Disparity of Density in the Age of Mobility: Analysis by Opinion Formation Model

Round 1

Reviewer 1 Report

·        The author mentions that „This study focuses on the concentration of people in urban areas caused by increased mobility”. It is recommended to make some table or scheme including pushing and pulling factors of these processes. Or maybe is it possible to group that factors which are described in the text – even starting from Introduction we can see it.

·         Maybe it could be valuable to identify/describe the agents – who are they, maybe they can be grouped etc.

·         Probably it could be nice to see some research scheme/stages how it was implemented.

·         How this research can be adopted/applied in other countries/regions, etc.? Or is it just for big cities?

·         Conclusions seems to be very general. Maybe some recommendations could be provided?

Author Response

Thank you for your valuable comments on this paper. I have revised the paper in response to your comments, which I believe has made the content clearer and easier to understand. You have written about five points for my paper. I will explain my response to each of them.

1. I explained the Push and Pull factors related to migration at the end of the Introduction. Push factor is the increased cost of living associated with higher density and Pull factor is the density each person seeks (opinion). We explained that different agents have different tolerance for density costs and different opinions for density, so the problem becomes a complex system and ABM is necessary.
2. I consider the agents in this model to be households making residential choices. However, it may be appropriate to think of them as companies, for example. I have described this in the first paragraph of Section Methods.
3. I'm sorry but I wasn't sure what you meant by your third question, ”Probably it could be nice to see some research scheme/stages how it was implemented.” Are you asking about the methodology of the study? If it is insufficient to explain I used an ABM application called NetLogo, please let me know.
4. This study assumes an already highly populated metropolitan area in a country/region where people can migrate by their will. But we can also consider more sprawling suburbs by changing the distribution of agents in the initial state, or by changing the number of agents or density costs. We could also assume a country/region where people can hardly migrate by their will. This point is discussed in the last paragraph of the discussion.
5. I expanded conclusion. I added recommendations in conclusions. Future studies that developed the ABM with data of population or GIS could contribute to urban planning, make it possible to bring just cities.

Reviewer 2 Report

Author presented the paper devoted to study of a simple Agent-Based model on typical Cellular Automata grid. This approach is used to study the effect of potential creating and disappearing of areas which are common for people of similar status - what corresponds to the well-known gentrification phenomena.
Let me to start from the opinion that the attempts to model the social phenomena are very interesting especially due to their multifaceted character. It is not easy to consider a lot of elements of humen behavior and finalize it with some real result.

With this preliminary remark let me to notice that, in order to present such a model unambiguously, one has to define especially three elements (similar to the typical CA scheme): the set space, the grid where the spaces can occur and the rules to change the existing image. Although the model looks very interesting, I think that the presentation of model should be improved. My remarks concern especially.

The description of grid:
1.1 Author assumed patch size 31x31. Why? How does it correspond to reality? What would change if we assume anothee patch size?
1.2 "Each agent resides in one of the 991 patches" - comparing it with the paragraph from lines 158-160 we can ask the question if every agent is located in his own patch, so what are the sources of differences in denstity? How does if correspond to initial gaussian distribution of agents?
1.3 "we assumed no boundary conditions. An agent that moves out from the edge of the patch space emerges from the edge 149 from the opposite side."
Is Author sure that this description is correct? - If agent emerges in the same patch from the opposite side - it is the definition of boundary (sometimes called Born-vonKarman) conditions.

The rule:
2.1 The formulas (1-5) are unclear. In my opinion, it would be better to present it in the pure mathematical form. The, similar to self-consistent, form would be better visible. Some detaoils below.
2.2 How are \delta and \epsilon determined. The description is unclear and does not conform to the form of equations. It looks that authos notices here problems with the form of presentation.
2.3 Is the model synchronized or unsynchronized?
2.4 Does the "mobility" factor influence only eq.2?

Other remarks:
3.1 What is the range of agents' opinion? It is stated that "Agents’ opinions are represented by con-108 tinuous variables" but what does it mean in the sense of fig.3, where "opinion" usually decrease from ~20 to ~10?
3.2 What is the description of axes in fig.3? It is important in connection with question 2.3?
3.3 Author presents several sets of similar plots. In my opinion it would be better to organize the in such way that they can be compared one to another - but thois opinion is not crucial for my review. More important is that the captions are the same and oine has to look for the explanation of differences in text.
3.4 Are there any outliers on box-plots? This is very nice form of presenting data but such question still arise.
3.5 As I understand author assume the same mobility for all agents. Is it correct?

