Teaching basic numeracy, predictive models and socioeconomics to marine ecologists through Bayesian belief networks

Introduction

While there are considerable differences between students’ understanding and academic strengths worldwide, within much of the native English speaking world large proportions of students studying life science disciplines at higher education level have weaknesses with numeracy, and associated topics, such as statistics (Feser et al., 2013). In many cases, ‘fears’ of mathematics have arisen and continued throughout their schooling, however, avoidance of numeric topics is not possible in many life science disciplines, especially in subjects such as ecology, where statistics form an important part of any independent research (e.g. Chalmers & Parker, 1989).

Many case studies have demonstrated that quantitative skills in ecology can be better taught if taught in a subject context (i.e. analysing data the students have collected in field based studies – Bäumer, 1999; Nolan & Speed, 1999; Yilmaz, 1996). Despite this, many students remain unconfident of quantitative elements of their courses, and few have the confidence apply even simple mathematics outside the confines of a few simple statistical tests (Grainger, 2010; Tariq, 2002; Tariq, 2004).

A possible solution to increase quantitative skills and confidence in students is the use of Bayesian belief networks. In their simplest form, Bayesian belief networks are a method of formalising uncertainty or probability from a number of events (Grover, 2013). From an ecological community perspective, this could amount to the calculated probability of a species decreasing in abundance, but based on known increases in both food supply and predation risk (Hammond & Ellis, 2002; Stafford et al., 2013). However, traditional Bayesian belief networks do not cope well with reciprocal interactions (such as competition between two species), and revised methods using some aspects of Bayesian inference have been developed (Stafford R. and Gardner E. unpublished data). These revised methods also have a simple, user-friendly interface. They use Microsoft Excel as an interface, with a hidden VBA script performing the calculations. As such, the software used is familiar to the students, rather than complex modelling environments or coding platforms often used for predictive models.

Given the identified need for quantitative skills in graduates, and even in post-doctoral researchers (Grainger, 2010), the aim of this study was determine if it was possible to introduce predictive modelling to students at an early point in their education, and whether this predictive modelling would benefit student learning about ecology in general, rather than being seen as extra, and unnecessary, complexity in learning key concepts. To do this, we combined a field visit to a rocky shore, followed by an afternoon using a predictive belief network, initially based on their knowledge of the rocky shore. We quantified the success of the technique both through student questionnaires and through examining the solutions they provided to problems requiring the use of the predictive networks.

Methods

Student evaluation of learning

An anonymous questionnaire was provided to each student, asking how much they had learned about various topics during the day (from rocky shore ecology through to understanding probability and uncertainty – Figure 1; Supplementary File 4). In addition to ranking each on a 1–10 scale, they were asked to provide an answer as to where they thought they had learned most about the topic (either during the field lecture, or the afternoon computer session). Again, this was on a 1–10 scale, where 1 was only from the morning field session, 5 was equally from both sessions, and 10 was only from the afternoon session. The collection of these data from students was approved by the Science, Technology and Health ethics committee of Bournemouth University.

Figure 1. Contribution of the two different teaching approaches to student understanding of different learning outcomes.

For each learning outcome examined, the median score was 7. Contribution was calculated using the equations C₁ = M₁*((10-M₂)/10) and C₂ = 10-C₁, where C₁ is the contribution made by field-based lecture, M₁ is the median value of the students’ response to how much they learned about the topic (in this case, all equal to 7) and M₂ is the median value of the students’ response to how much they learned from the different teaching methods (1 indicating fully from the field-based lecture and 10 indicating fully from the computer-based practical).

