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--- 2017:groups:g4:start [2017/01/21 19:09] – [Beetles Preference of Parasitized Ants] group4
+++ 2017:groups:g4:start [2024/01/09 18:45] (current) – external edit 127.0.0.1
@@ Line 11: / Line 11: @@
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-===== Matrix =====
-<code>
-J =
-[ (r*((m*(b + h))/(k*(a*h - a*g*m*(b + h))) - 1))/((a*g*m*(b + h))/(a*h - a*g*m*(b + h)) + 1) - r*((2*m*(b + h))/(k*(a*h - a*g*m*(b + h))) - 1),       0, -(m*(b + h))/h]
-[                                                                                                -r*((m*(b + h))/(k*(a*h - a*g*m*(b + h))) - 1), - b - h,  (m*(b + h))/h]
-[                                                                                                                                             0,       h,             -m]
-</code>
 ===== Introduction =====
@@ Line 43: / Line 35: @@
   * Along the same lines, can beetles persist preying on ants in the absence of the parasitoid flies?
   * How does the behavior of parasitized ants alter the costs and benefits of predation and parasitism, from the point of view of the ant colony? For instance, if parasitized ants are still productive workers, the cost of being parasitized can be smaller than the benefit provided by predation.
+===== Questions =====
+Do parasitized ants go back to the colony?
+===== References =====
+{{ https://s-media-cache-ak0.pinimg.com/236x/c2/a1/eb/c2a1eb3d2e5a2b5de83d1b2c11528b48.jpg}}
+  * Mathis, K. A., and N. D. Tsutsui 2016 Dead ant walking: a myrmecophilous beetle predator uses parasitoid host location cues to selectively prey on parasitized ants. Proceedings of the Royal Society of London B 283:2016 1281
+  * Video of phorid flies in action: https://www.youtube.com/watch?v=pFVvOo1Qd_8
+====== Results ======
+===== Matrix =====
+<code>
+J =
+[ (r*((m*(b + h))/(k*(a*h - a*g*m*(b + h))) - 1))/((a*g*m*(b + h))/(a*h - a*g*m*(b + h)) + 1) - r*((2*m*(b + h))/(k*(a*h - a*g*m*(b + h))) - 1),       0, -(m*(b + h))/h]
+[                                                                                                -r*((m*(b + h))/(k*(a*h - a*g*m*(b + h))) - 1), - b - h,  (m*(b + h))/h]
+[                                                                                                                                             0,       h,             -m]
+</code>
 ===== Biological scenario and assumptions =====
@@ Line 48: / Line 59: @@
 We investigate two scenarios: one with a specialist beetle feeding exclusively on the parasitised ants and a second scenario with a generalist beetle, which feeds on both types of ants (normal and parasitised).
+===== Análisis de Nicolas =====
+The stability criterion gives a minimum predation rate performed by beetles. If we are over that minimum level, bettles are eating so many infected ants, so that affects flies and normal ants have no problem in converging to the capacity (asymptotic stability).
+If \mu(fly death rate) is greater, then the minimum predation rate is smaller and it is easier to normal ants to converge to capacity. Similar result is true, considering the parameter \gamma (incubation rate).
+If we are below the minimum level of predation rate, then there exists a coexistence equilibrium, so flies have a chance to survive by attacking ants.
+Formally, If \mu (fly death rate),\b (predation rate), are greater then the equilibrium number of ants N^* is bigger. If \alpha (attack rate of flies) is greater, then N^* is smaller.
 ===== Model assumptions =====
@@ Line 80: / Line 99: @@
 **Take this with a grain of salt, please.**
-Notice that this model is an extension of the previous one to include the specialization of beetles. There is a predation term of normal ants by beetles which is mediated by the proportion of normal and parasitized ants. We include two parameters /lambda_{N} and /lambda_{P} to weight the preference of beetles for parasitized ants due to their reduced aggressiveness.
+Notice that this model is an extension of the previous one to include the specialization of beetles. We consider the beetles population dynamic and assume it to be very specialist, so that beetles may only grow in the presence of ants. There is a predation term of normal ants by beetles which is mediated by the proportion of normal and parasitized ants. We include two parameters /lambda_{N} and /lambda_{P} to weight the preference of beetles for parasitized ants due to their reduced aggressiveness.
 //Assumptions//
-  - /lambda_{N} is very close to zero, which means beetles attack very few normal ants, which is indeed the case.
+  - Many many many...
-  - We consider the beetles population dynamic and assume it to be very specialist, so that beetles may only grow in the presence of ants.
-  -
+//Model//
-  - Ordered List Item and you c.
+{{ :2017:groups:g4:model_advanced.jpg?nolink |}}
+//Preference//
+Consider the functional response between beetles and parasitized ants.
+{{ :2017:groups:g4:functional_beetles_parasitized.jpg?nolink |}}
+Let me tell you why this might not be such a crazy idea. The paper reports that there is a constant removal of parasitized ants by the beetles, independent of the beetles population. This functional response suggests this behaviour when beetles are close to their carrying capacity, and the preference towards parasitized ants is very high.
 Here we will assume that we are dealing with a sufficiently small beetles population for interference with each other to be negligible.
@@ Line 182: / Line 209: @@
 //Functional Response//: the function relating the number of prey eaten by a single "average" predator to the size of the prey population.
-===== Questions =====
-Do parasitized ants go back to the colony?
-===== References =====
-{{ https://s-media-cache-ak0.pinimg.com/236x/c2/a1/eb/c2a1eb3d2e5a2b5de83d1b2c11528b48.jpg}}
-  * Mathis, K. A., and N. D. Tsutsui 2016 Dead ant walking: a myrmecophilous beetle predator uses parasitoid host location cues to selectively prey on parasitized ants. Proceedings of the Royal Society of London B 283:2016 1281
-  * Video of phorid flies in action: https://www.youtube.com/watch?v=pFVvOo1Qd_8
 ===== Reading List =====
@@ Line 194: / Line 215: @@
 Switching, Functional Response, and Stability in Predator-Prey Systems.
+===== Group presentantion =====
+  * [[http://200.145.112.249/webcast/files/Group%20IV_%20The%20Walking%20Dead%20Ant%20Tale-2.pdf|presentation]]