doc: added brief results of a simulation for the reference model R1

git-svn-id: https://tegsvn.uib.no/svn/tegsvn/tags/AHA_R/R1@6992 ad98353e-09f0-4531-9f56-ca5884d0cf98

simulation/RESULTS.md

+# Reference model R1 #
+## Overview of the simulation results ##
+
+### A brief outline of the model ##
+
+The reference model **R1** implementing elementary self-awareness follows the
+simple mesopelagic fish system developed by (Giske et al., 2013, 2014). Here
+a population of fish lives in a water column together with stochastic food
+(zooplankton) and predators. Zooplankton is randomly distributed within a
+thin vertical layer. Illumination changes according to the diurnal cycle
+and the zooplankton executes diurnal migrations in a pattern opposite to the
+light cycle: goes up at night and down the depth during the day.
+
+**This simple system provides physical gradients, environmental dynamics and
+significant stochasticity.**
+
+A fish can orient only by vision and therefore can directly interact only
+with objects that it can see, the same holds for the predators. Visibility
+of an object (visual range) is a complex function of its size, contrast and
+illumination level (Aksnes & Utne, 1997)⁠. To find food, the fish must
+follow the constantly changing vertical distribution of the food. Whenever
+the fish eats a food item, it obtains energy. All movements and simple
+being alive have certain energetic costs, so that the fish will quickly
+die of starvation if it does not find food or does not eat for any other
+reasons. If the fish eats a food item, all surplus energy not offset by the
+living costs goes to the growth and build up of the reproductive factor.
+
+The neurobehavioral system of the fish in the model is built according
+to the above architecture and has three survival circuits: hunger, fear
+and reproduction. It also has a behavioral repertoire including various
+movements (including vertical migrations) immobility, escapes, migration and
+can eat zooplankton food items that occur within the visual range. Behavior
+selection at each time step minimizes the expected emotional arousal by
+re-entrant assessment as described above. Overall, this seems to be a
+very complex optimization problem, especially because of the flexible,
+unpredictable and not fully deterministic link between the instantaneous
+environment and the behavioral action. It might even seem non-obvious if
+the genetic algorithm can solve it at all. However, inclusion of the same
+individual genetic weights for both determining GOS and prediction of GOS
+arousal provides a set of constraints greatly reducing the computational
+complexity. Furthermore, we use an adaptive genetic algorithm such that initial
+stages of the evolution are much less complex, complexity is increasing as
+the evolution proceeds. For example, the life cycle is initially very short
+and increases with repeated generations.
+
+#### R1 Model characteristics ####
+
+- **This is a very short and limited simulation over 100 generation. It is
+  used for simple illustrative purposes only.**
+
+- Food resource is created for new at the start of each generation and no
+  food is replenished between generations. This means that if the agents
+  eat all food at the start of the generation, no food is left. This makes
+  the optimization problem more complex with each new time step within
+  a generation.
+
+- Food items perform diel vertical migration in a pattern opposite to the
+  diel illumunation pattern.
+  ![Fig. 1](http://ahamodel.uib.no/otherinfo/desc_r1/plot-r1-01.svg)
+
+- The agents select all behaviours based on the minimum expected arousal
+  principle. That is, all behaviour is based on elementary self-awareness.
+
+- To ease the initial stages of evolution, adaptive genetic algorithm is
+  used. Here the number of time steps in the model is set to a single diurnal
+  cycle at the generation 1 (168) and increases to 560 at the generation 100.
+  The pattern of this increase is shown on the plot below. Mutation rate is
+  also changing according to
