A qualitative reasoning model of algal bloom in the Danube Delta Biosphere Reserve (DDBR)

Ecological Informatics 4 (2009) 282–298

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Ecological Informatics j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / e c o l i n f

A qualitative reasoning model of algal bloom in the Danube Delta Biosphere Reserve (DDBR) E. Cioaca a, F.E. Linnebank b, B. Bredeweg b,⁎, P. Salles c a b c

Danube Delta National Institute, Tulcea, Romania Human Computer Studies, University of Amsterdam, Amsterdam, The Netherlands Institute of Biological Sciences, University of Brasília, Brasília, Brazil

a r t i c l e

i n f o

Article history: Received 31 May 2009 Received in revised form 8 September 2009 Accepted 10 September 2009 Keywords: Qualitative Reasoning Garp3 Aquatic ecology Algal bloom Conceptual models

a b s t r a c t This paper presents a Qualitative Reasoning model of the algal bloom phenomenon and its effects in the Danube Delta Biosphere Reserve (DDBR) in Romania. Qualitative Reasoning models represent processes and their cause–effect relationships in a flexible and conceptually rich manner and as such can be used as instruments for capturing and sharing explanations of how systems behave. The DDBR model is based on expert knowledge and captures the main factors contributing to the dynamics of this aquatic ecosystem. Focal points of the model are the relationships between temperature, water pollution from the Danube catchment area, and cyanotoxins. These factors gravely affect aquatic biota and ultimately human wellbeing. In addition to capturing domain knowledge, this paper discusses solutions for representing typical patterns in ecological systems using Qualitative Reasoning techniques. © 2009 Elsevier B.V. All rights reserved.

1. Introduction The model described here aims at improving the understanding of the mechanisms that result in algal bloom and its effects on zooplankton and fish. Algal growth is influenced both by temperature and by the nutrient concentration, and under specific conditions these factors trigger excessive growth, characterizing the bloom conditions. The model presented in this paper was constructed according to the framework for formalising and implementing conceptual models (Bredeweg et al., 2008). Several techniques such as concept maps were used to structure and compile expert knowledge about the system before encapsulating it into the Qualitative Reasoning knowledge structures (Cioaca et al., 2006a,b). In this paper, we present a part of the final results from this work. In the following subsections we will first introduce the domain, Qualitative Reasoning, and the model goals. 1.1. Domain background The Danube Delta Biosphere Reserve (DDBR) in Romania is located at the mouth of the Danube River just before it reaches the Black Sea. The DDBR has been designated as a world heritage site and wetland of international importance since 1990 (http://www.ramsar.org/). This

⁎ Corresponding author. E-mail address: [email protected] (B. Bredeweg). 1574-9541/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.ecoinf.2009.09.010

status entails that all social and economic actions must comply with biodiversity conservation and protection measures in order to establish sustainable development. Within the DDBR, aquatic ecosystems represent the most important and extended environment for natural resources developed in this area. This is the case both from a scientific and from an economic perspective. Therefore, a great concern is focussed on water quality, as it is ‘responsible’ for DDBR biodiversity including human health. The Danube River water pollution is problematic, as recorded within the last decades (Gils et al., 2005). Contamination of DDBR water basically comes in two forms: heavy nutrient loads from agricultural fertilizers and heavy metals from industry (e.g. Teodorof et al., 2007; Cioaca et al., 2006a,b; Wachs, 2000). Water pollution in the DDBR has contributed to losses of biodiversity (Hooper et al., 2005). To reduce these negative effects, it is necessary to understand and communicate details on how pollutants are transmitted from the water to the biotic components (flora and fauna species: primary producers and consumers), due to the interdependency relations in the framework of the functional feeding groups (Oosterberg et al., 2000). Within the DDBR the most frequent species, which compose the phytoplankton algae, are the Diatoms. Diatoms are characterized by a high growth rate: when conditions in the upper mixed layer (nutrients and light) are favourable (e.g. in spring) their adaptive capabilities allow them to quickly dominate phytoplankton communities. As a functional feeding group they form a significant source of food for higher trophic levels, especially for Zooplankton (Cioaca et al., 2006a,b). However, in

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conditions with higher water temperatures, blue green algae growth occurs. Blue green algae are bacterial species named Cyanobacteria. Because of their photosynthetic abilities these autotroph species are included in the phytoplankton group. Most of the blue green algae species contain cyanotoxins in their cells. Being poisonous they ‘contribute’ to the water pollution, and to aquatic population mortality in general, if their concentration is high (Chorus and Bartram, 1999). Heavy nutrient loads lead to algal blooms when temperature conditions are favourable. The term phytoplankton (algal) bloom means that these strongly increase in number in a short period of time (of few days). Algal bloom is an indicator of eutrophication. Blue green algae bloom can take place along with diatoms bloom if nutrient inflow and water temperature are high. Effects of phytoplankton algae bloom can be: increase of water turbidity by phytoplankton high biomass, decrease of dissolved oxygen, increase of detritus after phytoplankton death and decomposition by bacteria, increase of water pollution due to cyanotoxins and detritus by the bottom sediment re-suspension process. The water surface covering of a severe algal bloom involving blue green algae therefore results in a lack of dissolved oxygen and light in the water and high toxicity. This results in very poor life conditions for aquatic populations. Die-offs of the populations in the dependent food chain can be the result (Cioaca et al., 2006a,b).

