Resources: Assessing, Obtaining, and Defending.

Up to now, we've been concentrating on interspecific competition (among different species); However, intraspecific competition (within a species) can be as important in shaping the distribution and density of a species. Intraspecific competition can result in intense selection pressure for both solitary and social species.
A simple model of resource assessment shows how a species might divide a resource that is patchy, unevenly distributed, or in short supply (Figure 1). Under low population density conditions, the risk of intraspecific competition (measured as search time) is low. This model would predict that animals should search in the rich habitat to maximize their resource intake. Under high population density, however, competition with other members of the species should make searching in sub-optimal habitats more attractive. Thus, if we have two habitats; one rich, the other poor, and individuals can move freely through the habitats then the first to arrive will choose the rich habitat. As more arrive and population density increases, the resources will be depleted or interference among individuals will increase the competition. There is a point where the poor habitat becomes more attractive since animals don't have to share limited resources.

This simple model was tested with sticklebacks (Figure 2). The feed rate on the right side of the tank was twice that of the left side of the tank. This resulted in the fish dividing up so that 2/3 were on the high feeding side and 1/3 fed on the low side of the tank (Figure 3). All fish feed at a maximal rate.

Any resource can result in intraspecific competition. Territorial behavior in birds is shown in figure 4. For this animation, high quality territories are shown in dark green near the stream. The first birds that move in choose these territories. Since they are more familiar with the habitat, they will have an advantage in defending the territory (and will fight harder to retain ownership as shown later in this section). As other birds move in, territorial boundaries are agreed upon. High quality territories are often smaller than low quality territories since they'll be more difficult to defend and because they'll have a greater resource density. Animals in the high quality territories can support greater numbers of offspring and pass on their territorial defense and assessment behaviors to the next generation, resulting in a population with high intraspecific competitive abilities. Those with poor intraspecific competitive abilities donate few genes to the next generation's gene pool.

Game Theory
During the mid-seventies Maynard-Smith borrowed a theory developed by the Pentagon to predict when an animal should fight to defend a resource. Since then, the predictions of game theory has been tested in a variety of animals, from spiders and birds through humans. Although the birds in our above example defend their territories with little danger to themselves over much of the breeding season (through territorial calls), one-on-one confrontations and all-out fights are common during the early procurement of territories. Although it is expensive and risky to assess, obtain, and defend a territory, it is even more costly in reproductive fitness to have a low quality territory, or none at all. The payoff is in reproductive fitness while the expense is measured in potential loss of fitness (through injury, cost of display, etc.).

Borrowing the terms hawks and doves from the military, hawks are expected to fight for a resource and will injure or kill their opponents. The up side of being a hawk is that you'll get all the resource. The down side is that you may be injured or killed. Doves, on the other hand, only display (sing, bluff, etc.) and do not engage in fights to the death. The up side is that doves don't get killed, but they may not get a resource.

• As an example, let's assume that the winner gets +50 points, and that the loser of a confrontation gets 0 points. Injury costs either -100 points, and the cost of display is -10 points. These scores are a measure of fitness. The payoff matrix for these scores is sown in figure 5.
• Looking at a Hawk-Hawk confrontation, each bird has a 50% chance of winning or losing; thus the benefit of winning or losing is multiplied by 0.5 (in the matrix: 0.5(50)+0.5(-100)). The payoff for a Hawk-Hawk confrontation is -25 points.
• For a Hawk-Dove pairing, the Hawk always wins and, since the Dove runs off, the Hawk is in no danger of being injured. The payoff is therefore +50.
• Doves don't attack so a Dove-Hawk confrontation never takes place (the payoff is 0).A Dove-Dove confrontation is again a 50:50 chance of winning. The upside of winning is calculated as 0.5(50-10); while the cost of losing is 0.5(-10); either way, the winner or loser will have to bear the cost of display.

If a population were composed entirely of doves, then the score averages out to +15 points.If, however, a mutation occurs that produces a hawk behavioral type (excess testosterone production, for example), the mutant hawk will always win against doves and gain 50 points. Therefore, a population of all doves is not an evolutionary stable strategy (ESS) since a single hawk genotype will quickly start to take over.

A population of all hawks doesn't work either since the average score is -25 and any dove mutation will do better (0 is better than -25). All hawk is not an ESS either.

A mix of hawks and doves should be stable when the average score for a hawk is equal to the average score for a dove. This point is (for the above payoffs):

H = -25h + 50(1-h)
Where: h is the proportion of hawks in the environment and
D = -0h  + 15(1-h)

This stable situation occurs when hawks are 0.5833 of the population and doves are 0.4167. Figure 6 shows the results of varying the Hawk:Dove proportions. Note that 100% hawks or 100% doves doesn't work, although a population weighted toward a high proportion of hawks will be stable.

