Social integration as a determinant of inequalities in green space usage: Insights from a theoretical agent-based model

Visiting urban green spaces (UGS) benefits physical and mental health. However, socio-economic and geographical inequalities in visits persist and their causes are under-explored. Perceptions of, and attitudes to, other UGS users have been theorised as a determinant of visiting. In the absence of data on these factors, we created a spatial agent-based model (ABM) of four cities in Scotland to investigate intra- and inter-city inequalities in UGS visiting. The ABM focused on the plausibility of a ‘social integration hypothesis' whereby the primary factor in decisions to visit UGS is an assessment of who else is likely to be using the space. The model identified the conditions under which this mechanism was sufficient to reproduce the observed inequalities. The addition of environmental factors, such as neighbourhood walkability and green space quality, increased the ability of the model to reproduce observed phenomena. The model identified the potential for unanticipated adverse effects on both overall visit numbers and inequalities of interventions targeting those in lower socio-economic groups.

1 Scotland's people and nature survey 2014 -Exploratory regression analysis   4 Individual runs Figure 1 shows the progression of median visits to UGS in each city throughout one simulation run. After initial turbulence, SES differenciation emerges during the first year, and stabilises before the end of the second year.

Median visits to UGS in randomised runs
A set of experiments was performed in which the effect of socio-economic segregation is removed by randomising the location of agents within each city. Figure  2 shows median visits per SES in these runs, where we also assume t = ht = 0.5, i.e that all agents seek to visit UGS populated by a majority of agents of the desirable group. Without segregation, cities with a majority of high SES agents (Edinburgh and Aberdeen) accrue more visits, as high status agents (who are al-ways homophilic) are nearly always surrounded by a majority of similar agents, especially for lower values of h, i.e when there are fewer heterophilic low status agents. In the only city with a majority of low SES agents, Glasgow, high SES agents visit substantially less times, as their homophilic preference is satisfied only occasionally. In this city low SES agents visit more, however their median number of visits stays low, as the fraction of heterophilic low SES agents is also frustrated by the scarcity of high SES agents. As this fraction increases, and more low SES agents seek the company of the scarce high SES agents, visits decrease for all agents.

Impact of age differentials
Age difference as source of dissatisfaction is also implemented in the model. We assume that agents of 65 years of age or above are unsatisfied if the UGS is populated by 70% or more agents of age 30 or below. The impact of this constraint on the overall model behaviour is, however, limited. Figure 3 shows the parameter combinations giving rise to the observed phenomena when age is considered as a dissatisfaction factor or not.
(a) no-age (b) age

Sensitivity analysis: impact of factor a
We performed sensitivity analysis on model parameter a. This value is a factor in the equations which adjust an agent's probability of visiting UGS after assessing other agents against the tolerance thresholds in a previous visit (Section 4.4, main paper). It represents the "intensity" of attitude change after a positive or negative experience at the UGS. In the main paper we set a = 0.25. Here we test values of a = 0.01, a = 0.1 and a = 0.4 with t = ht = 0.5, h = 0.66 including walkability and UGS quality. The diagrams below show the progression of visits across a model run under different values of a. Among other things, factor a determines the speed by which the patterns in the model develop. Figure 4 shows that for the lowest tested value (a = 0.01) the dynamic of the model is only incipient in all four cities: the curves of median visits to UGS stay almost flat for all SESs for most of the simulation, starting to rise only towards the end. This is expected because when attitudes change at a very low pace the patterns emerge over a longer time frame.
For the tested values of a > 0.01, the dynamic of the model seems to be fairly constant, although it displays some sensitivity to the parameter. Specifically, we note that conditions 1-3 described in the main paper (Section 5) are verified slightly less frequently for a = 0.25 while confirming a trend for which these are found true more often for higher values of h and ht ( Figure 5).