Southern-Summer School on Mathematical Biology

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2020:groups:g7:start [2020/01/15 19:29] – group72020:groups:g7:start [2024/01/09 18:45] (current) – external edit 127.0.0.1
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 Further well-grounded questions from the group are welcome. Further well-grounded questions from the group are welcome.
  
-===== Our Basic Model =====+===== References =====
  
-Let F be our population of flowers, P our population of regular pollinators and R our population of robbers.+[[https://www.nature.com/articles/s41598-019-44741-y|Varma & Sino, 2019. Nectar robbing in bellflower (Sesamum radiatum) benefited pollinators but an unaffected maternal function of plant reproduction]] 
 + 
 +[[https://link.springer.com/article/10.1007%2Fs11515-007-0068-5|Zhang et al 2007. Effects of nectar-robbing on plant reproduction and evolution]] 
 + 
 +===== Group discussions: ===== 
 + 
 +We will model a network with 3 species interacting with 3 ecological processes: 
 + 
 +- Mutualism between the plant and the pollinator 
 + 
 +- Predation of the robbers in the flowers 
 + 
 +- Competition by interference between pollinators and robbers for nectar 
 + 
 +DESCRIPTION OF THE SYSTEM 
 + 
 +**PLANTS-FLOWERS** 
 + 
 +- Dioecious: both male and female organs in the same flower 
 + 
 +- Obligate outcrossing mating strategy: the flower must be pollinated by pollen from another flower, and it must be done by an animal visiting. 
 + 
 +- Pollination is specialized, i.e. done by one species of animal. 
 + 
 +- We will model the population of flowers instead of plants, i.e., considering one flower per plant. 
 + 
 +- The plant has negligible costs in producing more nectar when it is depleted by the visitors (pollinators and nectar robbers) 
 + 
 +- The production of nectar is proportional to the number of flowers 
 + 
 + 
 +**POLLINATORS** 
 + 
 +- Specialized in the species of plant. The population can only grow with nectar consumption in the system. 
 + 
 +- It can die "naturally" by other causes in a constant rate. 
 + 
 +- It has the behavior to increase the flower visit rates (and pollination) in searching for nectar when the amount of nectar per flower is low. But it has no cost for increasing the visitation rate. 
 + 
 +- It doesn't know how much nectar there is in the flower, so the pollinators can visit and pollinate the flower even though it has no nectar. 
 + 
 +- Pollinator growth rate related to nectar consumption has a saturation point, in which even though the nectar amount increases the number of pollinators does not increase anymore. 
 + 
 +**NECTAR ROBBERS** 
 + 
 +- Generalist species. They can robber nectar from other plants out of our system, but it is limited by a carrying capacity in the environment. 
 + 
 +- It consumes nectar from the flower competing by interference with the pollinators by nectar resources 
 + 
 +- Robbers don't know how much nectar there is in the flower, so it opens holes in flowers regardless of the amount of nectar. They damage (kill) flowers independently of the nectar amount. 
 + 
 +- Robbers' growth rate related to nectar consumption has a saturation point, in which even though the nectar amount increases the number of robbers does not increase anymore. 
 + 
 + 
 +Let F be the population of flowers, N the amount of nectar available, P the population of pollinators and R the population of nectar robbers.
  
 We assume in our model: We assume in our model:
  
-- The flowers can reproduce by self polination and have carrying capacity.+
 - The pollinators and the flowers have a mutualistic interaction:  - The pollinators and the flowers have a mutualistic interaction: 
   - The flowers benefit from pollinator's visit for nectar - it increases flower growth rate.   - The flowers benefit from pollinator's visit for nectar - it increases flower growth rate.
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 {{:2020:groups:g7:fixedpoints1.png?650}} {{:2020:groups:g7:fixedpoints1.png?650}}
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 ===== Sharing the code with the group ===== ===== Sharing the code with the group =====
  
-[[https://drive.google.com/file/d/1WriP7dRB2rcuG5Wm8tMQ09kd2z256d2L/view?usp=sharing|Code in R]]+[[https://drive.google.com/file/d/1pQYsZ-r8vOxRM2S_BiFMWxH4345OC4s-/view?usp=sharing|Code in R]]
  
 [[https://drive.google.com/file/d/1Va0REMJPCTG4hcyVhpHAid9A6IB9oReY/view?usp=sharing|Code in Python]] [[https://drive.google.com/file/d/1Va0REMJPCTG4hcyVhpHAid9A6IB9oReY/view?usp=sharing|Code in Python]]
  
-===== References ===== 
  
-[[https://www.nature.com/articles/s41598-019-44741-y|Varma & Sino, 2019. Nectar robbing in bellflower (Sesamum radiatum) benefited pollinators but unaffected maternal function of plant reproduction]] 
- 
-[[https://link.springer.com/article/10.1007%2Fs11515-007-0068-5|Zhang et al 2007. Effects of nectar-robbing on plant reproduction and evolution]] 
2020/groups/g7/start.1579116578.txt.gz · Last modified: 2024/01/09 18:45 (external edit)