The mismatch between current statistical practice and doctoral training in ecology

Ecologists are studying increasingly complex and important issues such as climate change and ecosystem services. These topics often involve large data sets and the application of complicated quantitative models. We evaluated changes in statistics used by ecologists by searching nearly 20,000 published articles in ecology from 1990 to 2013. We found that there has been a rise in sophisticated and computationally intensive statistical techniques such as mixed effects models and Bayesian statistics and a decline in reliance on approaches such as ANOVA or t tests. Similarly, ecologists have shifted away from software such as SAS and SPSS to the open source program R. We also searched the published curricula and syllabi of 154 doctoral programs in the United States and found that despite obvious changes in the statistical practices of ecologists, more than one-third of doctoral programs showed no record of required or optional statistics classes. Approximately one-quarter of programs did require a statistics course, but most of those did not cover contemporary statistical philosophy or advanced techniques. Only one-third of doctoral programs surveyed even listed an optional course that teaches some aspect of contemporary statistics. We call for graduate programs to lead the charge in improving training of future ecologists with skills needed to address and understand the ecological challenges facing humanity.ECU Open Access Publishing Support Fun

Lifespan theorem for constrained surface diffusion flows

We consider closed immersed hypersurfaces in $\R^{3}$ and $\R^4$ evolving by a class of constrained surface diffusion flows. Our result, similar to earlier results for the Willmore flow, gives both a positive lower bound on the time for which a smooth solution exists, and a small upper bound on a power of the total curvature during this time. By phrasing the theorem in terms of the concentration of curvature in the initial surface, our result holds for very general initial data and has applications to further development in asymptotic analysis for these flows.Comment: 29 pages. arXiv admin note: substantial text overlap with arXiv:1201.657

Assessment of the Mate Retention Inventory-Short Form Using Item Response Theory

The mate retention inventory (MRI) has been a valuable tool in the field of evolutionary psychology for the past 30 years. The goal of the current research is to subject the MRI to rigorous psychometric analysis using item response theory to answer three broad questions. Do the individual items of the MRI fit the scale well? Does the overall function of the MRI match what is predicted? Finally, do men and women respond similarly to the MRI? Using a graded response model, it was found that all but two of the items fit acceptable model patterns. Test information function analysis found that the scale acceptably captures individual differences for participants with a high degree of mate retention but the scale is lacking in capturing information from participants with a low degree of mate retention. Finally, discriminate item function analysis reveals that the MRI is better at assessing male than female participants, indicating that the scale may not be the best indicator of female behavior in a relationship. Overall, we conclude that the MRI is a good scale, especially for assessing male behavior, but it could be improved for assessing female behavior and individuals lower on overall mate retention behavior. It is suggested that this paper be used as a framework for how the newest psychometrics techniques can be applied in order to create more robust and valid measures in the field of evolutionary psychology

Prey Responses to Predator Chemical Cues: Disentangling the Importance of the Number and Biomass of Prey Consumed

To effectively balance investment in predator defenses versus other traits, organisms must accurately assess predation risk. Chemical cues caused by predation events are indicators of risk for prey in a wide variety of systems, but the relationship between how prey perceive risk in relation to the amount of prey consumed by predators is poorly understood. While per capita predation rate is often used as the metric of relative risk, studies aimed at quantifying predator-induced defenses commonly control biomass of prey consumed as the metric of risk. However, biomass consumed can change by altering either the number or size of prey consumed. In this study we determine whether phenotypic plasticity to predator chemical cues depends upon prey biomass consumed, prey number consumed, or both. We examine the growth response of red-eyed treefrog tadpoles (Agalychnis callidryas) to cues from a larval dragonfly (Anax amazili). Biomass consumed was manipulated by either increasing the number of prey while holding individual prey size constant, or by holding the number of prey constant and varying individual prey size. We address two questions. (i) Do prey reduce growth rate in response to chemical cues in a dose dependent manner? (ii) Does the magnitude of the response depend on whether prey consumption increases via number or size of prey? We find that the phenotypic response of prey is an asymptotic function of prey biomass consumed. However, the asymptotic response is higher when more prey are consumed. Our findings have important implications for evaluating past studies and how future experiments should be designed. A stronger response to predation cues generated by more individual prey deaths is consistent with models that predict prey sensitivity to per capita risk, providing a more direct link between empirical and theoretical studies which are often focused on changes in population sizes not individual biomass

Trivial, Strongly Minimal Theories Are Model Complete After Naming Constants

We prove that if M is any model of a trivial, strongly minimal theory, then the elementary diagram Th(MM) is a model complete LM-theory. We conclude that all countable models of a trivial, strongly minimal theory with at least one computable model are 0 -decidable, and that the spectrum of computable models of any trivial, strongly minimal theory is Σ05

The open XXZ-chain: Bosonisation, Bethe ansatz and logarithmic corrections

We calculate the bulk and boundary parts of the free energy for an open spin-1/2 XXZ-chain in the critical regime by bosonisation. We identify the cutoff independent contributions and determine their amplitudes by comparing with Bethe ansatz calculations at zero temperature T. For the bulk part of the free energy we find agreement with Lukyanov's result [Nucl.Phys.B 522, 533 (1998)]. In the boundary part we obtain a cutoff independent term which is linear in T and determines the temperature dependence of the boundary susceptibility in the attractive regime for $T\ll 1$. We further show that at particular anisotropies where contributions from irrelevant operators with different scaling dimensions cross, logarithmic corrections appear. We give explicit formulas for these terms at those anisotropies where they are most important. We verify our results by comparing with extensive numerical calculations based on a numerical solution of the T=0 Bethe ansatz equations, the finite temperature Bethe ansatz equations in the quantum-transfer matrix formalism, and the density-matrix renormalisation group applied to transfer matrices.Comment: 35 pages, 8 figure

Charge and spin dynamics in the one-dimensional t−Jzt-J_z and t−Jt-J models

The impact of the spin-flip terms on the (static and dynamic) charge and spin correlations in the Luttinger-liquid ground state of the 1D $t-J$ model is assessed by comparison with the same quantities in the 1D $t-J_z$ model, where spin-flip terms are absent. We employ the recursion method combined with a weak-coupling or a strong-coupling continued-fraction analysis. At $J_z/t=0^+$ we use the Pfaffian representation of dynamic spin correlations. The changing nature of the dynamically relevant charge and spin excitations on approach of the transition to phase separation is investigated in detail. The $t-J_z$ charge excitations (but not the spin excitations) at the transition have a single-mode nature, whereas charge and spin excitations have a complicated structure in the $t-J$ model. In the $t-J_z$ model, phase separation is accompanied by N\'eel long-range order, caused by the condensation of electron clusters with an already existing alternating up-down spin configuration (topological long-range order). In the $t-J$ model, by contrast, the spin-flip processes in the exchange coupling are responsible for continued strong spin fluctuations (dominated by 2-spinon excitations) in the phase-separated state.Comment: 11 pages (RevTex). 14 Figures available from author