By: L. Carvalho, G. Rusch and I. Winfield
WWW: M. Karlsen & A. L. Madsen

14 October 2014
Revised 24 October 2015

The Loch Leven case study examines the relationship, over time, between the ecological condition of Loch Leven, a lake in Scotland, and the delivery of a number of ecosystem services, particularly recreational angling for wild brown trout.

To support this work a Bayesian network for visualising and communicating the relationships between ecological condition and fishing quality and fishing service has been developed. This has a number of components and assumptions including:

*Habitat quality*in the lake is represented by chlorophyll-a concentrations, which are widely used across Europe as a measure of the ecological health, or status, in the European Water Framework Directive.Fishing quality is represented as Catch Per Unit Effort (CPUE) and is measured as the number of brown trout caught per hour of fishing. Analysis of Loch Leven data indicates that brown trout

*CPUE*is negatively affected by the*stocking of rainbow trout*and positively affected by improving*habitat quality*. Both*habitat quality*(algal blooms) and the*stocking of rainbow trout*also have a negative effect on the*reputation*of the lake as a wild brown trout fishery.

The model assumes that fishing quality (*CPUE*) and *reputation* in turn
affect the final ecosystem service delivered, measured here as *Boat
effort* (annual number of hours of fishing) and associated social and
economic benefits to anglers and to Loch Leven fishery.

The node *Habitat quality* has five possible states *bad*, *poor*,
*moderate*, *good* and *high*. The nodes *CPUE* and *Boat
effort* have states *low*, *medium* and *high* while the node
*Reputation* has states *bad* and *good*. The (causal) relations
between the nodes are defined by the structure of the model. For
instance, *Habitat Quality* has an impact on *Reputation* of the site.

This simplistic Bayesian network above is *static* in the sense that it
does not capture the dynamics of the system. We are interested in
examining the development of the ecological condition of the ecosystem
over time. This means that the model should be extended to a dynamic
model. The dynamic model is developed as a dynamic Bayesian network
(DBN) as shown below.

In order to turn the *static* model into a *dynamic* model we need to
specify how the system changes between two time steps. This is the
transition probability distribution (or matrix). We assume the
process to be stationary and first order Markov. This means that the
probability distributions do not change over time and the future is
independent of the past given the present. The length of a time step in
the model is one year. This means that the model divides (or slices)
time into steps of one year. In this particular example we are
considering a time period from 1998 to 2027.

The shaded node *T_Habitat quality* at the top is a temporal clone of
the node *Habitat quality* and as such it represents *Habitat quality*
at the previous time step. There is one transition
probability distribution in the network defining a probability distribution over
*Habitat Quality* at time *t* given *Habitat Quality* at time
*t-1*.

As shown below, the user can for each time step select the value of
one or more variables and observe the probability distributions over,
for instance, *Habitat quality* and *Boat Effort* in future years. The
purpose of the map is to illustrate graphically the condition (WFD status) of the
lake using the probability distribution over *Habitat quality*.

The model has been constructed using a combination of historical data and expert judgments. The historical data covers the period from 1972 to 2014.

The model is still under development and this web-site should - for now - only be considered as a demonstration of the potential use of DBNs for modelling ecosystem services. In particular, the quantification of the model based on data analysis and expert knowledge is being refined. The conditional probability distributions and, in particular, the probabilities encoding the transition between time steps have to be refined. The current quantification should only serve as an illustration of the potential of DBNs.

Each time step represents the state of the ecosystem for one specific year.

Each state of *Habitat Quality* has a unique colour (blue, green,
yellow, orange and red for states high, good, moderate, poor and bad,
respectively). The underlying colour of the map is determined by the
highest probability state. The intensity of the colour is
determined by the confidence in the classification of the state
(in case of equal probability between states with maximum probability,
the state with lowest rank is selected). For instance, if *Habitat
Quality* is high with probability 100%, then the colour is blue with
full intensity while the colour is blue with half intensity, if the
probability of high is 50%.

Full compatibility of the maps can be viewed with IE11 or Firefox 33.

Below are some HUGIN widgets for interacting with the dynamic Bayesian network (click on the probability bar to select a specific state for a node or remove evidence). As mentioned above the time difference between each time slice is one year. The first time slice shown below represents 1998. The model covers the time period from 1998 to 2027. To simplify the interface only a selected set of years are shown to the user, but the selection can be changed using the select boxes above the maps.

The period from 1998 to 2027 is divided into five equidistant periods (i.e., 1999-2003, 2004-2009 etc.). For each period there is a map and a set of belief bars and dropdown menus. Above the map it is possible to select any year in the corresponding period to adjust the settings of the model for that year.

When the web page is loaded, historical data for the period 1998 to
2012 are loaded into the model. The model can be used to examine the
likely impact of changing habitat quality (or WFD status) on the
fishing quality, reputation of the fishery and the fishing effort
(service demand). For example, you can use the tool to examine the
impact on a fishery of achieving the WFD target of *good*
ecological status by 2027 in the 3rd WFD River Basin Cycle.

**Summary of probabilities of Habitat Quality from 1998-2027**

As an example, assume *Habitat quality* is known to be *moderate* and
*Reputation* to be *bad* in 2013, then *Habitat quality* is *moderate*
with probability 51.8% in 2016 and 51.4% in 2022 and onwards.

Nicholson, A. E. and Flores, M. J. (2011) Combining state and transition models with dynamic Bayesian networks. Ecological Modelling 222, pp 555-566.

Useful references for those interested in BBN include:

Kjærulff, U. B. and Madsen, A. L. (2013) Bayesian Networks and Influence Diagrams: A Guide to Construction and Analysis. Springer, Second Edition.

For further details on the Loch Leven case study contact: Laurence
Carvalho (laca(at)ceh(dot)ac(dot)uk)

For further details on the use of Bayesian networks and web
deployment of models contact: Anders L Madsen (alm(at)hugin(dot)com)