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magnitudes and derivatives for one or more quantities over the course of a number of states (also known as a ‘behaviour path’). 1.3. Model goals The model presented in this paper is constructed to model the behaviour of DDBR aquatic ecosystem flora and fauna populations. The aim is to focus on water pollution, its negative effects and the ways they are transmitted through the food chain from abiotic components to biotic components (flora and fauna). The specific model goals are the following: • To model the phenomenon of algal bloom and the propagation of this effects on the food chain. This includes a detailed explanation of the mechanism of algal bloom. • To improve environmental modelling techniques with Qualitative Reasoning solutions for typical ecological phenomena such as a detailed mechanism for biological growth processes. In addition, we strive for a functionally ‘clean model’, which specifically means that the state-graphs generated when simulating should have no dead end paths. Section 4.1.2 explains this concept in more detail. 2. Model implementation

1.2. Qualitative Reasoning Qualitative Reasoning models can be used as tools for education and decision-making, particularly in domains such as ecology for which numerical data is often unavailable or hard to come by (Petschel-Held, 2005). Furthermore, Qualitative Reasoning models are explicit thereby requiring domain experts to make definite statements concerning the mechanisms being modelled. This makes statements falsifiable and discussable, thereby aiding scientific advancement. Qualitative Reasoning is a formalism that abstracts from real valued numerical data, focusing on system states exhibiting essential distinct behaviour. Garp3 (http://www.Garp3.org) is a fully operational workbench for knowledge capture that provides tools for building Qualitative Reasoning models, simulating them and inspecting the results, using various graphical aids (Bredeweg and Salles, 2009). Typical Garp3 models involve many different ingredients: Entities represent the structural elements of the system, and agents represent the structural elements exogenous to the system. Configurations indicate the structural relations between entities (and agents). Quantities are associated to entities and agents, representing their dynamic properties. Each quantity can take on values from predefined sets (quantity spaces) of symbols. These quantity space elements represent points and intervals on the real number scale. Points (also called landmarks) typically indicate where behavioural changes occur. Quantities also have an associated derivative indicating in what direction the quantity is changing. Derivatives are calculated using causal relations. These are presented in the form of positive and negative direct influences (Influences: I+, I−), and positive and negative indirect influences (Proportionalities: P+, P−). Influences are typically associated with primary processes, whereas proportionalities propagate these changes (Forbus, 1984). Other dependences include several types of correspondences (indicating corresponding values) and inequalities {b, ≤, =, ≥, N}. A model is built from scenarios representing starting configurations of ingredients, and model fragments that represent conditional knowledge chunks using the above described ingredients. A simulation is generated by searching for all applicable model fragments for a given scenario, resulting in one or more states. These are then analysed for possible transitions (changing values, changing inequalities, etc) generating successor states. This process continues until no more new states are found. The output is a state-graph showing all states and their transitions. Each state contains a substantial amount of information and can be inspected using several diagram types. The value history is an important diagram listing the successive

Our model of the DDBR ecosystem involves 18 different entities (including the intermediate concepts in the subtype hierarchy), 2 agents, 5 configuration types, 13 quantities, 56 model fragments and 12 scenarios. The most important entities and agents are listed in Table 1. An overview of the causal and structural dependencies in the DDBR model is given in Fig. 1. Each of the processes and their associated relations captured in this diagram are explained in the following sections. To complete our overview of the model ingredients, Table 2 lists all quantities involved. 2.1. Exogenous quantities Two agents are active in the model: Farming and Land, these represent the agricultural activities and the surrounding land respectively. These agents are not part of the system being modelled but they affect it. Their influence on the system is modelled by their associated quantities Average temperature and Nutrient Runoff. Both quantities use exogenous behaviour patterns to generate their behaviour independent of the rest of the system (Bredeweg et al., 2007). The patterns used are simple patterns such as ‘increasing’, ‘decreasing’ or ‘steady’, which result in a positive, negative or zero derivative respectively. Note that an exogenously increasing or decreasing quantity may stop in the last point of the quantity space. Apart from Average temperature and Nutrient Runoff always being exogenous, Carrying capacity is considered exogenous in one small concept scenario, and in this case it is driven by the exogenous pattern ‘positive parabola’. This makes the quantity go up to its highest magnitude, stop and then go down to its lowest magnitude. Table 1 Agents and entities in the DDBR model. Entity or agent Danube Delta Diatoms Cyanobacteria

Description

The ecosystem of interest. This population represents the healthy algal species in the system. This population is a type of Blue Green Algae (BGA), representing the unhealthy algal species in the system. Zooplankton Represent first dependent species. Fish Represent second dependent species (higher up the food chain). Land (agent) The land surrounding the DDBR ecosystem determines the river's temperature. Farming (agent) The farming activities near a water body, which (may) have a significant influence on the nutrient levels in the water due to the use of fertilizers.

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Fig. 1. Dependency overview for the DDBR model. For illustrative purposes this view was generated using a dedicated scenario that mixes two possible perspectives for Biomass growth.

2.2. Biomass growth

Table 2 Quantities present in the DDBR model. Quantity Biomass

Description

The current biomass of a population, used to represent the size of the population. Average temperature The average temperature of the overall ecosystem. Cover The degree to which the surface of a water body is covered by algae. This water surface cover forms a barrier that blocks out light and oxygen. Cyanotoxins The total amount of cyanotoxins in a water body contained in living blue green algae or released directly in the water by dead blue green algae. Water temperature The actual temperature of a water body. Light The amount of sunlight entering a water body. Mortality rate The process of biomass loss, due to the death or negative growth of individuals in a population. Nutrients The amount of nutrients dissolved in the water. Nutrient runoff The amount of nutrients removed from the soil by erosion or leaching from the catchment area. Dissolved oxygen The amount of oxygen dissolved in a water body. Production rate The process of biomass production, due to the growth and increase in the number of individuals in a population. Carrying capacity The population biomass that could theoretically be sustained by the environment in specific conditions.

