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Results for “Mathematical Biosciences”

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8 recordsLinked to original sources
USGS2011

Dynamics of a plant-herbivore-predator system with plant-toxicity

A system of ordinary differential equations is considered that models the interactions of two plant species populations, an herbivore population, and a predator population. We use a toxin-determined functional response to describe the interactions between plant species and herbivores and use a Holling Type II functional response to model the interactions between herbivores and predators. In order to study how the predators impact the succession of vegetation, we derive invasion conditions under which a plant species can invade into an environment in which another plant species is co-existing with a herbivore population with or without a predator population. These conditions provide threshold quantities for several parameters that may play a key role in the dynamics of the system. Numerical simulations are conducted to reinforce the analytical results. This model can be applied to a boreal ecosystem trophic chain to examine the possible cascading effects of predator-control actions when plant species differ in their levels of toxic defense.

Mathematical Biosciences↗
USGS2015

Effects of dispersal on total biomass in a patchy, heterogeneous system: Analysis and experiment

An intriguing recent result from mathematics is that a population diffusing at an intermediate rate in an environment in which resources vary spatially will reach a higher total equilibrium biomass than the population in an environment in which the same total resources are distributed homogeneously. We extended the current mathematical theory to apply to logistic growth and also showed that the result applies to patchy systems with dispersal among patches, both for continuous and discrete time. This allowed us to make specific predictions, through simulations, concerning the biomass dynamics, which were verified by a laboratory experiment. The experiment was a study of biomass growth of duckweed ( Lemna minor Linn.), where the resources (nutrients added to water) were distributed homogeneously among a discrete series of water-filled containers in one treatment, and distributed heterogeneously in another treatment. The experimental results showed that total biomass peaked at an intermediate, relatively low, diffusion rate, higher than the total carrying capacity of the system and agreeing with the simulation model. The implications of the experiment to dynamics of source, sink, and pseudo-sink dynamics are discussed.

Mathematical Biosciences↗
USGS2023

Book review: Quasispecies as a unifying concept in population dynamics

The quasispecies concept had two independent origins. One source was the theoretical ideas of Manfred Eigen and Peter Schuster in the 1970s. Studying the self-organization and evolution of primitive RNA molecules, they defined quasispecies as a distribution of mutant viral genomes generated by the mutation-selection process. In particular, the quasispecies nucleotide distribution consists of a singular fittest genotype, called the master sequence, surrounded by similar mutant spectra. The other source of the quasispecies concept can be traced to the growing empirical knowledge on RNA viruses formulated around the same time. Genomic sequencing of viral RNA indicated a variety of nucleotide sequences, or a distribution of sequences. Mutations in both Eigen’s theoretical system in the RNA viruses are not rare, as RNA is structurally less stable than RNA, but common, preventing the fittest genotype from becoming dominant. Virologists have adopted the quasispecies concept, with some papers on Covid-19 using the construct to explain that virus’s behavior.

Mathematical Biosciences↗
USGS2000

Dynamics of prey moving through a predator field: a model of migrating juvenile salmon

The migration of a patch of prey through a field of relatively stationary predators is a situation that occurs frequently in nature. Making quantitative predictions concerning such phenomena may be difficult, however, because factors such as the number of the prey in the patch, the spatial length and velocity of the patch, and the feeding rate and satiation of the predators all interact in a complex way. However, such problems are of great practical importance in many management situations; e.g., calculating the mortality of juvenile salmon (smolts) swimming down a river or reservoir containing many predators. Salmon smolts often move downstream in patches short compared with the length of the reservoir. To take into account the spatial dependence of the interaction, we used a spatially-explicit, individual-based modeling approach. We found that the mortality of prey depends strongly on the number of prey in the patch, the downstream velocity of prey in the patch, and the dispersion or spread of the patch in size through time. Some counterintuitive phenomena are predicted, such as predators downstrean capturing more prey per predator than those upstream, even though the number of prey may be greatly depleted by the time the prey patch reaches the downstream predators. Individual-based models may be necessary for complex spatial situations, such as salmonid migration, where processes such as schooling occur at fine scales and affect system predictions. We compare some results to predictions from other salmonid models. (C) 2000 Elsevier Science Inc.

