BIOL / MATH 2350
Miniproject Options
1. This project is based on bacteria in biofilms. Such bacteria produce Extracellular
Polymer Substances (EPS), which enable them to attach to surfaces and to each other,
and produce a state that is resistant to antibiotic treatment. The growth rate of bacteria
depends on how much nutrient is available to them. With a high supply of nutrient,
bacteria tend not to produce much EPS and they grow rapidly. With a lower supply of
nutrient, bacteria produce more EPS and grow slowly. Model the dynamics of nutrient,
bacteria, and EPS under different nutrient supplies.
2. This project is related to arctic plant-soil interactions as affected by climate warming.
Plants grow in relation to the concentration of nutrient in the soil, and are eaten by
mammalian herbivores such as voles. In their urine and feces, the voles recycle some of
the nutrient they consume from plants, using the remainder for their own growth. As
temperature increases, soil nutrient supply increases, so plants can grow more rapidly.
Model the dynamics of plants, nutrient, and herbivores under different temperatures.
3. This project concerns bison and prairie grass. Bison eat prairie grass above a certain
height, at a rate that depends on how much tall grass there is. The birth rate of bison
depends on their rate of ingestion of tall grass, and bison are also killed by wolves at a
constant per capita rate. Tall grass plants reproduce, and their offspring are short grass
plants that are not eaten by bison. Short grass plants grow into tall grass plants and
become vulnerable to being eaten by bison. The goal is to model the following two
situations.
A. Short grass plants grow into tall grass plants at a constant rate.
B. Bison excrete as feces a portion of the tall grass they ingest. Their feces
fertilize the short grass so that it grows into tall grass more rapidly.
4. Plants photosynthesize, grow and produce biomass in relation to the concentration of
available nitrogen in soil. Plant biomass is removed by a variety of processes; some
biomass falls to the soil as “plant litter” and becomes incorporated into detritus and soil
organic matter. Soil detritus contains nitrogen, but this nitrogen is not readily available to
plants. However, during decomposition, detritus slowly releases some of its nitrogen
content as available nitrogen that plants can then use for more growth. University
groundskeepers want to manage a large grass lawn so that the amount of detritus is high
to decrease the “carbon footprint” of the university. The carbon contained in detritus has
been removed from the atmosphere by photosynthesis, lowering the amount of
atmospheric carbon dioxide and offsetting the “greenhouse effect”. They can decide how
much available nitrogen to add as fertilizer to stimulate grass growth, how often to mow
the lawn (how rapidly plant biomass is removed), and what proportion of mowed
clippings to leave on the ground as detritus. How will these factors affect the amount
detritus in the soil over the long term?
5. Unicellular, flagellated protists are important predators of bacteria in aquatic
ecosystems. In predation experiments lasting several days with one predator species and
several prey species, some distinct dynamical patterns were seen for different prey
species:
 Bacteria immediately began to decline and did so linearly or exponentially
throughout the experiment, while predators immediately began to grow and did so
linearly or exponentially throughout the experiment.
 Bacteria immediately began to decline and did so linearly or exponentially
throughout the experiment, while predators either did not grow or slowly declined
throughout the experiment.
 Bacteria did not decline and remained constant, while predators either did not
grow or slowly declined throughout the experiment.
 Bacteria and predators did not change for the first few days of the experiment, and
then bacteria declined while predators grew for the remainder of the experiment.
Construct one more models that produce as many of these dynamical patterns as possible.
It is thought that bacterial species differ in the content of a critical nutrient that the
predators need, and that bacteria might produce a compound on the surface of their cells
that predators must recognize in order to ingest the bacteria. These factors could vary
between prey species or change over time to affect the dynamics during experiments.
6. Consider a complex microbial infection that involves two infectious species. The
immune system responds to the infection by sending phagocytes that prey on and kill the
microbes. Even if the two infectious species grow independently of each other (e.g.
according to separate logistic equations), they may interact because each of them elicits
phagocytes that kill the other species. This interaction is complicated because the two
infectious species can differ in factors such as how strongly they elicit phagocytes, and
how effectively the phagocytes can kill them. Can you identify circumstances under
which one infectious species is eliminated while the other survives, versus circumstances
where both infectious species persist?
7. This problem concerns mosquitoes of the genus Culex that transmit West Nile Virus.
These mosquitoes breed in small bodies of standing water of varying sizes. Adults fly
around and mate, the females lay their eggs in such bodies of water, then the larvae grow
up in the water and metamorphose into adults. Thus the abundance of Culex mosquitoes
across a regions such as North Texas is strongly influenced by the availability of suitable
habitat for larvae. One approach to modeling populations that live in numerous, small
habitats is to consider as variables the number or proportion of habitats that is occupied
by the population, rather than to consider numbers of individuals (this is called the
“metapopulation” approach, and it is conceptually similar to modeling infectious diseases
by focusing on the number or proportion of infected hosts). For Culex mosquitoes, it is
convenient to consider two types of habitats, very small bodies of standing water that
cannot contain the predators of the mosquitoes, and somewhat larger bodies of water that
can support predators that attack Culex mosquitoes (e.g. mayfly larvae), as well as fish
such as mosquito fish (Gambusia species) that attack both Culex larvae and other insects
such as mayfly larvae.
Based on this scheme, small bodies of water could exist in two states: (1) empty,
or (2) containing Culex larvae. Larger bodies of water could exist in four states: (1)
empty, (2) containing Culex larvae, (3) containing predators of Culex such as mayfly
larvae, or (4) containing mosquito fish and no Culex or mayflies. Transitions from empty
to Culex-containing states occur when mosquitoes naturally colonize empty water bodies.
Transitions from empty or Culex-containing states to states containing mayfly larvae
occur when mayflies naturally colonize larger bodies of water (and eliminate Culex if
they are present). Mosquito fish only occur when they are stocked by public health
workers and they eliminate both Culex and mayfly larvae when stocked. Water bodies
containing Culex become empty when mosquito larvae mature and fly away (which takes
a few days). Water bodies containing mayfly larvae become empty when these larvae
mature and fly away (which takes a few months).
As an alternative to spraying, public health campaigns against West Nile Virus
can focus on two measures: (1) draining bodies of standing water, and (2) stocking larger
bodies of standing water with mosquito fish. Draining converts proportions of small and
large bodies of water to an additional state that cannot be colonized by any organisms,
but it might be harder to eliminate smaller bodies of water. (Note that dry weather also
makes habitat unavailable, and is more likely to remove small bodies of water). Stocking
of mosquito fish can only be done in larger bodies of water. Explore how these public
health measures might be used to reduce the overall abundance of Culex mosquitos. (And
possibly also the influence of weather variations, such as wet weather that increase the
abundance of smaller bodies of water more than it does larger bodies of water).