The size of a population is determined by its biomass, represented in the model by the quantity Biomass. For any species, biomass growth is a process that takes time and is dependent of several factors. In our model, for each population these factors are aggregated into the single quantity Carrying capacity. This concept matches the standard concept of carrying capacity (Odum and Barrett, 2005) in the sense that it refers to the highest stable magnitude of biomass under specific environmental conditions. Carrying capacity determines the equilibrium state of Biomass. It represents the size that an existing population will take on if conditions remain stable for enough time to allow

Environmental Factors

Carrying capacity

Time

Growth Process

Biomass

Fig. 2. The context of the growth process of biomass. Environmental factors determine the Carrying capacity and given time the Biomass can grow towards this theoretical optimum.

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Biological entity

285

Growth process full causal

Aquatic population Aquatic biological entity

Biomass

Carrying capacity

Zlch

Zlch

High

High

Critical

Critical

Low

Low

Zero

Zero

Mortality rate Production rate Processes Processes Plus

Plus Zero

Zero

Fig. 3. The first model fragment for the perspective: Full causal growth dynamics. This fragment captures the direct influences on Biomass.

Biomass to catch up with Carrying capacity. Fig. 2 illustrates this context of biomass growth. The mechanisms for aggregating the environmental factors into Carrying capacity are described in Sections 2.3 and 2.5. For the growth process itself, which relates these two quantities, we have specified two alternative views, one explaining the phenomenon on a detailed level, and one treating it as a ‘black box’ mechanism. In the detailed view, described in Section 2.2.1, the internal dynamics of the growth process are modelled exposing the behaviour of the system on a fine-grained scale. An important property of this view is that the effects of the time factor are covered. In the black box approach, time effects are not covered. These details are described in Section 2.2.2. The two perspectives on the growth process are triggered by a modelling assumption connected to the species entity. These assumptions are: Full causal growth process and Simple growth process. An example of this construction can be found in Fig. 3. 2.2.1. First perspective: full causal growth dynamics Two new quantities are introduced in the full causal growth process view. These are Mortality rate and Production rate as shown in Fig. 3. As in Nuttle et al. (2009)"; Mortality rate represents the rate of biomass loss. This quantity has a negative influence (I−) on Biomass. Production rate represents the rate of biomass increase. This quantity has a positive effect (I+) on Biomass. Biomass determines the qualitative value of Production rate and Mortality rate. If Biomass is Zero1 then both Mortality rate and Production rate will be Zero. This fact is

1 Refers to the qualitative point value ‘zero’ in the quantity space of the quantity (see e.g. Fig. 3).

represented by single value correspondences. If Biomass is above Zero then so are Mortality rate and Production rate. This fact is represented using a separate model fragment with a conditional value assignment (not shown). 2.2.1.1. Ambiguity. The influences from Mortality rate and Production rate have an ambiguous effect, which is resolved using inequality information (Fig. 4). The hypothesis is that if Carrying capacity N Biomass, then conditions are favourable for growth, so Production rate will be greater than Mortality rate. The opposite is true in the case where Biomass N Carrying capacity, and similarly no net growth (Production rate =Mortality rate) will take place when Biomass=Carrying capacity. This knowledge is elegantly captured in the following qualitative inequality: Carrying capacity−Biomass = Production rate−Mortality rate:

2.2.1.2. Feedback. Proportionalities are used to represent the feedback of the dynamics of Biomass on Production rate and Mortality rate, as well as proportionalities indicating the effect of Carrying capacity on Production rate and Mortality rate. If Carrying capacity increases the potential for growth will increase relatively so Production rate should go up (P+) and Mortality rate should go down (P−) and vice versa. The effects of change in Biomass are a little different: an increase will result in a larger population leading to larger Production rate and Mortality rate (both P+) and vice versa. It could also be argued that an increase in Biomass would cause the potential for growth (relative to Carrying capacity) to diminish and that the relation to Production rate should therefore be the inverse (P−). This

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Full causal growth process

Growth process full causal

Aquatic population Aquatic biological entity

Carrying capacity Zlch High Critical Low Zero

Production rate Processes Plus Zero

Biomass

Zlch High Critical Low Zero

Mortality rate Processes Plus Zero

Fig. 4. The second model fragment for the perspective: Full causal growth dynamics. This fragment captures the inequality relating all four quantities as well as the feedback relations on Production rate and Mortality rate.

relative relationship is true in several cases; the effect of a changing Biomass on Production rate and Mortality rate is inherently not very specific. However, this approach leads to dead end paths in the case of Carrying capacity being Zero and Biomass going to Zero. Then Production rate will not go to Zero as it should because it will be increasing. This issue can be addressed by modelling the precise behaviour of Production rate and Mortality rate using more complex mechanisms and factors than only Carrying capacity and Biomass. However, for the purpose of the model described here these details are redundant, hence this simplification is reasonable.

