Are Mathematical Models Useful for Understanding Ecological Dynamics?

The use of mathematical models in ecological research has been increasing in recent years, as the need for accurate predictions of different phenomena continues to rise (Augusiaka, Van den Brinka, & Grimm 2014, Duarte et al. 2003). While models can provide useful insights or predictions for populations and ecological systems, there are limits that prevent their development and use from meeting the current demand (Chatzinikolaou 2012, Duarte et al. 2003, Rykiel 1996). There are many suggestions as to what these limitations are, and while some are valid and inhibit the development and use of models in ecology, this does not mean that models are inherently useless or impractical (Chatzinikolaou 2012, Duarte et al 2003, Levins 1966, Rykiel 1996).

There are several main arguments supporting the idea that models are not useful for understanding ecological and population dynamics and structure. Duarte et al. (2003) argue that the majority of ecologists do not have sufficient training in modeling, and therefore without having the proper skills to collect data with the purpose of creating a model, any collected data will introduce uncertainty into their models, decreasing their reliability. Another limitation along this line includes misinterpretation of the actual characteristics of the studied ecosystem or population, and poor estimation of parameters or initial conditions (Beckage, Gross, & Kauffman 2011, Chatzinikolaou 2012, Duarte et al. 2003). Without proper mathematical skills or by not accurately representing the ecosystem, population, or estimated parameters, the model’s reliability is compromised. Unreliable models will produce unreliable results or predictions, making them poor choices for analyzing data or making predictions. Levins (1966) argues that every model will have some sort of weakness, and it is up to the modeler to decide whether it will be how general the model is, how realistic it will be, or how precise it will be. No model will have all three characteristics and therefore can only be strong in two of these categories (generality, realism, or precision), leaving it weak in the remaining category (Levins 1966). Determining the credibility of a model is a challenge in itself due to the controversy over whether any model actually can be validated, as well as the lack of widely accepted standards as to what determines validation (Rykiel 1996). Despite all of these limitations with either the models themselves or how they are applied, there are strong arguments that models can still be useful in ecological research. Two arguments are not against models themselves, but rather the limitations involved in their development. The issue of a lack of training in mathematical modeling in ecologists can be solved by including it in university curricula, or through increased communication between ecologists and modelers (Duarte et al. 2003). The problem of inaccurate estimations of parameters or initial conditions can be corrected for by incorporating extra experiments or collecting additional data, which would form a more accurate picture of the population or ecological process being modelled (Beckage, Gross, & Kauffman 2011, Duarte et al. 2003).

While there are limitations to the models themselves, they are still successfully used in ecology and are accepted by scientists (Chatzinikolaou 2012). Levins (1966) acknowledged that all models will have a weakness, but many authors recommend creating models so they will be realistic and general rather than precise, indicating that despite their inherent limitations, models can still prove useful in ecological research (Duarte et al. 2003, Levins 1966). However, less general models designed for specific populations or ecosystems can still be useful (Duarte et al. 2003). Other than imposing widely accepted standards for validating models, determining and/or “proving” the credibility of a model is left up to the modeler (Augusiaka, Van den Brinka, & Grimm 2014). Many authors argue that as long as the modeler and those using a specific model are aware of its intended purpose and limits, models can be successfully utilized in ecological research (Chatzinikolaou 2012, Duarte et al. 2003). Widespread use would also aid in determining a model’s credibility, as each time it is used successfully strengthens the scientific community’s confidence in it (Duarte et al. 2003). Even if a model fails to produce accurate results or predictions, this lets the modeler know that there is room for improvement (Duarte et al. 2003).

While the use of mathematical models in ecology is not without its limits, models can still be successfully used in many research studies on populations and ecological processes (Chatzinikolaou 2012, Duarte et al 2003, Levins 1966, Rykiel 1996). Despite inherent weaknesses and difficulties determining credibility, as long as the modeler and users are aware of the purpose and drawbacks of each model they are using, models can help provide much needed overviews or predictions of many ecosystems or populations (Chatzinikolaou 2012). In the face of climate change and negative anthropogenic effects on environments and ecosystems worldwide, models can help identify the nature of environmental issues, expose any knowledge gaps, make predictions, and steer the direction of future research (Chatzinikolaou 2012).