{"id":{"repo_id":"udel","oai_identifier":"oai:udspace.udel.edu:19716/30785"},"canonical_url":"https://search.dev.ndltd.org/etd/udel/oai:udspace.udel.edu:19716/30785","repository":{"repo_id":"udel","name":"University of Delaware","base_url":"https://udspace.udel.edu/server/oai/request"},"display":{"title":"Stochastic modeling of Karlotoxin's influence on prey","abstract":"Karlodinium veneficium is type of dinoflagellate that feeds on planktonic species such as Storeatula major.It is associated with fish kills due to harmful algae blooms by releasing a compound called Karlotoxin. This toxin is known to affect their prey's bio-locomotion by stunning them and slowing them down. In this dissertation, we investigate whether the toxin plays a crucial role in aggregating the prey around the predators. The effect of aggregating prey around the predators is ecologically significant since it greatly boosts K. veneficium's feeding and reproduction rate, leading to a population surge, eluding a possible mechanism for producing algal blooms. ☐ We closely examine the toxin's influence on the prey's probability density distribution under the Goldstein-Kac modeling framework with different assumptions on their relative speed in 1-D, with either the predator being stationary or swimming at a constant speed. When the predator is stationary, we fully solve the prey's density distribution for all times, and verify the result by a Monte-Carlo simulation. For a swimming predator, we find the steady-state density distribution of prey analytically. When the predator's speed is strictly greater (or less) than the prey, the results are verified by Monte-Carlo simulations. When their relative speed has roots, singularities occur in the Goldstein-Kac system, and we perform a local analysis for prey's density at steady-state near the roots using the method of Frobenius, and use the result to derive a scheme for finding the analytical solution. For the relative speed in this case, assuming a right-swimming Karlodinium, the roots will occur at the left and right of the Karlodinium and we can get at worst an integrable singularity and at least a local maximum in the wake (the left root), depending on the flipping rate and the slope of the relative speed at this root. Near the other root, the prey's density in either direction can be represented by a Taylor series and is thus smooth. With the presence of roots for the relative speed, the analytical solution is verified by a finite difference scheme due to poor performance in Monte-Carlo simulations. ☐ For all the cases mentioned above, toxin changes the prey's distribution and in most cases leads to aggregation, however the maximum density does not always occur where the toxin has the highest concentration. In reality, such a result suggests that toxin density greatly influences the prey's distribution, however the distribution is also a result of predator and prey's relative movement. When their relative speed is of single sign, the toxin dominates. When their relative speed fluctuates around 0, both the toxin and their relative movements contributes to prey's distribution.","abstract_html":"Karlodinium veneficium is type of dinoflagellate that feeds on planktonic species such as Storeatula major.It is associated with fish kills due to harmful algae blooms by releasing a compound called Karlotoxin. This toxin is known to affect their prey's bio-locomotion by stunning them and slowing them down. In this dissertation, we investigate whether the toxin plays a crucial role in aggregating the prey around the predators. The effect of aggregating prey around the predators is ecologically significant since it greatly boosts K. veneficium's feeding and reproduction rate, leading to a population surge, eluding a possible mechanism for producing algal blooms. ☐ We closely examine the toxin's influence on the prey's probability density distribution under the Goldstein-Kac modeling framework with different assumptions on their relative speed in 1-D, with either the predator being stationary or swimming at a constant speed. When the predator is stationary, we fully solve the prey's density distribution for all times, and verify the result by a Monte-Carlo simulation. For a swimming predator, we find the steady-state density distribution of prey analytically. When the predator's speed is strictly greater (or less) than the prey, the results are verified by Monte-Carlo simulations. When their relative speed has roots, singularities occur in the Goldstein-Kac system, and we perform a local analysis for prey's density at steady-state near the roots using the method of Frobenius, and use the result to derive a scheme for finding the analytical solution. For the relative speed in this case, assuming a right-swimming Karlodinium, the roots will occur at the left and right of the Karlodinium and we can get at worst an integrable singularity and at least a local maximum in the wake (the left root), depending on the flipping rate and the slope of the relative speed at this root. Near the other root, the prey's density in either direction can be represented by a Taylor series and is thus smooth. With the presence of roots for the relative speed, the analytical solution is verified by a finite difference scheme due to poor performance in Monte-Carlo simulations. ☐ For all the cases mentioned above, toxin changes the prey's distribution and in most cases leads to aggregation, however the maximum density does not always occur where the toxin has the highest concentration. In reality, such a result suggests that toxin density greatly influences the prey's distribution, however the distribution is also a result of predator and prey's relative movement. When their relative speed is of single sign, the toxin dominates. When their relative speed fluctuates around 0, both the toxin and their relative movements contributes to prey's distribution.","abstract_has_math":false,"creators":["Pei, Hansen"],"institution":"University of Delaware","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2021,"date_issued":"2021","date_published":"2021","updated_at":"2026-07-24T05:11:20Z","subjects":["Aggregation","Microswimmer","Pattern formation","Plankton","Stochastic model"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.58088/6ddc-bc88"],"render_values":[{"text":"https://doi.org/10.58088/6ddc-bc88","href":"https://doi.org/10.58088/6ddc-bc88","code":true}]}]},"links":{"outbound_url":"https://udspace.udel.edu/handle/19716/30785","outbound_label":"Repository record","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Pei, Hansen"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2022-04-14T11:57:46Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2022-04-14T11:57:46Z"]},{"key":"dc:date.issued","label":"Date","values":["2021"]},{"key":"dc:publisher","label":"Institution","values":["University