This is achieved by using a proportionality and a full quantity correspondence. This ensures a complete qualitative equality and thereby a continuous equilibrium; Biomass instantly mirrors Carrying capacity if it changes. See Fig. 1 for examples of the simplified growth (Diatoms, Zooplankton, and Cyanobacteria) and of the full causal growth (Fish). As mentioned before, the option for having one or the other perspective on growth is optional for each population and it can be set in the scenario using the assumptions labels ‘Full causal growth process’ and ‘Simple growth process’. 2.3. Determining carrying capacity for primary producers

2.2.1.3. Behaviour at Zero. Note that the consequences of this model fragment are only in effect when Biomass is above Zero. At Zero no population is present and Production rate and Mortality rate are Zero and equal no matter how great the potential expressed by Carrying capacity. In this case, another model fragment (not shown) is in effect which only places the proportionalities from Biomass to Mortality rate and Production rate. It does not place the inequality, or the proportionalities from Carrying capacity to Production rate and Mortality rate. Because of this structure a population cannot leave Zero once it reaches this point. Therefore this detailed view captures the concept of extinction. The start of a new population through colonisation or immigration (Salles and Bredeweg, 2006; Salles et al., 2006) is not covered in our model however. 2.2.2. Second perspective: simplified growth dynamics In some scenarios, the focus is less on the internal growth dynamics and more on the factors determining Carrying capacity and also on the propagation of the effects of Biomass. To keep the simulation concise and insightful in these cases, a less detailed perspective on the growth process is required. This simplified view on growth dynamics in our model implements a direct coupling of Carrying capacity and Biomass.

For algal species, the primary producers, Nutrients and Water temperature are the two major factors that determine Carrying capacity. The relationship between Nutrients and Carrying capacity is straightforward: the higher the Nutrients, the higher the Carrying capacity can be (Padovesi-Fonseca and Philomeno, 2004). The relationship with Water temperature is more dynamic. Initially a higher Water temperature leads to a higher Carrying capacity, but when a certain optimal value for Water temperature is reached the relationship reverses because each species has a maximum temperature at which it can survive (Suzuki and Takahashi, 1995). A high Carrying capacity is only possible if both Water temperature and Nutrients conditions are favourable. 2.3.1. Algal bloom Algal bloom occurs when a population (suddenly) becomes very large. In the model bloom is said to occur if the Biomass of a population is equal or greater than Critical. The factor determining Biomass is of course Carrying capacity, and the behaviour of this quantity is discussed in Section 2.3. An important effect of algal bloom is the covering of the water surface. This is reflected by the quantity Cover whose behaviour is discussed in Section 2.4.

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2.3.2. Quantity spaces The quantity space of Carrying capacity is {Zero, Low, Critical, High}. At Zero or Low there is no algal bloom. At Critical (a point value) the bloom is minimal and at High there definitely is an algal bloom. Note that a landmark such as Max is not used. This is because such a landmark would cause dead end paths in the simulation. It intuitively indicates the situation where both Nutrients and Water temperature are precisely optimal, but given, for example, an increasing or decreasing Water temperature these optimal conditions would only last for an instant and therefore the landmark should be reached and then immediately left again in the opposite direction which is impossible because of continuity reasons. The quantity space used for Nutrients is similar to that of Carrying capacity, but it does include the Max landmark. The role of the landmark Critical is pivotal again, determining if Nutrients is high enough to have a possible High Carrying capacity as a result. The quantity space of Water temperature has more landmarks to accommodate the optimal regions and turnover points for different species. Fig. 5 illustrates the generic quantity space landmarks for Water temperature and the relations with Carrying capacity. The general idea is that if Water temperature is outside of the favourable range (below Low boundary or above High boundary), then Carrying capacity is Low. If Water temperature is inside of the favourable region, then Carrying capacity can be Low, Critical or High. If Nutrients is Low and Water temperature is in the favourable region, then Carrying capacity can be High if other conditions are also good. The optimal landmark indicates the ideal Water temperature, which is the turnover point where the proportionality from Water temperature to Carrying capacity changes sign. At the optimal landmark itself there is no proportionality in effect. 2.3.3. Model fragments A set of model fragments is used to implement the knowledge needed for determining the Carrying capacity magnitude and derivative of algal species. As mentioned before, Water temperature has a changing proportionality on Carrying capacity. The proportionality from Nutrients to Carrying capacity (P+) is always in effect. Table 3 enumerates the remaining conditional knowledge captured in the model fragments. The effect of this is that the Carrying capacity is Low (or Zero) if any condition is unfavourable and Carrying capacity is ambiguous in the other cases, except when conditions are at their maximal landmark; then Carrying capacity must be in the High interval. Note that the ‘generate all values’ mechanism present in Garp3 (Bredeweg et al., 2007) must be used here to ensure that Carrying capacity takes on all possible magnitudes in initial states. Also note that because each species has different landmarks, a separate branch of model fragments implementing the mapping from Water temperature and Nutrients to Carrying capacity is needed for all species.

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Table 3 Conditional knowledge for determining the value of Carrying capacity for algal species given Water temperature and Nutrients. Conditions: Nutrients/Water temperature

Results: Comments: Carrying capacity

Nutrients = Zero

Zero

Nutrients = {Low, Critical}

Low

Water temperature = out of favourable range (including boundary landmark) Water temperature= in favourable range Nutrients = {High, Max} Water temperature = Optimal Nutrients = Max

Low

{Low, Critical, High} High

In our model zero Nutrients is the only condition causing zero Carrying capacity. A ‘fatal’ region for Water temperature is not included. (Landmark included: see Section 4.2.1). Unless of course Nutrients = Zero (landmark included: see Section 4.2.1) When both factors are favourable Carrying capacity can be high, but this is not necessary. Only when both factors are at their peak Carrying capacity is unambiguously high.

