Are ecological machine learning tools a relevant asset to population dynamic analysis?

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Are ecological machine learning tools a relevant

asset to population dynamic analysis?

Research Proposal Master Earth Sciences Future Planet Ecosystem Science

Student | BSc Draaijer, R. Student ID | 10528504

Daily Supervisor | MSc Rademaker, M. Examiner | Dr. Smallegange, I.M. Assessor | Dr. van Loon, E.E.

Royal Netherlands Institute for Sea Research (NIOZ) University of Amsterdam (UvA)

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Ecosystems are prone to external disturbances that can lead to changes in the community structure of ecosystems and push the system into alternative stable states. Anticipating on changes in community structure through ecological forecasting – using methods to predict change in these ecosystems – can prevent major ecosystem shifts. Recent innovations made in the field of artificial intelligence encourage the use of machine learning approaches in ecological forecasting. However, we can only safely use these new methods to predict future change if they make their predictions based upon a correct conceptual understanding of ecological relations.

SCIENTIFIC SUMMARY |

This research proposal considers current methods in ecology that are used to analyse complex temporal (inter)dependencies between the environment and species populations. These population dynamics often arise from individual-level demographic processes, that can emerge in different population equilibria over time. Many ecological questions are centred around understanding these temporal dynamics by unravelling their underlying mechanisms. A useful tool that contributes to that understanding are ecological prediction analyses. These analyses are commonly performed using population models, that account for variation between individuals, such as physiologically structured population models (PSPMs). These theoretical models contribute to our understanding of population dynamics and are a powerful tool in prediction of demographic variation in communities.

A relatively recent advancement is the increasing use of machine learning (ML) models to aid in understanding observed temporal ecological patterns. Due to the growing ecological datasets at our disposal, more and more opportunities arise to develop such ML models to answer ecological questions and make ecological predictions. Therefore, ML models seem a promising tool to population biologists to generate accurate ecological predictions from large datasets. However, it still remains unclear if these predictions are based on relevant ecological interactions to provide accurate predictions.

To test whether ML approaches are able to learn complex ecological relationships from data, it is necessary to evaluate its performance in retrieving relationships from ecological datasets. This will be done through generation of a synthetic temporal ecological dataset with predefined relationships between the variables, using a PSPM. Consequently, it is evaluated if the ML model is able to correctly retrieve the ecological relationships from this dataset. Through assessment of such newly introduced ML methods we can decide whether these major current approaches are of use in ecological forecasting.

KEYWORDS |

Machine learning, population dynamics, ecological prediction analysis, deep learning, population model, ecological patterns, modelling

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INTRODUCTION |

In a world of ongoing change due to anthropogenic influences, environments organisms depend on constantly endure stress and ecosystems are pushed to their limits. Consequently, global biodiversity levels continue to decline and conservation efforts are high on the agenda. Understanding population responses to such changes has come to be increasingly pertinent for effective conservation management and ultimately for anticipation on these major environmental challenges (e.g. global warming, biodiversity loss and rapidly spreading diseases) (Clark et al., 2001; Crowl, Crist, Parmenter, Belovsky, & Lugo, 2008; Naeem, 2002).

Studies concerning population dynamics have proven to be insightful in unravelling mechanisms underlying the complex population responses that arise from environmental perturbations (Koons, Iles, Schaub, & Caswell, 2016; Ozgul, Coulson, Reynolds, Cameron, & Benton, 2012; Stott, Hodgson, & Townley, 2012). The field of ecological predictive modelling has proven especially suitable for this task (Petchey et al., 2015). Predictive models have made it possible to analyse interactions between environmental perturbations and population shifts. Changes in dynamics often arise from individual-level demographic processes that result in different population equilibria over time (Beisner, Haydon, & Cuddington, 2003). Modelling changes in these equilibria and constructing generic models for these phenomena is a key challenge in ecology, considering the complex nature of the dynamics.

