### EACH

### Curriculum Guide

## Main Page, Curriculum Guide

## 1. Overview of the Guide

This Guide offers 1) a general description of the Altruism and Cooperation models developed at the EACH project, 2) a proposed structure for presenting the models, and 3) a sample curriculum guide that encapsulates the approach that we have adopted in past sessions with students. The sessions follow the general format of beginning with a preactivites discussion, in which we get a feel for the students' background in evolutionary theory and their expectations for interacting with the models, then having the students interact with the Altruism set (including discussion periods), and finally having them interact with the Cooperation set (also with discussion periods).

## 2. Description of the Activities

The EACH project models are designed to expose students of evolution to the complex dynamics of evolutionary systems. In particular, these models emphasize that the evolution of altruism and cooperation is possible when the interaction of environmental conditions (such as harshness or physical barriers) and social factors (such as grouping) are taken into account. The primary goal of the EACH models is to address students’ conceptions of fitness, and to give them a hands-on approach to exploring selection at the gene-level, individual-level, and group-level. Through exploring these multiple levels of fitness students are encouraged to move beyond the notion of the "survival of the fittest" as the dominance of a strong individual, and to consider fitness as an emergent phenomenon, existing at different levels, and contingent upon many environmental and social factors.

The EACH project is structured around two sets of seed models that encourage students to predict the outcome of certain evolutionary scenarios. Each set has two models. The first model in each set is designed to allow the students to explore the structure of the model and to expose their basic intuitions about what the results should be. This model has what we will call the ‘expected’ result, and thus allows the students to integrate their intuitions with their expectations for the model. By developing this sort of familiarity with the first model, students feel comfortable trying to anticipate the results of the model, and provide reasons why these results should be the case.

The second model in each set introduces new environmental and/or social parameters that affect the group-level dynamics of the populations of selfish and altruistic agents. These changes allow for the surprising consequence that altruistic and/or cooperative behavior is more fit. The movement from the first to the second model within each set is intended to demonstrate how the introduction of environmental and social considerations into population dynamics can dramatically change how we understand individual, group, and gene-level fitness. What this curriculum emphasizes is the movement between these perspectives, and how the intuitive assumption of thinking about fitness as individual strength can generate misleading inferences about the survivability of group-level traits such as cooperation and altruism.

There are two key assumptions made in this serial ordering of the models in each set. First, we assume that by allowing students to become familiar with the "unsurprising" reasoning involved in the first model of the set, they will engage in trying to explain why the model has the results that it does. Second, we assume that once students have articulated their intuitions about how the model works, when they see the outcome of the second model in the set, it places the challenge to their intuitions directly before them. They become aware of the assumptions they are making and the difficulties in their own intuitions about the system; thus the students are engaged in trying to figure out how they can think differently about the scenario in order to understand this ‘surprising’ outcome.

There are two sets of models in the basic EACH curriculum. The Altruism set and the Cooperation set. The sets are presented serially, so the Altruism set is worked through first (Altruism model 1 followed by Altruism model 2), and then the Cooperation set, in the same order. The basic idea is that students develop familiarity with the first Altruism model, and then find the striking result that in the second Altruism model altruism can survive under certain environmental and social conditions. This process is described in more detail below. The important point is that before and after each model in the set students are encouraged to discuss the parameters and conjecture about what will happen (before the model is run), or why what happened did happen (after the model is run). It is often helpful to allow them to run the model several times, and to play with the parameter space until they are comfortable with the basic behavior of the model.

After students have discussed the outcomes of the Altruism set, they are presented with the Cooperation set. Once the parameters are described to them, students quickly have a feel for what outcome to expect from the first Cooperation model. After seeing the first model’s results, the students are asked to put their learning to the test and devise a way to get the cooperators to survive. The final cooperation model presents one possible solution, but the same idea can be implemented in many ways, and we encourage hands-on model development as part of this final stage of the curriculum. Allowing students to introduce new physical elements, or extend the parameter space is an important way of getting them to think through their new ideas in a more concrete way. It is also important, as a matter of closure, to make sure that students understand the theoretical significance of whatever solution they ultimately implement.

