Stereotaxic Viral Injection and Gradient-Index Lens Implantation for Deep Brain <em>In Vivo</em> Calcium Imaging

A miniature fluorescence microscope (miniscope) is a potent tool for in vivo calcium imaging from freely behaving animals. It offers several advantages ...

University of Wyoming

Mistletoes are common aerial stem-parasites and their seeds are dispersed by fruit-eating birds. In the mutually beneficial relationships between mistletoes and bird species that disperse mistletoes' seeds, the preference of birds for infected trees influences the spread of mistletoes and the spatiotemporal pattern formation of mistletoes. We formulate a deterministic model to describe the dynamics of mistletoes in an isolated patch containing an arbitrary number of trees. We establish concrete criterions, expressed in terms of the model parameters, for mistletoes establishing in this area. We conduct numerical simulations based on a field study to reinforce and expand our results.

Spatiotemporal variation of mistletoes: a dynamic modeling approach.

In this paper we study the effects that woody plant chemical defenses may have on interactions between boreal hares that in winter feed almost entirely on twigs. We focus particularly on the fact that toxin concentration often varies with the age of twig segments. The model incorporates the fact that the woody internodes of the youngest segments of the twigs of the deciduous angiosperm species that these hares prefer to eat are more defended by toxins than the woody internodes of the older segments that subtend and support the younger segments. Thus, the per capita daily intake of the biomass of the older segments of twigs by hares is much higher than their intake of the biomass of the younger segments of twigs. This age-dependent toxicity of twig segments is modeled using age-structured model equations which are reduced to a system of delay differential equations involving multiple delays in the woody plant-hare dynamics. A novel aspect of the modeling was that it had to account for mortality of non-consumed younger twig segment biomass when older twig biomass was bitten off and consumed. Basic mathematical properties of the model are established together with upper and lower bounds on the solutions. Necessary and sufficient conditions are found for the linear stability of the equilibrium in which the hare is extinct, and sufficient conditions are found for the global stability of this equilibrium. Numerical simulations confirmed the analytical results and demonstrated the existence of limit cycles over ranges of parameters reasonable for hares browsing on woody vegetation in boreal ecosystems. This showed that age dependence in plant chemical defenses has the capacity to cause hare-plant population cycles, a new result.

Modeling the dynamics of woody plant-herbivore interactions with age-dependent toxicity.

A mathematical model which incorporates the spatial dispersal and interaction dynamics of mistletoes and birds is derived and studied to gain insights of the spatial heterogeneity in abundance of mistletoes. Fickian diffusion and chemotaxis are used to model the random movement of birds and the aggregation of birds due to the attraction of mistletoes, respectively. The spread of mistletoes by birds is expressed by a dispersal operator, which is typically a convolution integral with a dispersal kernel. Two different types of kernel functions are used to study the model, one is a Dirac delta function which reflects the special case that the spread behavior is local, and the other one is a general non-negative symmetric function which describes the nonlocal spread of mistletoes. When the kernel function is taken as the Dirac delta function, the threshold condition for the existence of mistletoes is given and explored in terms of parameters. For the general non-negative symmetric kernel case, we prove the existence and stability of spatially nonhomogeneous equilibria. Numerical simulations are conducted by taking specific forms of kernel functions. Our study shows that the spatial heterogeneous patterns of mistletoes are related to the specific dispersal pattern of birds which carry mistletoe seeds. 

Spatiotemporal mutualistic model of mistletoes and birds.

Wolbachia is possibly the most studied reproductive parasite of arthropod species. It appears to be a promising candidate for biocontrol of some mosquito borne diseases. We begin by developing a sex-structured model for a Wolbachia infected mosquito population. Our model incorporates the key effects of Wolbachia infection including cytoplasmic incompatibility and male killing. We also allow the possibility of reduced reproductive output, incomplete maternal transmission, and different mortality rates for uninfected/infected male/female individuals. We study the existence and local stability of equilibria, including the biologically relevant and interesting boundary equilibria. For some biologically relevant parameter regimes there may be multiple coexistence steady states including, very importantly, a coexistence steady state in which Wolbachia infected individuals dominate. We also extend the model to incorporate West Nile virus (WNv) dynamics, using an SEI modelling approach. Recent evidence suggests that a particular strain of Wolbachia infection significantly reduces WNv replication in Aedes aegypti. We model this via increased time spent in the WNv-exposed compartment for Wolbachia infected female mosquitoes. A basic reproduction number [Formula: see text] is computed for the WNv infection. Our results suggest that, if the mosquito population consists mainly of Wolbachia infected individuals, WNv eradication is likely if WNv replication in Wolbachia infected individuals is sufficiently reduced.