Population models like physiologically structured population models (PSPMs; Metz and Diekmann, 1986; Metz and de Roos, 1992) are commonly adopted predictive population models and focus mainly on individual-level processes giving rise to population-level patterns. PSPMs are a powerful tool in prediction of demographic variation in communities (De Roos & Persson, 2013; De Roos & Persson, 2001). Inclusion of feedback mechanisms between population density and the environment provide the PSPMs with a more or less realistic approach to ecological niche modelling. Besides, because of the mechanistic characterization of individual-level dynamics they are especially well-suited to model community changes as a consequence of individual-level processes. For example, PSPMs are used to predict local abundance patterns of populations according to life-cycle stages and environmental factors (Ainseba, Picart, & Thiéry, 2011; Gilioli, Pasquali, & Marchesini, 2015). Other applications of these models comprise of investigation of evolution of individual traits (e.g. reproductive age) dependent on external variation (Diekmann, Gyllenberg, Metz, Nakaoka, & de Roos, 2010; Durinx, Metz, & Meszéna, 2008). Altogether, PSPMs are rather robust models and generally applicable across multiple taxa, simulating complex ecological relationships within the chosen system.

Recently, besides the commonly used predictive models, there has been a lot of interest in contemporary machine learning (ML) methods to generate ecological predictions (Christin, Hervet, & Lecomte, 2019; Olden, Lawler, & Poff, 2008), like population responses (Botella, Joly, Bonnet,

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Monestiez, & Munoz, 2018). These advancements may facilitate an extension of the toolkit available to population biologists in accurate prediction of population responses, as these ML methods are able to cope with expandingly large (ecological) datasets (Luo et al., 2011). Previous studies have shown that it is possible to apply ML models to ecological datasets, like deep learning (Christin et al., 2019). Accordingly, a ML approach to prediction models could therefore be a good asset and contribute to further understanding of the complexity at the roots of population dynamics.

Although these ML models hold great promise to be applied in ecological forecasting, it still remains unclear whether these predictions are accurate and found on ecologically relevant relationships (i.e. based on ecological theory). Therefore, the aim of this study is to assess whether machine learning frameworks are suitable for identification of underlying ecological relationships in population responses to environmental change. Results of this study may suggest the additional use of ML methods in ecological predictive analyses, as well as an alternative approach for identification of relationships in temporal ecological datasets.

To conduct the analysis, a ML model will be evaluated on its performance in retrieving underlying causal relationships in an artificially generated ecological dataset. Firstly, the ecological relationships in a consumer-resource interaction-based model will be defined and implemented in a PSPM and subsequently will generate a synthetic dataset. The dataset will yield different demographic variables over a time series, which will serve as input for the ML model – a model that is based on a temporal causal discovery framework and will be extended to handle ecological multiple-species interactions data. Finally, it will be analysed whether the identified causalities by the ML model coincide with the predefined causalities that are used to design the PSPM (and generate the dataset). If this ML approach proves to be successful, it can be considered a useful tool that can be employed to effectively mimic the complexity underlying population dynamics and ultimately in ecological forecasting. Contrarily, when this method falls short, it highlights the complications of using ML approaches in resolving ecological questions.

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METHODS |

We will aim to evaluate the ability of various machine learning models to derive known ecological relationships from an artificially generated ecological dataset. Exact relationships within observational survey datasets are unknown, therefore we will use a physiological structured population model (PSPM) to generate a synthetic dataset with known relations. The synthetic dataset consists of time series following from predefined causal relationships of consumer-resource interactions parameterised in the PSPM. The temporal causal relations will be represented by a causal temporal graph. We then train the machine learning models, to retrieve the temporal causal graph from the time series. Final evaluation of the model is performed by comparative analysis of the initial temporal causal graph that is implemented in the PSPM and the causal graph retrieved by the machine learning model algorithm.

