Modeling the evolution of herbicide resistance in weed species with a complex life cycle.

A growing number of weed species have evolved resistance to herbicides in recent years, which causes an immense financial burden to farmers. An increasingly popular method of weed control is the adoption of crops that are resistant to specific herbicides, which allows farmers to apply the herbicide during the growing season without harming the crop. If such crops are planted in the presence of closely related weed species, it is possible that resistance genes could transfer from the crop species to feral populations of the wild species via gene flow and become stably introgressed under ongoing selective pressure by the herbicide.

Spectral properties of a non-compact operator in ecology.

Ecologists have recently used integral projection models (IPMs) to study fish and other animals which continue to grow throughout their lives. Such animals cannot shrink, since they have bony skeletons; a mathematical consequence of this is that the kernel of the integral projection operator T is unbounded, and the operator is not compact. To our knowledge, all theoretical work done on IPMs has assumed the operator is compact, and in particular has a bounded kernel.

A discrete/continuous time resource competition model and its implications.

We use a mixed time model to study the dynamics of a system consisting of two consumers that reproduce only in annual birth pulses, possibly at different times, with interaction limited to competition for a resource that reproduces continuously. Ecological theory predicts competitive exclusion; this expectation is met under most circumstances, the winner being the species with the greater 'power', defined as the time average consumer level at the fixed point. Instability of that fixed point for the stronger competitor slightly weakens its domination, so that a resident species with an unstable fixed point can sometimes be invaded by a slightly weaker species, leading ultimately to coexistence.

Analysis of a Length-Structured Density-Dependent Model for Fish.

We present a length-structured matrix model for fish populations in which the probability that a fish grows into the next length class is a decreasing nonlinear function of the total biomass of the population. We present mathematical results classifying the dynamics that this density-dependent model predicts. We illustrate these results with numerical simulations for an invasive white perch population and show how the mathematical results can be used to predict the persistence and/or boundedness of the population as well as an equilibrium structure that is dominated by small fish.

Predicting impacts of chemicals from organisms to ecosystem service delivery: A case study of insecticide impacts on a freshwater lake.

Assessing and managing risks of anthropogenic activities to ecological systems is necessary to ensure sustained delivery of ecosystem services for future generations. Ecological models provide a means of quantitatively linking measured risk assessment endpoints with protection goals, by integrating potential chemical effects with species life history, ecological interactions, environmental drivers and other potential stressors. Here we demonstrate how an ecosystem modeling approach can be used to quantify insecticide-induced impacts on ecosystem services provided by a lake from toxicity data for organism-level endpoints.

Predicting impacts of chemicals from organisms to ecosystem service delivery: A case study of endocrine disruptor effects on trout.

We demonstrate how mechanistic modeling can be used to predict whether and how biological responses to chemicals at (sub)organismal levels in model species (i.e., what we typically measure) translate into impacts on ecosystem service delivery (i.

A framework for predicting impacts on ecosystem services from (sub)organismal responses to chemicals.

Protection of ecosystem services is increasingly emphasized as a risk-assessment goal, but there are wide gaps between current ecological risk-assessment endpoints and potential effects on services provided by ecosystems. The authors present a framework that links common ecotoxicological endpoints to chemical impacts on populations and communities and the ecosystem services that they provide. This framework builds on considerable advances in mechanistic effects models designed to span multiple levels of biological organization and account for various types of biological interactions and feedbacks.

Sensitivity and elasticity analysis of a Lur'e system used to model a population subject to density-dependent reproduction.

Sensitivity and elasticity analyzes have become central to the analysis of models in population biology and ecology. While much work has been done applying sensitivity and elasticity analysis to study density-independent (linear) matrix and integral projection models, little work has been done to study the sensitivity and elasticity of density-dependent models, especially integral projection models. In this paper we derive sensitivity and elasticity formulas for the equilibrium population n of a structured population modeled by a Lur'e system, which consists of a linear system plus a nonlinearity modeling density-dependent fecundity.

Frequency-dependent population dynamics: effect of sex ratio and mating system on the elasticity of population growth rate.

When vital rates depend on population structure (e.g., relative frequencies of males or females), an important question is how the long-term population growth rate λ responds to changes in rates.

Modeling and analysis of a density-dependent stochastic integral projection model for a disturbance specialist plant and its seed bank.

In many plant species dormant seeds can persist in the soil for one to several years. The formation of these seed banks is especially important for disturbance specialist plants, as seeds of these species germinate only in disturbed soil. Seed movement caused by disturbances affects the survival and germination probability of seeds in the seed bank, which subsequently affect population dynamics.

Integral control for population management.

We present a novel management methodology for restocking a declining population. The strategy uses integral control, a concept ubiquitous in control theory which has not been applied to population dynamics. Integral control is based on dynamic feedback-using measurements of the population to inform management strategies and is robust to model uncertainty, an important consideration for ecological models.

Bounds on the dynamics of sink populations with noisy immigration.

Sink populations are doomed to decline to extinction in the absence of immigration. The dynamics of sink populations are not easily modelled using the standard framework of per capita rates of immigration, because numbers of immigrants are determined by extrinsic sources (for example, source populations, or population managers). Here we appeal to a systems and control framework to place upper and lower bounds on both the transient and future dynamics of sink populations that are subject to noisy immigration.

Disturbance frequency and vertical distribution of seeds affect long-term population dynamics: a mechanistic seed bank model.

Seed banks are critically important for disturbance specialist plants because seeds of these species germinate only in disturbed soil. Disturbance and seed depth affect the survival and germination probability of seeds in the seed bank, which in turn affect population dynamics. We develop a density-dependent stochastic integral projection model to evaluate the effect of stochastic soil disturbances on plant population dynamics with an emphasis on mimicking how disturbances vertically redistribute seeds within the seed bank.

Global asymptotic stability of plant-seed bank models.

Many plant populations have persistent seed banks, which consist of viable seeds that remain dormant in the soil for many years. Seed banks are important for plant population dynamics because they buffer against environmental perturbations and reduce the probability of extinction. Viability of the seeds in the seed bank can depend on the seed's age, hence it is important to keep track of the age distribution of seeds in the seed bank.

Global asymptotic stability of density dependent integral population projection models.

Many stage-structured density dependent populations with a continuum of stages can be naturally modeled using nonlinear integral projection models. In this paper, we study a trichotomy of global stability result for a class of density dependent systems which include a Platte thistle model. Specifically, we identify those systems parameters for which zero is globally asymptotically stable, parameters for which there is a positive asymptotically stable equilibrium, and parameters for which there is no asymptotically stable equilibrium.

Model complexity affects transient population dynamics following a dispersal event: a case study with pea aphids.

Stage-structured population models predict transient population dynamics if the population deviates from the stable stage distribution. Ecologists' interest in transient dynamics is growing because populations regularly deviate from the stable stage distribution, which can lead to transient dynamics that differ significantly from the stable stage dynamics. Because the structure of a population matrix (i.

Parameterizing the growth-decline boundary for uncertain population projection models.

We consider discrete time linear population models of the form n(t+1)=An(t) where A is a population projection matrix or integral projection operator, and n(t) represents a structured population at time t. It is well known that the asymptotic growth or decay rate of n(t) is determined by the leading eigenvalue of A. In practice, population models have substantial parameter uncertainty, and it might be difficult to quantify the effect of this uncertainty on the leading eigenvalue.