+  [ga_mutat_adaptive](http://ahamodel.uib.no/doxydoc/classthe__population.html#a3dd42184e1f4e3cad9ef2d887c2c0286)
+  function.
+  ![Fig. 1](http://ahamodel.uib.no/otherinfo/desc_r1/plot-r1-02.svg)
+
+### Basic results ###
+
+The agents evolving over one hundred generations exhibit a steadily increasing
+growth. The number of agents that wrew at the end of each generation showed
+a steady increasing pattern.  The number of agents that were alive at the
+end of each generation reduced initially (up to generation 60), but started
+to rise with further generations (after generation 80).
+
+![Fig. 1](http://ahamodel.uib.no/otherinfo/desc_r1/plot-r1-03.svg)
+
+#### Feeding and growth
+
+Due to the increasing optimization complexity caused by the lack of food
+replenishment within a generation, body length and the feeding rate of the
+evolving agents stopped growing after approximately generation 30.
+
+![Fig. 1](http://ahamodel.uib.no/otherinfo/desc_r1/plot-r1-04.svg)
+
+However, this was caused by efficient optimization--the agents were able
+to eat out almost all of the food available in the environment. This is
+illustrated by the following plot that shows the percentage of food items
+in the environment that were still available (not eaten) at the end of each
+generation. This plot also shows the average perceived number of food items
+by the agents.
+
+![Fig. 1](http://ahamodel.uib.no/otherinfo/desc_r1/plot-r1-05.svg)
+
+Clearly, the agents were able to eat out nearly all food resource available
+to them in the environment. Thus, approximately after generation 40, their
+encounter rate with the food items fell to nearly zero.
+
+The following plot shows the pattern of food consumption (feeding rate,
+the number of food items eaten at each time step per alive agents) over the
+time steps at the last generation (100).
+
+![Fig. 1](http://ahamodel.uib.no/otherinfo/desc_r1/plot-r1-06.svg)
+
+It is clear that the agents eat out most of the food already during the
+first half of the life cycle.
+
+#### Predator avoidance
+
+With each new generation, predation success (numbe of agents killed per time
+step) reduced. Thus, the agents evolved more efficient predator avoidance
+tactics. The predator perception by the agents (number of predators that they
+see) also showed a reducing pattern, but there was a significant sigmoidal
+fluctuation. This might have several different interpretations.
+
+![Fig. 1](http://ahamodel.uib.no/otherinfo/desc_r1/plot-r1-07.svg)
+
+#### Response to conspecifics
+
+The agents evolved avoidance of conspecifics, presumably to reduce food
+competition. Predator and conspecific perception had similar cyclic patterns
+that probably reflect changes of visibility and depth.
+
+![Fig. 1](http://ahamodel.uib.no/otherinfo/desc_r1/plot-r1-08.svg)
+
+
+### General conclusions ###
+
+- **The AHA model results in a realistic adaptive evolution of the agents over
+  the generations.**
+
+- **The significant complexity and indeterminancy caused by elementary
+  self-awareness of the agents (their ability to assess and predict their
+  emotional state) does not preclude evolutionary optimization.**
+
+- **Evolutionary adaptation of the agents in these conditions involve more
+  efficient capture of food items, avoidance of predators and avoidance of
+  conspecifics (reducing food competition).**
+
+### References ###
+
+- Aksnes, D. L., & Utne, A. C. W. (1997). A revised model of visual range in
+  fish. Sarsia, 82(2), 137–147. http://doi.org/10.1080/00364827.1997.10413647
+
+- Giske, J., Eliassen, S., Fiksen, Ø., Jakobsen, P. J., Aksnes, D. L.,
+  Jørgensen, C., & Mangel, M. (2013). Effects of the emotion
+  system on adaptive behavior. The American Naturalist, 182(6),
+  689–703. http://doi.org/10.1086/673533
+
+- Giske, J., Eliassen, S., Fiksen, O., Jakobsen, P. J., Aksnes, D. L.,
+  Mangel, M., & Jorgensen, C. (2014). The emotion system promotes diversity
+  and evolvability. Proceedings of the Royal Society B: Biological Sciences,
+  281, 20141096–20141096. http://doi.org/10.1098/rspb.2014.1096
+