected in the fetus. The newborn was diagnosed in the early neonatal period with meconium pseudocyst secondary to ileum volvulus perforation.</p> <p>Conclusions</p> <p>The prenatal appearance of a meconium pseudocyst can be complemented by other signs of bowel obstruction (if present) such as polyhydramnios and fetal bowel dilatation. This is an original case report of interest to all clinicians in the perinatology and fetal ultrasound field. We consider that the utility of this case is the recognition that a meconium pseudocyst might appear without the typical ultrasound features and should be considered as a differential diagnosis when an echogenic intra-abdominal cyst is seen.</p

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

Supplement 1. Annotated MATLAB code for the garlic mustard time series simulations (Fig. 2), bifurcation diagrams (Figs. 3 and 5), and sensitivity analysis (Fig. 4).

<h2>File List</h2><div> <p><a href="gm_base.m">gm_base.m</a> (MD5: e7fb5521368309b82bb6de5aab9a34af)</p> <p><a href="gm_eq.m">gm_eq.m</a> (MD5: 47369b5cbd71dd1046156b5ff0d3614a)</p> <p><a href="gm_perturb.m">gm_perturb.m</a> (MD5: 3cf150712150c71d91a9c98273da1335)</p> <p><a href="padcat.m">padcat.m</a> (MD5: 983d735ada7f82d76a002ceeb2ab68f1)</p> <p><a href="rev_blkdiag.m">rev_blkdiag.m</a> (MD5: 5a944cdf632c571e23607a740d5d3b5b)</p> <p><a href="unique_no_sort.m">unique_no_sort.m</a> (MD5: 0f4724bec6aa5e951b0dfa98339a3f5f)</p> </div><h2>Description</h2><div> <p>gm_base.m - Base code to produce time series (Fig. 2) or bifurcation diagrams (Figs. 3 and 5) for the seasonal garlic mustard model.</p> <p>gm_eq.m - A slightly modified version of gm_base.m that returns all the seasonal population vectors in the seasonal 8-cycle (for the given management parameters).</p> <p>gm_perturb.m - Code to perform sensitivity analyses for the seasonal garlic mustard model (Fig. 4).</p> <p>padcat.m, rev_blkdiag.m, unique_no_sort.m - Functions used in the gm_perturb.m file.</p> </div