Modelling ecological relations

Consumer-resource models are used to explain population dynamics that are shaped by trophic interactions between individuals of different species. Population level changes therefore ultimately arise from individual level processes. Such individual-level processes are dependent on life histories of species, and are well represented in structured population models concerning consumer-resource interactions. These structured models use a set of differential equations describing size dependent interactions between individuals and their environment based on species specific life history parameters and rates (e.g. De Roos et al., 2008). The population responses are then represented through a set of time-series describing the temporal dynamics of each species, emerging from the complex non-linear relationships in the model.

PSPMs are a type of structured population model and will be used to model population responses emergent from predefined ecological relations. The PSPM is modelled through the derivative of the relationship between individual physiological characteristics and the environment’s condition. Also, density-dependence is covered by the means of explicit populational feedback mechanisms that are incorporated in the model (De Roos, 2020). This model receives input for a variety of variables, including 1) environmental variables (i.e. resource density, predation density), 2) individual state variables (i.e. body size, maturity), 3) vital rates (i.e. mortality, growth, reproduction), 4) individual’s impact on its environment, and 5) environmental steady state conditions. With this input, the PSPM computes a number of demographic variables that indicate temporal populational change, these include population growth, equilibria, and stable states (see Figure 1). By including multiple species in the PSPM the model is able to simulate consumer-resource interactions and consequently the population dynamics of each species.

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Figure 1. Example of time-series data obtained from predefined ecological relations. Various variables (individual- and environment related) are used for input in the PSPM model, and subsequently produces the prediction of corresponding time-series of the demographic variables (X1, X2 … Xn). Each node depicts a variable, with the

directed links indicative of causal relationships with different weights. Reprinted and adapted for the objective of this proposal from “Causal Discovery with Attention-Based Convolutional Neural Networks” by Nauta, M., Bucur, D., and Seifert, C., 2019, Machine Learning and Knowledge Extraction, 19, p. 3. Copyright 2019 by MDPI Basel.

Machine learning tools in ecology

Machine learning (ML) is an application of artificial intelligence that focuses on computer algorithms whose performance improves upon dataset exposure. This improvement enables the algorithm to eventually recognize patterns by training the algorithm with sample data. Recognition of patterns is dependent on extracted features from the dataset – either the algorithm is provided with prior feature identification, or the algorithm is able to extract the features itself through learning. These are referred to as supervised and unsupervised learning respectively. Therefore, unsupervised learning can be used to execute tasks without explicitly being programmed to perform that particular task (Hastie, Tibshirani, & Friedman, 2009). The main advantages of unsupervised ML models are their independence of explicit identification of features (i.e. human supervision), its effectiveness in processing big data, and handling complex (feedback) relationships.

Applications of ML for ecology in previous studies include methods as decision trees, random forests, and neural networks (Thessen, 2016) and have proven to benefit ecologists in making predictions for various purposes (see Wiley et al., 2003; Kuo et al., 2007; Pichler et al., 2020). Especially artificial neural networks are of interest when modelling ecological relations, as they represent multilayer networks that are fully connected and require no prior knowledge about the input data. This complete connectedness of the system has the advantage of being able to represent complex relations among variables (i.e. simulate cascading effects). While a single artificial neural network is already able to simulate complex patterns, it only concerns one layer performing nonlinear transformation to the input layer (see Figure 3). Deep learning (DL) algorithms concern multiple layers performing such

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models are suitable to model extensive systems with the inclusion of these multiple layers between input and output (see Figure 3).

DL is especially well suited for pattern recognition (e.g. population patterns), as it addresses the data through an automated learning process that disentangles the data in multiple bins, and thereupon learns (through backpropagation) complex features that represent the data best. Besides, because of the backward propagational architecture of DL, it facilitates the discovery of convoluted structures in large high dimensional datasets (LeCun, Bengio and Hinton, 2015). Moreover, convolutional neural networks (CNN), a class of DL, have the ability to retain spatial information. These networks use convolution to extract features from the data and consequently categorize them. Hence, it seems that CNNs (and ML methods in general) are able to aid in understanding underlying processes of observed patterns, in addition to the classical models used for ecological prediction.