A note on the serial ordering of the sets. The Altruism set is the more difficult conceptually than the Cooperation set — for it requires a richer descriptive understanding of how the parts of the model are interacting. However, by getting students familiar with they way that this model works, and allowing them to develop an intuitive feel for it, we find that they are well prepared to think critically about the Cooperation set. The Cooperation models are more embodied, and the concepts are much more intuitive to most users. Thus, after the students have had to think through the "biology" of the Altruism models, and the mechanisms that allow for the survival of altruism, they show remarkable insight into the problem presented by the second Cooperation model.

## 3. The PreActivities Discussion

- What is fitness?
- What do you think makes an agent more fit than another agent?
- Do you think that altruistic behavior can survive in competition for resources with selfish behaviors? Why?

## 4. The Altruism Set

Altruism Model 1 (Before)

- What do you think the outcome of the model will be?
- Which population has the higher fitness? Why?

__I. Explanation of the model__

The first model used in the EACH project was a conservative model of evolutionary behavior based on current theory in evolutionary biology. This first model has two types of agents: selfish and altruistic. The premise of the model was that each agent would look around to its neighbors and see whether they were altruistic or selfish. For each altruistic neighbor, the agent increased its fitness by a fixed value. Thus, each agent with altruistic neighbors would have a higher fitness in the reproductive lottery. Each agent then calculated its fitness with one of the following equations:

If I am a selfish individual, my fitness is 1 + my benefit from my altruistic neighbors.

If I am an altruistic individual, my fitness is 1 — the cost of being an altruist + my benefit from my altruistic neighbors.

The values of ‘benefit’ and ‘cost’ are slider-variables that are set at values such that the cost of being an altruist significantly weakened the fitness value of altruists, while the benefit from the neighboring altruists were only significant when there were two or more of them. Each agent is at the center of a five-agent neighborhood. To enter the reproductive lottery, each agent looks at its neighbors (in the four cardinal directions) and assesses their fitnesses. All of the altruistic agents’ fitnesses are summed (including the central agent, if it is an altruistic agent), and all of the selfish agents’ fitnesses are summed (including the central agent, if it is a selfish agent). These sums constitute the weight of altruistic ‘seeding,’ and the weight of selfish ‘seeding’, respectively, for the center spot in the reproductive lottery. To complete a generational cycle, a random number is picked between 0 and the total of the weights for a spot. The spot is then given to the type of agent whose weighted chance fell on the side of the random number. The higher an agent-type’s weight, the greater the chance that that type of agent will win the spot.

__II. Questions__

**Altruism Model 2 (Before)**

- How will the harshness and disease conditions affect the populations?
- How will the new environmental factors affect the fitness of the selfish and altruistic individuals?

__I. Explanation of the Model__

The second model, based on recent work in the evolutionary biology of cooperation and altruistic behavior, introduces a new element to the model: adversity. The second model adds a slider-variable called >‘Harshness,’ and a slider variable called ‘Disease.’ The harshness variable gives each empty "patch" (a unit of the screen that is not occupied by a selfish agent or an altruistic agent) a chance of staying empty (resisting population) each turn. Envisioning the model-world as an environment in which individuals need to occupy a space on the grid in order to live, the harshness variable limits population growth by, at each clock "tick" making some of the spaces uninhabitable The disease variable is incorporated into the reproductive lottery for each spot. The value of this variable corresponds to the chance that an agent that occupies a spot on the grid will fail to reproduce, and thus that the spot will become empty. The introduction of these elements into the model alters the relationship between individuals and their environment. The new threats to the well-being of individuals reframe the importance of group behavior on individual success. This second model has a much richer parameter space -- students can explore the effects of the various harshness and disease values on the stability of the altruistic and selfish populations.

