In the domain of evolutionary biology, there is a high interest in understanding how fostering selfish (individualistic) and altruistic (or cooperative) behavior can influence natural selection and benefit group members under particular de- mographic conditions. These members can organize themselves into "small trait groups", a collection of individuals that influence one another’s behaviors. In nature, traits usually aim at reproductive benefits, increased chances of feeding and higher protection from predation. Those traits commonly result in coope- rative behaviors, with many examples found in nature, such as schools of fish, flocks of birds or herds of bisons.
The ECEC model thus aims at investigating the evolution of two different coope- rative traits: alarm calling and feeding restraint. Alarm calling is a trait which benefits only individuals near the alarm-caller (i.e. prey presence, natural re- sources proximity, etc.). This trait is uniquely taken for self-benefice. Feeding restraint, on the other hand, considers that an individual action takes into con- sideration the common interest of the group to which an individual belongs. This is the classic example of altruistic behavior among non-humans. or pru- dent predation behavior found in certain type of animals.
The majority of works that try to explain those behaviors through models, are mostly quantitative models of group selection or, alternatively, make use of sy- stems of equations (Pepper and Smuts, 2000). However, there are some limi- tations in modeling traits based on purely mathematical models1. Instead of
using equations, the authors advocate the use of a multi-agent systems appro- ach to pursue their investigation, due to MAS ability to represent the behaviors and interactions of individuals in a more direct and natural way, to incorporate variation over space and time, and to incorporate non-linear dynamics capacity. To represent the ECEC model using MAS approach, (Pepper and Smuts,2000) considered a model consisting of a two dimensional grid, wrapped in both axes (to avoid edge effects) containing two kinds of entities: plants and foragers. The main idea is the study of the survival of two populations of agents that depends on the spatial configuration. The representation of ECEC is depicted in Figure 4.1
1According to (Williams,1966), those type of models either require simplifying assumptions,
such as homogeneous randomly mixed populations and infinite population sizes, or in some cases, population structure (the division of a population into more or less discrete groups) must be assumed a priori.
4.2. The ECEC Model 51
Figure 4.1 – ECEC representation : Foragers distributed in a spatial grid of plants
4.2.1
The plant and its behavior
The Plants are created only once and have a fixed location. They do not move, die, or reproduce. A plant’s only behavior is to grow (and be eaten by foragers). The plants vary only in their biomass, which represents the amount of food energy available to foragers. At each time unit, this biomass level increases according to a logistic growth curve:
Xt+1 = Xt+ rXt
1 − Xt K
where Xt+1 is the plant’s biomass over time, r is reproduction rate, and K the capacity rate.
4.2.2
The Foragers and its behavior
In order to study two types of behaviors with different traits, the model con- sidered two types of Foragers: Restrained foragers and Unrestrained foragers. Their only difference is their feeding behavior, explained in section4.2.4. The foragers, thus, have the following common behaviors: they consume energy, they move, they feed, they reproduce and, eventually, they die.
4.2.3
The foragers’ energy consumption behavior
At each step, the Foragers burn energy according to their catabolic rate. This rate is the same for all foragers. It is fixed to 2 units of energy per time period. Foragers lose energy (catabolic rate, 2 points) regardless of whether or not they move.
4.2.4
The foragers’ feeding behavior
When "Restrained" foragers eat, they take only 50% of the plant’s energy (bi- omass). In contrast, when "Unrestrained" foragers feed, they take 99% of the plant’s biomass, so that plants can continue to grow after being fed on, rather than being permanently destroyed. However, when all foragers eat, they feed on the plant in its current location, increasing their own energy level by redu- cing the same amount of the plant’s biomass.
4.2.5
The foragers’ reproductive behavior
Foragers reproduce if their energy reaches the fertility threshold (100 energy units). Their offspring keep the same heritable traits (i.e. same feeding beha- vior). In that case, it reproduces asexually, creating an offspring with the same heritable traits as itself (e.g. feeding strategy). At the same time the parent’s energy level is reduced by 50 energy units, the offspring’s initial energy (50 energy units). The newborn offspring will occupy the free place nearest to their parent.
4.2.6
The foragers’ move behavior
In their search for food, Foragers examine their current location and their sur- roundings. From those locations not occupied by another forager, they choose the one containing the plant with the highest biomass. If the chosen plant yields enough food to meet their catabolic rate (2 units of energy) they move there. If not, they move instead to a randomly chosen adjacent free place not occupied by any forager. This movement rule leads to the migration of foragers from de- pleted patches, and simulate the behavior of individuals exploiting local food sources while they last, but migrating rather than starving in an inadequate food patch.
4.2. The ECEC Model 53
4.2.7
The foragers’ die behavior
If its energy level drops to zero, a forager dies. Foragers do not have maximum life spans.
4.2.8
Model initial values and execution
The model is executed in the following order: the plants grow, then, foragers eat, then reproduce, then move, then die (if the energy level reaches zero). That sequence of behaviors can also be visualized in the form of an activity diagram, as shown in Figure4.2
Figure 4.2 – Activity diagram representing the sequence of behaviors to be executed during an ECEC model simulation
Table 4.1 – ECEC model’s initial values
Variable Entity Initial value
Biomass Plant Random value
between 0 and K
K Plant 10
r Plant 2
Catabolic
Rate All foragers 2 units of energy Fertility
Threshold All foragers 100 units of energy Energy All foragers 50 units of energy Harvest rate Restrained Forager 0.5 (or 50% of the plant’s biomass) Harvest rate Unrestrained Forager 0.9
In order to initialize the model, some initial values are required. The plant must have initial values for its biomass, K and r. Those variables are used in the growth behavior of the plant. Foragers also possesses initial values that are used in the description of some of their behaviors. The catabolic rate is the amount of energy that foragers lose over time and has a default value of 2. The fertility threshold is the max energy value of a forager before it reproduces. It is fixed as 100. Finally, the initial energy of all foragers is set as 50. Those values are listed in Table4.1