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--- 2020:groups:g7:start [2020/01/14 21:15] – group7
+++ 2020:groups:g7:start [2024/01/09 18:45] (current) – external edit 127.0.0.1
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 ===== 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://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: =====
-=== Sharing the code with the group ===
+We will model a network with 3 species interacting with 3 ecological processes:
-[[https://drive.google.com/file/d/1WriP7dRB2rcuG5Wm8tMQ09kd2z256d2L/view?usp=sharing|link do codigo no gdrive]]
+- 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:
+- The pollinators and the flowers have a mutualistic interaction:
+  - The flowers benefit from pollinator's visit for nectar - it increases flower growth rate.
+  - The pollinator eats flower nectar and increases its population size.
+  - The pollinators can't survive without flowers
+- The robbers and the flowers have a predator-prey-like interaction.
+  - The robbers eat nectar and damage the flower
+  - The robbers can't survive without flowers
+  - The robbers will not increase linearly as the number of flowers increases because it saturates, i.e. robbers can not eat as much as flower there are available
+- The robbers and the pollinators compete for the nectar.
+  - The robbers can force the pollinators to change their behavior, making them increase their outcrossing rate and visit more flowers due to nectar scarcity. This is beneficial to the flower population.
+With these assumptions, we proposed
+{{:2020:groups:g7:model1.png?500}}
+All parameters are non-negative. K is the carrying capacity of the flowers purely through self-pollination.
+In this model, the resource the robbers and pollinators compete for, nectar, is taken into account implicitly. The immediate problems we saw with the model were
+  * No account of the nectar dynamics. In fact, in this model competition persists independently of the population of flowers.
+  * The indefinite linear growth of the benefit to the flower in the number of robbers via a ternary interaction is unrealistic.
+We have the following fixed points:
+{{:2020:groups:g7:fixedpoints1.png?650}}
+===== Sharing the code with the group =====
+[[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]]