2.3.4. Temperature ranges Each species has a different optimal temperature range. Since in our model two algae populations are active, the quantity space of Water temperature needs to accommodate the relevant landmarks for both populations. These different regions may be (partially) overlapping leading to several possible quantity space organisations, some of which are shown in Fig. 6. Note that there are many possibilities and favourable temperature regions for species may have very different spans. The quantity space of Water temperature in our model is relatively large and has the following values: {Zero, Very low, Diatoms minimum, Bga minimum diatoms optimal, Bga low diatoms high, Bga optimal diatoms maximum, Bga high, Bga maximum, Very high, Highest}. In the model, the Cyanobacteria (Blue Green Algae, BGA) prefer a somewhat higher Water temperature than the Diatoms. Hence, the Water temperature regions are implemented using the 3rd option shown in Fig. 6 (RHS). This option has a partial overlap (High diatoms/Low BGA) and two coinciding landmarks (Optimum diatoms =Low boundary Bga and High boundary diatoms = Optimum Bga), therefore it allows both algae populations to bloom at the same time as well as separately, and the coinciding landmarks minimize the state space for the simulation leading to a concise state-graph without sacrificing expressive power on the modelled concept. Notice that the specific real world values of the landmark Critical may be somewhat arbitrary, so whilst it is unlikely for unrelated landmarks to coincide in general, it causes no problem in the context of a qualitative model.

Temperature

Temperature

Temperature

Water Temperature

CC low

| too high high boundary

PCC low, critical or high

CC low

A A

| good, above optimal optimal | good, below optimal low boundary

P+

A

B

B

B

| too low

Fig. 5. Generic temperature ranges indicating the effect of Water temperature on Carrying capacity (CC) for temperature dependent species.

Fig. 6. Quantity space arrangements for two temperature dependent populations A and B. On the LHS the two species require different temperature regions while on the RHS the regions largely overlap (and the species thus potentially coexist).

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2.4. Cover and cyanotoxins Algal bloom has several effects. Firstly, the water is covered by the sheer biomass of the algae population thereby blocking sunlight and oxygen from entering the water. Our model has implemented two views on this phenomenon. The first is that the blue green algae and the Diatoms both add up to form this layer, which is represented by the quantity Cover. This is shown in Fig. 7. As a result of the qualitative summation used in this view, the value of Cover is ambiguous if both Biomasses are in different intervals. To eliminate this ambiguity in simulations focusing on other behavioural aspects an alternative view is also implemented in which Cover depends solely on the Biomass of the Cyanobacteria. Here a positive proportionality (P+) and a full quantity correspondence are used (model fragment not shown). This view is an ecologically plausible simplification since blue green algae contribute most to the cover effect in eutrophic conditions (Irwin Keating, 1978). Both views can be activated using modelling assumptions. An example of this can be found in Fig. 7. The propagation of the effect of Cover on Light and Dissolved Oxygen is straightforward. They use a similar quantity space and are the inverse of Cover. This is implemented using negative proportionalities and value correspondences. Another important effect of algal bloom is that blue green algae contain cyanotoxins. These are released when organisms ingest the algae higher up the food chain, or when the algae die. We have chosen not to model this distinction, because its effects are similar; the ingestion of the water is problematic whether it contains dissolved toxins or living blue green algae (Chorus and Bartram, 1999). In the model, the Biomass of the blue green algae determines the level of cyanotoxins in the water body using a positive proportionality (P+) and a full quantity correspondence (model fragment not shown). 2.5. Determining Carrying capacity for secondary species Zooplankton and Fish each depend on four factors: food, toxins, light and oxygen (Cioaca et al., 2006a,b). In this context the Biomass of the species lower in the food chain represents the food. This relation is

Algal bloom

modelled using the ‘feeds on’ configuration. As can be seen in Fig. 1, the food of Zooplankton is the Diatoms and the food of the Fish is the Zooplankton. Both species have a fairly simple quantity space for their Carrying capacity and Biomass equal to the one used for the algae: {Zero, Low, Critical, High}. Two views are implemented for describing the relation between the driving factors and the Carrying capacity of each species. These views are mutually exclusive and controlled using the modelling assumptions Dependent species weakest link and Dependent species addition. Both views share the same causal model. The dependent Carrying capacity is negatively proportional (P−) to Cyanotoxins and positively proportional (P+) to Light, Dissolved Oxygen, and the Biomass of the ‘food species’. A value correspondence indicates that when Biomass is Zero, Carrying capacity will be Zero too. The idea of the weakest link perspective is that if any driving condition is not in the optimal interval (low toxins, high food/light/ oxygen), then Carrying capacity will be low. Only if all conditions are good then Carrying capacity can be high, but still this is not necessarily the case. This ambiguity is necessary for a concise implementation as will be shown in Section 4.2.1. The implementation uses a set of model fragments defining all cases of ‘no-good’ conditions. Next to these constraints the Garp3 ‘generate all values’ mechanism ensures that the remaining freedom in attaining all values possible is used. The addition perspective is based on the fact that Cover depends solely on the Cyanobacteria population if the simple cover assumption is used (see Section 2.4). This population also determines Cyanotoxins. In this case, the factors Light, Dissolved Oxygen and Cyanotoxins are therefore always qualitatively correlated. They can be treated as a single ‘conditions’ variable. This leads to the case of having food and ‘conditions’ as the two defining factors. The idea is to implement a qualitative addition of these factors to get to Carrying capacity. Table 4 shows the relationships for this view. This view is ambiguous if both factors are in a different interval. Because of the limited applicability of this view (depends on the simple cover assumption) and because of the fact that it also produces slightly bigger state-graphs than the weakest link view, it is not our preferred

Aquatic ecosystem Aquatic ecosystem

Lives in Lives in Diatoms Diatoms

Blue green algae Blue green algae ==

==

Aquatic population Aquatic biological entity Biomass Zlch High Critical Low Zero

Aquatic population Aquatic biological entity Biomass

Cover Zlch High Critical Low Zero

Zlch High Critical Low Zero

Cover mechanism bga and diatoms

Fig. 7. The model fragment for the complex cover mechanism adding the blue green algae and the diatoms. Note that next to the addition of the quantities, an addition of the landmarks is necessary to achieve correct results.

