7 lochs: ecology & maths


As part of a team comprised of Willie Miller and Ines Triebel of Willie Miller Urban Design and Janet Benton of Benton Scott Simmons Landscape Architecture, we submitted a design strategy for the 7 Lochs Wetlands Park in Gartcosh, in the eastern belt of Glasgow, UK.

The design brief asked for proposals for a green bridge(s) to alleviate the damage that the local M73 Motorway has done to the wetlands corridor. The M73, running north/ south, completely bisects the corridor and is an obvious hinderance to the continuity of the wetlands ecological habitat in the area.

The first question that our team asked, was ‘why do we need a green bridge’? And it was a valid question, one that other teams surely didn’t strive to answer, and most likely was never really a pressing issue for the judging panel either… However, why does the wetlands park need a green bridge? The unanimous answer is that the M73 is not just an eyesore, but it causes major disruption to local wildlife. Our team couldn’t agree more, however there is more to this puzzle… If the M73 disrupts the habitat, what else does? What about the railway going through the park, or the B-roads?

When approaching the design brief in this way, we were able to uncover the ‘fragments’ of the wetlands corridor.


So, although the most obvious fragmentation is caused by the motorway, there are still other fragments that maybe are not as sharply divided one from the other, but most be addressed and remedied if any bigger endeavours (green bridge) are to be successful. This means then that the fragments must be connected, or reconnected for that matter.


This is an obvious statement but how and where do we try to emphasize these connections? Since I love to think in numbers and shapes, if we are to consider each of these fragmented areas as a 2D geometric shape, we can identify the centroid of the fragmented zone. Theoretically, the centroid of each of these mini- habitats would be the sanctuary area of the habitat, the place that is furthest away from the dangers of high speed vehicles along the barriers. When analysing the habitat in this way, as the agglomeration of the fragmented habitats, we would then strive to link the centroids of each of the mini- habitats together. The centroid of the fragmented habitats is calculated by basic geometric principles.

centroids formula

If the barriers, the roads, railways and motorways are the least safe places for the local habitat (animals, insects, birds and vegetation), then the intersection of these barriers would be the most hazardous for living organisms. Thus, to link one fragmented habitat to another, the safest crossing point would be that which is furthest away from the intersection of the barriers. Geometrically, this point is referred to as the midpoint. The midpoint is also calculated by standard geometric principles.

midpoint formula

By constructing the series of centroid to centroid connections (via the midpoint of the boundaries) within all the fragmented habitats in the study area, we reveal a network of connections in the area.

centrality analysis

This network was analysed through an assessment of betweenness centrality, a measure of the degree to which a point is on the path from many places to many other ones. In other words, a node in the network that has a high betweenness measure may be a place that is traversed naturally from many places to many others. A node with low betweenness centrality, although part of the network, may not regularly be a part of paths regularly taken in the network.

The results of this centrality study reveal that the nodes (midpoints on the barriers of the fragmented habitat zones) with the highest betweenness index are theoretically the more important place-to-place links in our network. That would imply then, that the intervention at these sites would need to be scaled appropriately for the importance of the site in the overall network. So, a more central crossing point would need a stronger intervention while places with lower scores of betweenness would need little or no further work to ensure a continuity in the local habitat.

But how did our team decide exactly how to intervene in the different crossings points? I developed a mathematical algorithm which takes into account, for any two fragmented habitats, their size, the centrality index of the midpoint between them and the width of the boundary and generates a score between 1 and 100. This intensity generating index relies on the principles outlined above, but can be reiterated:

– larger fragmented habitats have more ‘safe’ area.

– high betweenness centrality scores for the connections imply the need for a stronger intervention

– wider boundaries need stronger interventions.

Intensity Index

This algorithm provides us with a clear and repeatable evidence for the type of intervention that is necessary in different places. Let me reiterate that this project’s brief was to design a green bridge, but when we consider the green bridge as a crossing point, we must consider the other crossing points in the network and try to understand how they all work together and how the overall success in the area is not just linked to a single crossing point, but rather to the overall network of crossings.

Before applying this formula to determine the necessary impact and intensity of the various crossings in our network, a study was conducted to determine what types of interventions would be viable and effective. At the motorway, the most destructive boundary in the corridor, a grade and section analysis reveals that there is significantly more potential for green tunnels than green bridges.

Because the motorway is built mostly at grade, it would be insensitive and ineffective to try to build over the motorway. Creating connections underneath the motorway is not only more natural for animal, hydrological and vegetation movement, but it is significantly less intrusive and independent research corroborates that it would be more enticing for animals to use and easier for them to adjust to.

We derived a list of feasible interventions both from our very, very creative brainstorming sessions at Tinderbox and through research evaluating other similar interventions. We can understand these interventions by the intensity of the intervention and the scale of it. For example, an intense intervention would result in large changes in an area, or it would be more expensive. An intervention with a larger scope would be an intervention that affects a larger area. For example, a simple fence would be not very intense, however it would have a large scope if the fence is quite long.



After applying the Intensity Generating Index, we decided which interventions could possibly work at the different midpoint crossing locations we identified earlier.

Key diagram

Our wonderful Ines came up with some excellent key diagrams, illustrating what our ‘green bridge’ could look like… Anyone reading this will quickly say that these are not bridges! And they shouldn’t be. There are already numerous culverts underneath the motorway which happen to be located at almost exactly the midpoint of the barrier of the motorway. These culverts can be modified to provide a continuous provision for the local wildlife, allowing connections of all aspects of the local habitat: water, insects, flying animals and large and small animals. This type of connection could never be achieved with an overground bridge.



second section

If the motorway is already built at grade, why would you want to build even more over that grade? I mean, a bridge then would have to be twice as tall as would be recommended and this would mean that it would take longer for local animals to learn to use the connection, if they were to use it at all.


I can conclude that a bridge is not the right solution for the 7 Lochs Wetland Park, not should it be. The contest asked for a green bridge simply to try to appease those in charge, who really haven’t grasped the problem at hand… It was meant to be an architectural endeavour, alone. Meaning, the brief wanted something that could be photographed and spoken about, not a true solution to the underlying problems.

Don’t think that I am bitter in defeat! In fact, our stated goals, as a team, were not to win! We wanted to enjoy doing an interesting project and conducting research, and testing our ability to work together for the first time as a team. In fact, there were other entries that at least recognised that more needs to happen that just a bridge, but if there is anything that we learned, it was really that the project wasn’t about building a green bridge, it was about building egos…

Team Members: Janet Benton, Jacob Dibble, Ines Triebel, Willie Miller

I would like to thank my three colleagues for a very exciting project and for giving me an opportunity to prove my mettle and show off my mathematical abilities! Thank you.

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