Modelling Wolbachia infection in a sex-structured mosquito population carrying West Nile virus.

Resource selection is widely appreciated to be context-dependent and shaped by both biological and abiotic factors. However, few studies have empirically assessed the extent to which selective foraging behaviour is dynamic and varies in response to environmental conditions for free-ranging animal populations. Here, we assessed the extent that forage selection fluctuated in response to different environmental conditions for a free-ranging herbivore, moose (Alces alces), in Isle Royale National Park, over a 10-year period. More precisely, we assessed how moose selection for coniferous versus deciduous forage in winter varied between geographic regions and in relation to (a) the relative frequency of forage types in the environment (e.g. frequency-dependent foraging behaviour), (b) moose abundance, (c) predation rate (by grey wolves) and (d) snow depth. These factors are potentially important for their influence on the energetics of foraging. We also built a series of food-chain models to assess the influence of dynamic foraging strategies on the stability of food webs. Our analysis indicates that moose exhibited negative frequency dependence, by selectively exploiting rare resources. Frequency-dependent foraging was further mediated by density-dependent processes, which are likely to be predation, moose abundance or some combination of both. In particular, frequency dependence was weaker in years when predation risk was high (i.e. when the ratio of moose to wolves was relatively low). Selection for conifers was also slightly weaker during deep snow years. The food-chain analysis indicates that the type of frequency-dependent foraging strategy exhibited by herbivores had important consequences for the stability of ecological communities. In particular, the dynamic foraging strategy that we observed in the empirical analysis (i.e. negative frequency dependence being mediated by density-dependent processes) was associated with more stable food web dynamics compared to fixed foraging strategies. The results of this study indicated that forage selection is a complex ecological process, varying in response to both biological (predation and moose density) and abiotic factors (snow depth) and over relatively small spatial scales (between regions). This study also provides a useful framework for assessing the influence of other aspects of foraging behaviour on the stability of food web dynamics.

Negative frequency-dependent foraging behaviour in a generalist herbivore (Alces alces) and its stabilizing influence on food web dynamics.

In this paper, compartmental pharmacokinetic models are built to predict the concentration of toxic phytochemical in the gastrointestinal tract and blood following oral intake by an individual vertebrate herbivore. The existing single and multiple dose pharmacokinetic models are extended by inclusion of impulsive differential equations which account for an excretion factor whereby unchanged toxins are excreted in the feces due to gastrointestinal mobility. An index α is defined to measure the fraction of bioavailability attributed to the excretion factor of gastrointestinal motility. Sensitivity analysis was conducted and suggests, for any toxin, the bioavailability index α depends mostly on absorption rate of toxin from gastrointestinal tract into the blood, frequency of elimination due to gastrointestinal motility, and the frequency of toxin intake, under the model assumptions.

Multiple Dose Pharmacokinetic Models Predict Bioavailability of Toxins in Vertebrate Herbivores.

Industrial bioreactors use microbial organisms as living factories to produce a wide range of commercial products. For most applications, yields eventually become limited by the proliferation of "escape mutants" that acquire a growth advantage by losing the ability to make product. The goal of this work is to use mathematical models to determine whether this problem could be addressed in continuous flow bioreactors that include a "stem cell" population that multiplies rapidly and could be used to compete against the emergence of cheater mutants. In this system, external stimuli can be used to induce stem cell multiplication through symmetric cell division, or to limit stem cell multiplication and induce higher production through an asymmetric cell division that produces one stem cell and one new product-producing "factory cell". Our results show product yields from bioreactors with microbial stem cells can be increased by 18% to 127% over conventional methods, and sensitivity analysis shows that yields could be improved over a broad range of parameter space.

Rongsong Liu

Department of Mathematics and Statistics

University of Wyoming

Stereotaxic Viral Injection and Gradient-Index Lens Implantation for Deep Brain In Vivo Calcium Imaging

Rongsong Liu

.css-o250i3{font-size:18px;font-family:Open Sans,sans-serif;line-height:21.6px;}Department of Mathematics and Statistics

University of Wyoming

Stereotaxic Viral Injection and Gradient-Index Lens Implantation for Deep Brain In Vivo Calcium Imaging

Department of Mathematics and Statistics