Figure 2. Simplified representation of the subtypes of artificial intelligence to be used in this study. Overarching category artificial intelligence covers the subcategories machine learning, deep learning and convolutional neural networks. Each darker circle encompasses an increasing specified category of the prior category. Note that only the types of machine learning covered in the methods of this research are included and more subtypes of machine learning methods are available.

C O N O L I O N A L N E R A L N E O R K A R I F I C I A L I N E L L I G E N C E M A C H I N E L E A R N I N G D E E P L E A R N I N G

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Figure 3. Two artificial neural networks with one or multiple layers. Shown are the differences between a basic artificial neural network with only one layer between input and output (hidden layers) and a deep artificial neural network with multiple hidden layers. Reprinted and adapted for the objective of this proposal from “What are neural networks?” by IBM (2020). Copyright 2020 by IBM Cloud Education.

Temporal Causal Discovery Framework

A machine learning method that has proven to be useful in various domains and is able to find causal relationships in time series is described by Nauta, Bucur and Seifert (2019). This temporal causal discovery framework (TCDF) fits in the class of convolutional neural networks (CNN), and illustrates a promising causal associative model which is highly flexible for various disciplines. In this study, TCDF will receive the artificially generated temporal data from the PSPM as input, to convolutionally compute the causal relationships among the given variables (see Figure 2). Because of the inclusion of hidden layers in the framework, it is able to distinguish between direct and indirect causal relations (hidden confounders). To get to the causal relations TCDF first performs several steps, which include 1) time-series prediction, 2) attention interpretation, 3) causal validation and 4) delay discovery (Nauta et al., 2019).

The time-series prediction computes the prediction for univariate time-series, which outputs a one-dimensional layer. Each series variable goes through a separate network to predict a time-series, and gets a so-called attention score attached to the variable used in prediction. This score indicates the weight a network attends to a time-series variable in predicting another time-series

Input layer Hidden layers Output layer

Deep Artificial Neural Network

Input layer Hidden layer Output layer

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variable. The output of this first step will thus also include a score for potential causes between the time-series variables.

These scores computed in the previous step are used in attention interpretation, to distinguish between non-causal relations, (in)direct causal relations, presence of confounders and feedback relations between each time-series variable. However, the model is unable to recognize spurious correlations, which stresses the importance of expertise when identifying relations among variables.

After interpretation of the scores the model finds true causes out of the potential causes recognized in the previous step. Assumptions for a potential cause to be a true cause are temporal precedence (i.e. cause precedes effect) and physical influence (i.e. manipulation of the cause changes its effect). Temporal precedence is covered through the use of temporal variables. Physical influence is accounted for through permutating (manipulating) the time-series variable values, so that it enables the model to effectively identify true causes from the potential causes. Whereas the model has the possibilities to accurately detect the presence of confounders included in the dataset, it is unable to identify hidden confounders with an unequal delayed causal effect on the time-series variables. This delayed effect is measured during the final delay discovery step, where the model also discovers the time steps between the prior identified true causes and its effects. As a result of these steps the temporal causal discovery graph with its directed relations between time-series variables is created (see Figure 4).

Figure 4. Example of temporal causal graph from time-series data. Time-series variables (X1, X2 … Xn) are used for

input in the TCDF model, and subsequently produces the temporal causal graph. Each node depicts the corresponding time series, with the directed links indicative of causal relationships with different weights. Reprinted from “Causal Discovery with Attention-Based Convolutional Neural Networks” by Nauta, M., Bucur, D., and Seifert, C., 2019, Machine Learning and Knowledge Extraction, 19, p. 3. Copyright 2019 by MDPI Basel.