Results

After a few questions regarding ‘what to do’, students (working in pairs) all produced sensible interaction links in the model. Typical initial questions involved which worksheets to fill in and a general reluctance to ‘break’ the software by doing something wrong. Filling in the probability values resulted in a minor problem of students not considering exactly what they were trying to predict (the probability of a species increasing, given that another species had increased – in this example, where most species interactions are negative, it may be easier to parameterise the model as probability of a species decreasing, given another had increased). Four of the six groups needed this re-explaining, however, once this was pointed out and otherwise independently, all groups managed to produce working belief network simulations which accurately predicted real results from previously conducted experiments. The only area where the majority of groups (five out of six) struggled was in complex, indirect interactions, which only occurred as a result of a tropic cascade. Most groups failed to predict the competitive interactions for space between seaweed species, despite correctly predicting the tropic relationships between grazers and green algae, but other than this one interaction, results were almost identical to the ‘expert’ parameterised networks created by the authors, and produced similar values to real experiments conducted on rocky shores (see Dataset 1 for real experimental data).

Student evaluations showed that students felt they had learned significant amounts about each topic, with median scores of 7 for all questions (with 25% and 75% quartiles between 6.5 and 9 in all cases). Knowledge of rocky shore ecology and ecological interactions was ranked as equally learned between the field and computer sessions (both with median values of 5) and knowledge of marine management and probability was greater in the computer based sessions (median scores of 7 and 8 respectively; Figure 1). In all cases, the full IQR was 2 or less indicating the majority of students scored in a similar manner (Dataset 2 provides the full data for each student – note, as the survey was optional, only 11 of the 12 students present completed this).

Discussion

This study indicates that students (even at a very early stage in their academic journeys) are capable of understanding and applying quantitative techniques if presented in a logical and intuitive way. Furthermore, it demonstrates that their ability to learn these techniques can be integrated with development of ecological knowledge and understanding; acting not as a hindrance to, but as a compliment to the understanding of key concepts.

Much previous research has demonstrated that quantitative methods need to be taught in the context of the academic discipline (Bäumer, 1999; Nolan & Speed, 1999; Yilmaz, 1996). However, this approach can often seem rather forced to students, especially early in their studies. Examples are often based around simple data collecting exercises rather than conceptual issues or real research projects. Although students are capable of performing statistical tests, for example, on a specific dataset at the time, they find it difficult to remember and transfer the knowledge to a novel situation (Chance, 2002). However, embedding more quantitative elements regularly to courses to enhance learning of key concepts may result in less fear being associated with dealing with numbers, and a greater ability to synthesise more quantitative information such as inferential statistics when required.

The role of technology in education is becoming a prominent issue, with a number of case studies demonstrating how it can be useful in the classroom and even during field work (France & Welsh, 2012; Webb & Stafford, 2013; Welsh & France, 2012). Simulations have also been used to teach complex ecological concepts such as experimental design in place of (or in addition to) field or laboratory based studies (Stafford et al., 2010). With on-going improvements to technology (e.g. development of specific apps for tablet computers), it may be possible to use spreadsheet models such as this directly in the field. An advantage of such an approach would be that the simulation app could be combined with field guides and information on the species being studied, potentially allowing a more fully immersive learning experience.

The simplicity of use of belief networks, especially when combined with a familiar user interface, was clearly demonstrated here, with students being able to make, parameterise and run simulations of ecological systems and coupled socio-ecological systems. These results add further weight to the intuitiveness of the approach. Combined with uncertainty in detailed knowledge of many marine ecosystems (in terms of exact population sizes, recruitment and species interactions - Hilborn & Walters, 1992; Magnusson, 1995; Pope, 1991), and the need to adhere to what could be perceived as ‘crude’ policy measures (e.g. no decrease in the population size of a certain species – DEFRA, 2012), models such as these used in this study would fit well with the demands and requirements of policy makers, providing sufficient detail for achieving policy goals with limited data and in an intuitive manner.

Data availability

F1000Research: Dataset 1. Data from manipulative experiment to assess community effects of dogwhelk manipulation (addition of 10 dogwhelks to each of 5 × ~1.5 × 1.5 × 1.5 m boulders) or periwinkle manipulation (addition of 10 periwinkles to 5 different, but similar sized boulders)., 10.5256/f1000research.5981.d41189 (Stafford & Williams, 2014a).

F1000Research: Dataset 2. Raw data values of student responses to surveys, 10.5256/f1000research.5981.d41190 (Stafford & Williams, 2014b).