Let's add a new strategy: Bourgeois: be a hawk if you own the territory, a dove if you do not. This strategy makes sense. If you already have gone to the work of assessing and obtaining a territory, you should work to defend it. If you don't own a territory, then you are unsure of the quality and shouldn't fight to obtain it. A population where Bourgeois own half of the territories is shown in figure 7. Note that a population that is entirely Bourgeois is an evolutionary stable strategy. Figure 8 shows the success of bourgeois as the proportion of hawks increases in the environment. Note that, except at low proportions, bourgeois manages to outdo hawks and that bourgeois always is better than dove.

Using the Game Theory Simulator
The components of the game theory simulator are shown in figure 9.

• Area A (Figure 9): Costs and benefits are input here. NOTE: enter all values as positive numbers. The program understands that losing and display are costs and will deal with them appropriately. Press the calculate button to see the results.
• Area B: Shows the payoff matrix for the Hawk-Dove contest. The ESS proportions of Hawks:Doves is calculated in the lower part of "B". Overall payoffs are also given (for the input data and at the calculated ESS
• Area C shows the payoff matrix and overall payoff for the Hawk-Dove-Bourgeois scenario.
• The top graph shows the effect of varying the proportion of hawks to doves. Low frequency Hawk populations are at 0 on the X-axis, high density at the right. For this combination of costs and benefits, the hawks do well at low densities, but being a hawk is bad if lots of other animals are hawks. The Y axis is the payoffs at the various hawk frequencies.
• The lower graph shows the effect of varying the propensity of bourgeois to fight. The left hand X-axis are pacifist bourgeois, the right hand war-like bourgeois.  The Y axis is the payoffs for the various bourgeois fighting frequencies.
• The data grids next to the graphs contain the raw data for the graph. The ClpBrdHD button will copy the Hawk-Dove data to the clipboard (upper grid). The ClpBrdHDB copies the Hawk-Dove-Bourgeois grid to the clipboard.

Figure 11 shows the outcome when the benefit of winning is reduced to 25. Note that the ESS has slid back to .375 and the costs for behaving as a hawk have increased. In figure 12 we have increased the payoff for winning from the default of 50 to 75. Note the change in the overall payoff and ESS frequencies.

1) What has this done to the Bourgeois simulation?
2) Explore the effects of changing the costs and benefits of Injury, losing, etc. on the outcome of the Hawk-Dove and Hawk-Dove-Bourgeois competitive scenarios. Explain the trends you discover.

Figure 13 shows the results for the default configuration using the "advanced options" while stepping the win payoff from 0 to 100. The advanced options will allow you to simulate positive losses or costs of display by stepping from a negative number (the regular option will not accept negative numbers; this was done so you don't confuse the simulation and equations).

3) Is the Dove behavior pattern ever selected for? Explain.
4) What is the approximate ESS for Hawks vs. Doves (Scroll through the grid)? What happens to Doves under these conditions?
5) Adjust the rest of the parameters to discover the relationships between each parameter and the outcome of the simulation. What have you found?

Figure 13 shows the advanced options; this time for stepping the Win payoff from 0 to 100

6) Discuss the implications of changing the Win payoffs as shown in figure 13
7) Explore each of the other options. Explain what you have seen from an evolutionary/ecological point of view.
8) Discuss how genes for aggressive and non-aggressive behaviors would sweep through a population to establish an ESS. Use examples from your simulations along with "real world" examples.

There are some conditions under which the cost of losing can be positive. If you are in a conflict with a relative (as in wolf packs), losing still allows you to pass genes through a relative. If, for example, you are fighting a brother, you would share half of his genes and, if your brother wins, you still have genes passed to the next generation. Assuming that the payoff for winning is 50 points, then the payoff for losing would be 25 points. NOTE: To simulate a positive loss, you must step from -25 to 25 under lose.

9) Run the above scenario and determine the ESS when the cost of losing is 0 and 25. Do these results surprise you? Try to explain why it would work this way. Also explain what has happened with the Bourgeois.

Conclusions

• The fighting strategy is frequency-dependent. The best strategy depends on what other animals are doing. Hawk is good in a dove environment, but is a loser when the frequency of hawk is high.
• An ESS is often a mix of hawks and doves.
• The ESS is dependent on the values of the scores in the game. If the scores are changed, then the stable mix of hawks and doves changes. As long as the cost of losing is greater than the payoff for winning, you always expect a mix. The payoffs and costs are difficult to measure in nature, although litter size, number of eggs, and egg mass have been used effectively.
• An ESS is resistant to invasion from alternate strategies.
• Animals do assess the weaponry of their opponents. Bourgeois individuals give up sooner when...
  • The opponent is larger.
  • The territory is owned, but is of poor quality.
  • Age-dependent: Young give up sooner than older animals (more reproductive years to lose; an old animal may only have a single season left).

Readings (Required):

1. Evolution of behavior.
2. Evolutionary Stable Strategies and Game Theory.  (Do the readings, but don't bother with the simulation).