Author Response

Thank you for your valuable comments on this paper. Your point about explaining the model clearly is very important. In revising the paper according to your comments, I believe I was able to improve the paper. You have written about ‘description of grid”, “the rule” and “other remarks”. I respond to each comment individually and explain how the paper was revised.

Description of grid

1. The patch size should depend on the number of agents. If the patch size is too small for 400 agents (e.g., 5x5=25 patches), there will no empty patches where agents can stay far away from other agents (low density). Agents of few resources will have to constantly run around due to high density costs. Conversely, if the patch size is too large (e.g., 100x100=10000 patches), all patches except for the center patches will be blank, making it difficult to understand the distribution of agents. I have tested several patch sizes and confirmed that 31x31 is appropriate for 400 agents. This is explained in the Methods section. I set the number of agents to 400 because I thought it would be better to have that number of agents to show the distribution of the amounts of resources. If the number of agents were too large, machine power would not be able to keep up, so the number of agents was set at 400.
2. Each agent resides in one of the 991 patches. But each patch is not occupied only one agents. Especially for the central patches, there can be more than one agent per patch, as Figure 1 shows. I think I had not explained this point well enough, so I explained it as follows. “Each agent resides in one of the 991 patches. ...Each patch is not occupied only by one agent. Multiple agents may coexist in a patch, particularly in the central patches.”
3. Thank you for pointing about boundary condition. The model assumes like Born-von Karman boundary condition, although I think a little bit different. So I wrote only boundary conditions.

The rule

1. Thanks for pointing this out. I agree with you that it would be better to make the variables in the mathematical forms, such as a, b, c, etc. However, when publishing a program on netlogo, it would be more difficult to understand the program if it were made by mathematical forms. Since I publish the netlogo program with the paper as attached, I would like to leave the formulas as they are now. Many of the research papers that have used netlogo so far have followed the method described in this paper. In order to make it a little easier to understand formula, I have underlined them.
2. \delta and \epsilon are independent variables. The values are given in the section Results. I added the explanation as "The value is 0.01, 0.001 or 0, as explained in the next section."
3. Agents are evicted, migrate, change their opinion asynchronously following the orthodox assumption of NetLogo. I explained it in the section Method. One turn is completed when all agents follow the procedure; the order of agents is randomly selected.
4. The variable mobility influences surely affect only equation (2); the range of visit (and therefore migration) of agents.

Other remarks

1. The possible range of opinion and density is 1/9 < opinion, density < 400/9. Actually, both values are within 5 - 20, due to the value of other variables, such as patch sizes, the number of agents, initial distribution of agents, and cost. I explained it in the section of Result.
2. The x axes show turn. One turn composes of 400 agents’ completion of the procedure described in Figure 2. I explained the composition of 1 turn following your comment of 2.3, so I think the readers don’t misunderstand the turn.
3. I ran three simulations with different values of δ and ε. For each figure, I added the values of δ and ε in its caption.
4. In box plot o represents outlier. I explained it in the caption.
5. As you commented, the variable mobility is same for all agents. However please note that agents of few resources cannot visit anyplace due to their few resources even if the variable mobility is high (equation 2). If the variable mobility is ∞, all agents can visit any places.

Reviewer 3 Report

This is an interesting study that combines opinion dynamics with migration.

In general, the manuscript is well done and I have no major objections, although the research is not of the highest quality. However, I would like to highlight a concern regarding the use of opinion dynamics in this context. As I understand opinion change, I am not sure that this concept can be easily applied to migration. The reason is that opinions are usually assumed to be rather short-lived, not very stable compared to the structural factors that drive or prevent someone from migrating or moving.

The authors should elaborate on the personal and situational variables that play a role in the desire or actual decision to move.

Author Response

Thank you for your valuable comments. As you pointed out, people do not migrate flexibly in response to their opinions for density that change in the short term. It is very important to explain the relationship between the model setting and reality, and I think the comments you received are a very important part of the foundation of the model.

The present model assumes people move freely to a very distant place, not to a neighborhood, in a state where the variable 'mobility' is high. In that sense, what this study is modeling is a hypothetical world in which people migrate more flexibly compared with the actual world. I have added to the discussion to call attention to this point. I also pointed out that the variable 'hesitation' can be added to the right-hand side of equation (3), as a factor that makes people hesitate to migrate. A large value of 'hesitation' can be set to make people more restricted to their residential area. However, this addition would be too complicated for this study, so I only mentioned that it is possible as a development of this study.