Initial simulation results for Model R1

Introduction

The reference model R1 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 zooplankton food 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. Thus, this simple system provides physical gradients, environmental dynamics and significant stochasticity. Decision making and action selection in the fish agents in R1 is based on elementary self-awareness: the ability of the agent to assess its own emotional state and use this information for decision making.

The Reference model R1 is doi:10.5281/zenodo.1215790 .

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 illumination pattern.
  • 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+ function.

Basic results

The agents evolving over one hundred generations exhibit a steadily increasing growth. The number of agents that were 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).

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.

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 at the end of each generation (note that the fluctuations in perception are caused by differences in the illumination level due to unequal number of time steps across all generations).

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).

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) at the last time step of each generation also showed a reducing pattern, but there was a significant sinusoidal fluctuation because of different illumination levels at the end of each generation (the number of time steps was unequal).

Response to conspecifics

The agents evolved avoidance of conspecifics, presumably to reduce food competition. Predator and conspecific perception at the end of each generation had similar cyclic patterns that reflect changes of visibility due to unequal number of time steps.

General conclusions

  • The AHA model results in an 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 involves more efficient capture of food items, avoidance of predators and avoidance of conspecifics (reducing food competition).

Citations

  • 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