of Delaware"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Aggregation","Microswimmer","Pattern formation","Plankton","Stochastic model"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.58088/6ddc-bc88"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://udspace.udel.edu/handle/19716/30785"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Karlodinium veneficium is type of dinoflagellate that feeds on planktonic species such as Storeatula major.It is associated with fish kills due to harmful algae blooms by releasing a compound called Karlotoxin. This toxin is known to affect their prey's bio-locomotion by stunning them and slowing them down. In this dissertation, we investigate whether the toxin plays a crucial role in aggregating the prey around the predators. The effect of aggregating prey around the predators is ecologically significant since it greatly boosts K. veneficium's feeding and reproduction rate, leading to a population surge, eluding a possible mechanism for producing algal blooms. ☐ We closely examine the toxin's influence on the prey's probability density distribution under the Goldstein-Kac modeling framework with different assumptions on their relative speed in 1-D, with either the predator being stationary or swimming at a constant speed. When the predator is stationary, we fully solve the prey's density distribution for all times, and verify the result by a Monte-Carlo simulation. For a swimming predator, we find the steady-state density distribution of prey analytically. When the predator's speed is strictly greater (or less) than the prey, the results are verified by Monte-Carlo simulations. When their relative speed has roots, singularities occur in the Goldstein-Kac system, and we perform a local analysis for prey's density at steady-state near the roots using the method of Frobenius, and use the result to derive a scheme for finding the analytical solution. For the relative speed in this case, assuming a right-swimming Karlodinium, the roots will occur at the left and right of the Karlodinium and we can get at worst an integrable singularity and at least a local maximum in the wake (the left root), depending on the flipping rate and the slope of the relative speed at this root. Near the other root, the prey's density in either direction can be represented by a Taylor series and is thus smooth. With the presence of roots for the relative speed, the analytical solution is verified by a finite difference scheme due to poor performance in Monte-Carlo simulations. ☐ For all the cases mentioned above, toxin changes the prey's distribution and in most cases leads to aggregation, however the maximum density does not always occur where the toxin has the highest concentration. In reality, such a result suggests that toxin density greatly influences the prey's distribution, however the distribution is also a result of predator and prey's relative movement. When their relative speed is of single sign, the toxin dominates. When their relative speed fluctuates around 0, both the toxin and their relative movements contributes to prey's distribution."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph.D."]},{"key":"dc:title","label":"Title","values":["Stochastic modeling of Karlotoxin's influence on prey"]}]}],"canonical_facts":{"dc:creator":["Pei, Hansen"],"dc:date.accessioned":["2022-04-14T11:57:46Z"],"dc:date.available":["2022-04-14T11:57:46Z"],"dc:date.issued":["2021"],"dc:description.abstract":["Karlodinium veneficium is type of dinoflagellate that feeds on planktonic species such as Storeatula major.It is associated with fish kills due to harmful algae blooms by releasing a compound called Karlotoxin. This toxin is known to affect their prey's bio-locomotion by stunning them and slowing them down. In this dissertation, we investigate whether the toxin plays a crucial role in aggregating the prey around the predators. The effect of aggregating prey around the predators is ecologically significant since it greatly boosts K. veneficium's feeding and reproduction rate, leading to a population surge, eluding a possible mechanism for producing algal blooms. ☐ We closely examine the toxin's influence on the prey's probability density distribution under the Goldstein-Kac modeling framework with different assumptions on their relative speed in 1-D, with either the predator being stationary or swimming at a constant speed. When the predator is stationary, we fully solve the prey's density distribution for all times, and verify the result by a Monte-Carlo simulation. For a swimming predator, we find the steady-state density distribution of prey analytically. When the predator's speed is strictly greater (or less) than the prey, the results are verified by Monte-Carlo simulations. When their relative speed has roots, singularities occur in the Goldstein-Kac system, and we perform a local analysis for prey's density at steady-state near the roots using the method of Frobenius, and use the result to derive a scheme for finding the analytical solution. For the relative speed in this case, assuming a right-swimming Karlodinium, the roots will occur at the left and right of the Karlodinium and we can get at worst an integrable singularity and at least a local maximum in the wake (the left root), depending on the flipping rate and the slope of the relative speed at this root. Near the other root, the prey's density in either direction can be represented by a Taylor series and is thus smooth. With the presence of roots for the relative speed, the analytical solution is verified by a finite difference scheme due to poor performance in Monte-Carlo simulations. ☐ For all the cases mentioned above, toxin changes the prey's distribution and in most cases leads to aggregation, however the maximum density does not always occur where the toxin has the highest concentration. In reality, such a result suggests that toxin density greatly influences the prey's distribution, however the distribution is also a result of predator and prey's relative movement. When their relative speed is of single sign, the toxin dominates. When their relative speed fluctuates around 0, both the toxin and their relative movements contributes to prey's distribution."],"dc:description.degree":["Ph.D."],"dc:identifier.doi":["https://doi.org/10.58088/6ddc-bc88"],"dc:identifier.uri":["https://udspace.udel.edu/handle/19716/30785"],"dc:publisher":["University of Delaware"],"dc:subject":["Aggregation","Microswimmer","Pattern formation","Plankton","Stochastic model"],"dc:title":["Stochastic modeling of Karlotoxin's influence on prey"],"dc:type":["Thesis"]},"updated_at":"2026-07-24T05:11:20Z"}