__II. Questions__

**Altruism Model 2 (After)**

- Gene-level, individual-level, group-level selection.
- The relationship between gene-level selection and within-group v. between group selection.
- What happens to make the altruists survive?
- What are the spatial properties of the populations when the altruistic population begins to grow?
- How do these spatial properties correspond the fitnesses of the various populations?
- Why were the selfish agents able to win in the first model, and not in the second model?
- Which agents are more fit: altruists or selfish agents? Why? What is fitness?

__I. Discussion__

__II. Questions__

## 5. The Cooperation Set

Cooperation Model 1 (Before)

- Which population will survive? Why?
- How is this model like the Altruism model?
- Which population has the higher fitness? What factors determine this fitness advantage?
- At what level(s) of selection, gene, individual, or group, is this fitness advantage determined?

I. Explanation of the model

The Cooperation model consists of two parts: cows and grass. The grass is designed to grow in such a way that above a certain height, it has a high percentage chance of growing back to its full height each turn, but below a certain height, it grows back very slowly. The high grass is thus considered to be healthy, or sustainable grass, and the low grass is considered to be unhealthy grass. In terms of the model, these variables can be expressed in terms of the following parameter settings: the maximum grass height is 10; the threshold for healthy grass is 5; the chance for growing back for healthy grass is 75%; and, the chance for unhealthy grass growing back is 30%. These parameters are all slider variables that have been put into the Cooperation model. There are two types of cows. The first type of cow, the "greedy", eats the grass as far down as possible. The second type of cow, the "cooperative", only eats the grass if it is above the fast-growth threshold. All the cows have the same metabolism, and require a fixed amount of food to live. Each turn they lose a percentage of their energy, and if their energy runs out, they die. Eating grass restores a cow’s energy by a fixed amount. Finally, if a cow’s energy reaches a certain threshold, it reproduces. In terms of the model, these variables can be expressed in terms of the following parameter settings: all the cows get 51 energy units for eating from a patch of grass; they all lose 10 energy units each turn for moving (regardless of how far they move); they all reproduce when their energy level reaches 101; and, they all lose 40 energy units for reproducing. These parameters, too, have been made into slider variables in the Cooperation model.

Thus, all things being equal, the only difference between the greedy cows and the cooperative cows is that the former eat all the grass and over-harvest the land, while the latter will go hungry rather than damage the well-being of the food supply.

__II. Questions__

Cooperation Model 1 (After)

- Why did the greedy agents dominate?
- What were the spatial properties of the interaction of the population?
- What factors affected the fitness of the greedy and cooperative populations?
- What could we change about the model to get the cooperative population to survive?
- Can we make an individual cooperator survive without making the cooperative population survive? How is the cooperative individual tied to his group in a way that the greedy agent isn’t?
- Group, individual, and gene-level selection — how these are represented in the behavior of the individual agents and the groups of agents.
- Discussion of various ideas to that will get the cooperative population to survive. Encourage ideas, and implement extensions of the Cooperation Model 1 — get students to discuss how these ideas are supposed to affect the populations, emphasizing the spatial aspects of the model and how to affect them.

I. Questions

II. Discussion

Cooperation Model 2 (Before)

- What will be the outcome of the model?
- What is the effect of keeping the populations localized? How will this affect fitness? How will this affect gene-level selection?

I. Explanation of the Model

The second Cooperation model introduces the variable of population viscosity into the model. Population viscosity as the limitation in a cow’s range of movement due to environmental barriers. The agents are then limited to their specific areas. So, if an agent has a sustainable, or cooperative practice, only it and its progeny reap the benefit of that behavior. And, if an agent has an overly consumptive behavior, only it and its progeny reap the rewards of that behavior.

__II. Questions __

Cooperation Model 2 (After)

- Why did the cooperative population thrive?
- Why was population viscosity important?
- How important is it that the offspring of a cooperative agent benefits from its parents’ cooperative behavior? What if unrelated, but cooperative agents, benefited from an agent’s cooperation? What is the difference between genotypic similarity and a kin relationship?
- What is altruism?
- What is fitness?

I. Questions