E. Cioaca et al. / Ecological Informatics 4 (2009) 282–298 Table 4 Implementation of the ‘addition view’ for determining the value of Carrying capacity for secondary species. ‘Conditions’

Food

Resulting Carrying capacity

Favourable

High or Critical Low Low Critical High Low or Critical High

High Low, Critical or High Low Critical High Low Low, Critical or High

Critical

Unfavourable

Givens for this conditional knowledge are the value of Biomass for the food species and the value of other ‘conditions’: Light, Dissolved Oxygen and Cyanotoxins.

choice. Hence, we have not incorporated any discussion of a simulation using this view in this paper, but we have chosen to incorporate it in the model because it provides an alternative option which may be interesting from a domain point of view because it allows secondary species to flourish in more varied situations. 3. Model results The behaviour covered by our model is quite broad. A full simulation containing all entities and using the most detailed mechanisms and views, produces a valid (stable single end state), but very large stategraph (consisting of 3126 states). In this paper, we therefore describe five smaller scenarios each showcasing a particular concept: 1. The determination of primary Carrying capacity given Nutrients and Water temperature. 2. The effect of the different temperature regions. 3. The determination and direct effects of Cover. 4. The determination of secondary Carrying capacity, the higher end of the food chain. 5. The full causal growth process. Table 5 lists the main properties of these scenarios. In the first four scenarios the mechanisms concerning algal bloom and its effects are considered with one or more populations in their full context. Scenario 2 uses the complex mechanism to determine Cover. The fifth scenario concerns the full causal growth dynamics mechanism and uses the complex mechanism representing this process. 3.1. Single algae population The first scenario is given in Fig. 8, it has a single blue green algae population and it illustrates how Water temperature and Nutrients together define the Carrying capacity of an algal population. Average temperature and Nutrient Runoff have exogenous behaviour (both increasing). The quantity Nutrients starts at Zero. The quantity Water temperature starts at the value Diatoms low. 3.1.1. Behaviour The state-graph of this simulation has 65 states. It has a single starting state where Carrying capacity is Zero and a single end state where it is Low. Many different paths are generated because of ambiguity. Firstly, Water temperature and Nutrients are unrelated so they may change their values in various orders. Secondly, several value combinations of Nutrients and Water temperature result in an ambiguous value for Carrying capacity (see Section 2.3). And related to that, the causal effect of the increasing Water temperature and Nutrients is ambiguous when Water temperature is above the optimal value. In this case, the increase of Nutrients has a positive effect whilst the increase of Water temperature has a negative effect. In the simulation paths can be distinguished where Nutrients reaches Max before Water temperature reaches Highest, as well as paths where the opposite is true and paths where they reach their final value at the same time. Algal bloom always occurs in paths where

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Nutrients is at Max when Water temperature reaches the optimal value for Cyanobacteria. In all other cases there are paths where Critical is the maximum value for Carrying capacity or it even remains in the Low interval. Fig. 9 gives the value history of a single path from start to end state.2 In this path Carrying capacity leaves Zero (from state 1 to 2) as soon as Nutrients leaves Zero. Next, when both determining factors become favourable Carrying capacity actually becomes High (states 23, 26 and 49, which is a possibility in this case and not a necessity) before it drops back to Low again (states 44, 30, 45, and 52) as Water temperature becomes too high for the population. As mentioned in the previous paragraph the movement of Carrying capacity is somewhat ambiguous which is reflected by the ‘premature’ stop and increase in states 30 and 45. 3.1.2. Interpretation This scenario concerns the general behaviour of algal populations under different Water temperature and Nutrient conditions. The quantities determining Carrying capacity (Nutrients and Water temperature) are affected by the exogenous behaviour of Average temperature and Nutrient Runoff (both increasing). The end state has an extreme value for Water temperature and is therefore not of much interest. The conclusions that can be drawn (and which are illustrated with this simulation) are that ‘to combat algal bloom’ the limiting of nutrient pollution is especially important when temperatures are favourable for the algae. 3.2. Two algal populations, simple cover mechanism Scenario 2 concerns both algal populations. The rest of its structure is equal to scenario 1. The quantity Nutrient Runoff has a steady exogenous behaviour and has magnitude Max. The quantity Average temperature has an increasing exogenous behaviour, Water temperature starts at magnitude Very low. 3.2.1. Behaviour In the state-graph (Fig. 10) three alternative paths can be distinguished (branching from state 7). This is because in the value Bga low diatoms high, Water temperature is favourable for both populations, but blooming is not required. The three paths represent the cases where both blooms occur separately, where they overlap, and where they half overlap at the Critical landmark. The latter case is shown in the value history given in Fig. 11. 3.2.2. Interpretation This scenario concerns the behaviour of two algal populations in different Water temperature conditions. It illustrates the effects of the Water temperature quantity space in the sense that the optimal Water temperature for each species is at a different magnitude and therefore both populations will bloom at different magnitudes for Water temperature (see Section 2.3.1). As in simulation 1 the end state has an extreme value for Water temperature and is therefore not of much interest. The main point that this simulation makes, is that the conditions for diatom and cyanobacterial bloom may be very similar and to predict the more harmful cyanobacterial bloom, precise knowledge of its threshold temperature and nutrient magnitudes is needed. 3.3. Two algal populations, complex cover mechanism Scenario 3 is almost identical to scenario 2. The difference is that it uses the complex mechanism to determine Cover (see Section 2.4).