Mathematical Biosciences↗
USGS2022

Wading bird foraging on a wetland landscape: A comparison of two strategies

Tactile-feeding wading birds, such as wood storks and white ibises, require high densities of prey such as small fishes and crayfish to support themselves and their offspring during the breeding season. Prey availability in wetlands is often determined by seasonal hydrologic pulsing, such as in the subtropical Everglades, where spatial distributions of prey can vary through time, becoming heterogeneously clumped in patches, such as ponds or sloughs, as the wetland dries out. In this mathematical modeling study, we selected two possible foraging strategies to examine how they impact total energetic intake over a time scale of one day. In the first, wading birds sample prey patches without a priori knowledge of the patches' prey densities, moving from patch to patch, staying long enough to estimate the prey density, until they find one that meets a predetermined satisfactory threshold, and then staying there for a longer period. For this case, we solve for a wading bird's expected prey intake over the course of a day, given varying theoretical probability distributions of patch prey densities across the landscape. In the second strategy considered, it is assumed that the wading bird samples a given number of patches, and then uses memory to return to the highest quality patch. Our results show how total intake over a day is impacted by assumptions of the parameters governing the spatial distribution of prey among patches, which is a key source of parameter uncertainty in both natural and managed ecosystems. Perhaps surprisingly, the foraging strategy that uses a prey density threshold generally led to higher maximum potential prey intake than the strategy for using memory to return to the best patch sampled. These results will contribute to understanding the foraging of wading birds and to the management of wetlands.

Mathematical Biosciences and Engineering↗
USGS2024

Effects of initial vegetation heterogeneity on competition of submersed and floating macrophytes

Non-spatial models of competition between floating aquatic vegetation (FAV) and submersed aquatic vegetation (SAV) predict a stable state of pure SAV at low total available limiting nutrient level, N , a stable state of only FAV for high N , and alternative stable states for intermediate N , as described by an S-shaped bifurcation curve. Spatial models that include physical heterogeneity of the waterbody show that the sharp transitions between these states become smooth. We examined the effects of heterogeneous initial conditions of the vegetation types. We used a spatially explicit model to describe the competition between the vegetation types. In the model, the FAV, duckweed ( L. gibba ), competed with the SAV, Nuttall's waterweed ( Elodea nuttallii ). Differences in the initial establishment of the two macrophytes affected the possible stable equilibria. When initial biomasses of SAV and FAV differed but each had the same initial biomass in each spatial cell, the S-shaped bifurcation resulted, but the critical transitions on the N -axis are shifted, depending on FAV:SAV biomass ratio. When the initial biomasses of SAV and FAV were randomly heterogeneously distributed among cells, the vegetation pattern of the competing species self-organized spatially, such that many different stable states were possible in the intermediate N region. If N was gradually increased or decreased through time from a stable state, the abrupt transitions of non-spatial models were changed into smoother transitions through a series of stable states, which resembles the Busse balloon observed in other systems.

Mathematical Biosciences and Engineering↗
USGS2011

Perceptions of strengths and deficiencies: Disconnects between graduate students and prospective employers

The US Botanical Capacity Assessment Project (BCAP) was initiated as a first step to gauge the nation's collective ability to meet the environmental challenges of the 21st century. The project, in which the authors of this article are involved, specifically aimed to identify multisector contributions to and gaps in botanical capacity in order to develop growth opportunities to address research and management problems. One of the primary gaps revealed by the BCAP surveys was that the skills graduate students identified as their greatest strengths closely matched the areas future employers (government and private sectors) identified as needing greatest improvement. Although our survey focused on only one discipline (botany), we suspect that the results are applicable throughout the science, technology, engineering, and mathematics disciplines. We suggest that it is critical for university faculty and administrators to team with professionals from government, nonprofit, and for-profit organizations to identify critical and desired knowledge and skill sets and implement the necessary curriculum changes to provide graduates with the tools they need.

BioScience↗
USGS2015

Now hiring! Empirically testing a three-step intervention to increase faculty gender diversity in STEM

Workforce homogeneity limits creativity, discovery, and job satisfaction; nonetheless, the vast majority of university faculty in science, technology, engineering, and mathematics (STEM) fields are men. We conducted a randomized and controlled three-step faculty search intervention based in self-determination theory aimed at increasing the number of women faculty in STEM at one US university where increasing diversity had historically proved elusive. Results show that the numbers of women candidates considered for and offered tenure-track positions were significantly higher in the intervention groups compared with those in controls. Searches in the intervention were 6.3 times more likely to make an offer to a woman candidate, and women who were made an offer were 5.8 times more likely to accept the offer from an intervention search. Although the focus was on increasing women faculty within STEM, the intervention can be adapted to other scientific and academic communities to advance diversity along any dimension.

BioScience↗