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Causal inference framework

Quantification of the causal relationships from the obtained temporal causal graph will be calculated with a causal inference framework (PCMCI) that is suited to analyse high dimensional time-series datasets and non-linear time dependencies (Runge, Nowack, Kretschmer, Flaxman, & Sejdinovic, 2019). This method focuses on the links between the identified relevant (i.e. true) causes rather than consideration of all possible causes (through iterative independent testing with a Markov algorithm), from which it then computes partial correlation coefficients and simultaneously searches for possible false positive links. For each link found the strength of correlation will be computed resulting in (positive or negative) coefficient strengths, and the significance of that link. Furthermore, PCMCI will be used for significance level optimization according to the Akaike information criterion.

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TIME SCHEDULE |

In a total of seven months I will implement the two aforementioned models and finalise the research project with a written thesis and a presentation. During the first two months I will be housed on the campus of the Royal Institute for Sea Research (NIOZ), to quickly get started with the project. This is when I will mainly focus on getting set up with the coding language Python (taking part in online Python course and implementing models) and research relevant literature. To efficiently make use of the time available, writing the thesis will be done throughout the seven months, whilst implementing, training and optimizing the models. After analysis there will be time available for possible delays when encountered with unforeseen difficulties during implementation and optimization. Otherwise, this time is spent writing and discussing the obtained results, besides preparing for the final presentation.

Figure 5. Gantt chart of the proposed research. This chart represents the time schedule based on the proposed research internship, covering a total of seven months. In this schedule the main components of the research are included – literature review, familiarizing with python, thesis writing, implementation of two models, optimization and training, model analysis, and finalizing the project with a presentation. Exact dates are to be confirmed upon approval of the proposed research.

FUNDING |

The research will be carried out under the supervision of three supervisors (daily supervisor, examiner and assessor) and is part of a collaboration between the Royal Institute for Sea Research (NIOZ) and

Ti e i e MSc The i

E E A C H I E H I I A D I B E D

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the University of Amsterdam (UvA). The personnel costs involved for supervision of the project will comprise of €7.440 (see Table 1) which will be compensated by both the NIOZ and the UvA. Additional costs for housing on Texel for the first eight weeks will be borne by the MSc student, together with a rent allowance funded from the NIOZ. Travel expenses from and to Texel will be provided by the MSc student, together with the extra costs for a massive online open course regarding Python coding.

Table 1. Budgetary plan of proposed research. Included in the table are personnel- and research costs involved.

INSURANCE AND SAFETY |

No safety regulations, besides the general advice and regulations of the Dutch National Institute for Public Health and the Environment (RIVM) considering COVID-19, for the proposed research are in effect.

EQUIPMENT |

The proposed research will be implemented in Python and Pytorch. Most computational methods and implementation of the models will be carried out on a macOS Catalina 10.15.7 computer with a 2.9 GHz Dual-Core Intel® Core™ i5 and Intel® Iris® Graphics 550 GPU, already in the possession of the MSc student.

B d e MSc T e

E E A C H I E H I I A D I B E D P E R S O N N E L S A L A R P E R H O R H O R S P E R E E K N M B E R O F E E K S T O T A L R E S E A R C H T O T A L C O S T S

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DATA MANAGEMENT |

Data will be managed according to the FAIR data principles (Wilkinson et al., 2016) and registration of the project as an open-source project hosted with open source data management software GitHub, Inc. The final version of the MSc Thesis will be available on the University of Amsterdam theses database (“Scripties - Bibliotheek - Universiteit van Amsterdam,” 2021).

ACKNOWLEDGEMENTS |

I would like to thank M. Rademaker and I.M. Smallegange for their valuable feedback and their devoted time. Also, I would like to thank A.M. de Roos and W. Bouten whom provided insight and expertise that greatly benefited the initial research outline. Finally, I would like to thank E.E. van Loon for the assessment of the final research proposal.

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Are ecological machine learning tools a relevant asset to population dynamic analysis?