2 State numbers are identifiers generated by the simulator and do not necessarily reflect successor states. Instead, transition arrows denote sequences of successor states.

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Table 5 Main properties of the five scenarios in the DDBR model. Number Entities/agents

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3.3.1. Behaviour The state-graph (Fig. 12) for this simulation is larger compared to the one for scenario 2. This is because in many states the qualitative addition of the Diatoms Biomass and the Cyanobacteria Biomass to determine Cover is ambiguous. If a High and a Low value are added the result can be Low, Critical or High. The value history (Fig. 13) shows the behaviour for a single path in this simulation, starting in state 1 and ending in state 60. Biomass (twice), Cover and Dissolved Oxygen are shown. Light is not shown, because it is equal to Dissolved Oxygen. In this path, firstly the Diatoms bloom (states 5, 6, 11, 14 and 32), and as this bloom decreases Cover becomes High (states 11, 14 and 32). This may seem strange but it is possible because the Cyanobacteria population is increasing at the same time. This increase may be stronger than the decrease of the Diatoms Biomass. When the Diatoms bloom ends the bloom of Cyanobacteria starts, and at first the Cover drops below Critical (state 41) before becoming High again (state 28 etc.). Note that both Biomass's are Critical at the same time and at this point Cover actually must be Critical too (state 39). Towards the end of the path the bloom decreases and becomes Low before the bloom ends. This is not arbitrary either, at the moment that the Cyanobacteria hit the landmark Critical (state 55) the addition is again specific in its outcome; Cover must be Low. Finally, note that throughout the entire path Dissolved Oxygen is exhibiting the opposite behaviour of Cover.

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3.3.2. Interpretation This scenario again concerns the behaviour of two algal populations under different Water temperature conditions. It is only different from scenario 2 in the complexity of the behaviour of Cover. This simulation illustrates how the Biomass of Diatoms and Cyanobacteria determines Cover, and how this quantity in turn determines Dissolved Oxygen and Light. An interesting idea that can be drawn from this simulation is that if the optimum temperatures of two species are far enough apart, then even though the temperature keeps increasing, the aquatic conditions (represented by Cover and Dissolved Oxygen) can fluctuate. In this simulation this is above and below the landmark Critical.

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Fig. 8. Scenario 1: Single algae population. Note the exclamation marks behind Nutrient Runoff and Average temperature, these indicate an exogenous behaviour. The value Max from Average temperature is set to be equal to the topmost landmark of Water temperature. To limit the exogenous behaviour a different equality may be chosen.

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The value history for a typical path is given in Fig. 16. Here we see Water temperature steadily increasing because this is exogenously defined (in its dependence on the Average temperature). In response the algal populations increase and in this particular path the secondary populations increase as well. The Diatoms bloom (states 15, 16, 25, 26, 36, 37, 49, 51, 39, 40, 47, 30, and 31), and the Zooplankton population, having enough food, reaches the value High (states 26, 36, 37, 49, 51, 39, and 40). The Fish in turn do the same (states 37, 49, and 51). As Water temperature increases further the Cyanobacteria take over (state 31), causing Cover and Cyanotoxins problems and forcing the Zooplankton and Fish populations to the Low value. A more focussed behaviour occurs from states 30 to 53. In these states the magnitude for Water temperature is Bga low diatoms high, and as a result there is no ambiguity for the dependent species' Biomass.

Biomass value and it is known as chatter (Kuipers, 1994). We will illustrate this with the initial 5 states of the simulation. Fig. 15 shows a partial value history of the Biomass quantities for Zooplankton and Fish in these states. Zooplankton Biomass is ambiguous because conditions are improving and worsening at the same time: Water temperature increases, causing the Diatoms to increase (food), but the Cyanobacteria also increase and therefore Cyanotoxins (see also Fig. 1 for the causal dependencies). Therefore Zooplankton Biomass can be decreasing, steady or increasing. In the latter case, the Biomass of the Fish is ambiguous too; their food source is increasing, but other conditions (Cyanotoxins, Cover) are worsening. Note that in the second half of the graph (Fig. 14) the cause of the ambiguity reverses; the increasing Water temperature causes the algal populations to diminish instead of grow, but this causes the other conditions (Cyanotoxins, Cover) to improve instead of worsen.

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the simulation Zooplankton and Fish Biomass are in fact fully restricted to the interval Low.

Food is decreasing (Diatoms) and other conditions are also worsening as the Cyanobacteria grow. The three paths in this phase of the simulation correspond to the three paths discussed in simulation 2 (Fig. 10). Note that whilst derivatives of the secondary populations may be ambiguous in many states, their value is quite constrained throughout the simulation. A diatom bloom must occur in the first half of the simulation, and a Cyanobacteria bloom cannot happen in this phase. The opposite is true in the second half of the simulation. In the first half of the simulation the Zooplankton Biomass may leave the Low interval if the diatom bloom is occurring, and the Fish Biomass may do the same if the Zooplankton is not Low. Finally, in the second half of

3.4.2. Interpretation This scenario is the most elaborate scenario of the model since all species are represented. It clearly illustrates how the ecosystem reacts to different temperatures given a high nutrient load (pollution). In such a system with all four populations, the relations between them are as given in Fig. 1. Firstly, Zooplankton is affected by the behaviour of the primary populations because they feed on the Diatoms, ingest the cyanotoxins, and need Dissolved Oxygen and light, which are

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3.5.2. Interpretation This last scenario illustrates the population dynamics for a population with fluctuating Carrying capacity. The phenomenon of overshoot (Odum and Barrett, 2005) is captured and the Biomass is behaving as expected. This simulation could be useful to illustrate the time lag that exists between changes in the environment determining the Carrying capacity and their effect on Biomass. Carrying capacity may be down to Zero well before Biomass reaches Zero. 4. Discussion

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determined by Cover. Secondly, Fish are affected. In turn they feed on the Zooplankton and are also negatively affected by high Cyanotoxins and Cover. The first half of the scenario offers relatively favourable aquatic conditions. Initially the rising temperature is favourable, primary producers increase as well as the secondary species, but in higher temperatures, the situation reverses, conditions worsen and all species but the blue green algae decrease to low values. This illustrates how, given a high nutrient load, the ecosystem is at the mercy of the seasonal solar input. 3.5. Single population, full causal growth dynamics Scenario 5 features only a single population and showcases the full causal growth dynamic mechanism. Carrying capacity and Biomass are set to start at Critical and the former is given the exogenous behaviour: positive parabola. This implements an increase to the highest possible magnitude followed by a decline to the lowest possible magnitude. The magnitude Critical is taken as a starting point because if the starting point Zero is taken then Biomass will stay there (see Section 2.2.1.3). 3.5.1. Behaviour The state-graph for this simulation is shown in Fig. 17 and a value history in Fig. 18. In state 1 Carrying capacity and Biomass are equal, therefore Production rate and Mortality rate are equal too and Biomass is steady. In the next state Carrying capacity increases to High and this introduces a difference with Biomass. This difference is reflected by a difference between Production rate and Mortality rate causing Biomass to start moving to catch up with the Carrying capacity. In the next states Biomass must keep moving in this direction until Biomass is equal to Carrying capacity again. This happens in state 10, four states after Carrying capacity reaches its maximum value (state 7) and turns around. The path taken therefore represents a situation with a significant lag. The path via state 6 represents the case where Biomass follows Carrying capacity more closely and catches up right as Carrying capacity stops to turn around. Later in this behaviour path Carrying capacity decreases all the way to Zero (state 23) whilst Biomass is still in the High interval, while again in the other paths Biomass follows Carrying capacity more closely. On the transition from state 27 to 30 it catches up as Carrying capacity reaches Zero. Throughout the simulation there is some ambiguity concerning the derivatives of Production rate and Mortality rate. In states where both Carrying capacity and Biomass are moving in the same direction Mortality rate is ambiguous. In states where Carrying

In the following subsections the model results as well as the model implementation will be discussed with respect to the model goals. Some related work will be discussed and some modelling recommendations will be made. 4.1. Model results discussion Our current set of scenarios mainly focuses on changes in temperature to illustrate the important effects of this factor on algal bloom. Future work could also focus on changing nutrient inflows to illustrate the effect of changing this polluting factor. Note that this functionality is definitely present in the model, but that we have deliberately chosen to analyse and present a coherent set of scenarios always varying the single primary temperature factor, since this illustrates the concepts in the model most clearly. In some simulations ambiguity produces state-graphs that are somewhat hard to interpret. Chatter, the random transitions of ambiguous quantities (Kuipers, 1994), may conceal the essential behaviours of the system. A mechanism for the aggregation of ambiguous states (Bouwer, 2005) and/or a system of ambiguity indicators would therefore be a valuable addition to the Garp3 software system. Regarding the use of exogenous quantities, the modelled systems have an open character, being driven by these external variables and we take the value of Water temperature to quite extreme values. The advantage of this is that we prove that our model performs well over the whole range of behaviour. The disadvantage is that the end states of simulations are not very interesting. Future research should investigate scenarios with limited parabolas and also scenarios with a more closed system character (steady values for the exogenous quantities). The latter type of simulations may result in interesting sets of equilibrium end states. 4.1.1. Equifinality As mentioned in the previous paragraph, although some of the scenarios have multiple initial states because of ambiguity, all scenarios produce a single end state. This behaviour may relate to the concept of equifinality as used by Beven and Freer (2001). In contrast to quantitative approaches however, qualitative models may exhibit equifinality not because of multiple structures and parameter settings, but because of ambiguity being resolved. Therefore alone we cannot take the concept as far. Also we can explain the phenomenon by noting that all end states are unambiguous because the simulations are driven by exogenous quantities that end in extreme values. Note that extreme values do not always lead to unambiguous end states. Scenarios could be constructed that have only Nutrients as a dynamic driving factor, and these would have multiple endpoints if the Water temperature is in the favourable range. Regarding equifinality in Qualitative Reasoning it therefore seems relevant to consider if we are dealing with an open or a closed system first. Then it can be assessed if the behaviour is a measure for the uncertainty in the model. And if there is not enough information in the model, whether it can be added, thereby removing these behaviour paths.

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4.1.2. Dead end simulations As mentioned in Section 1.3 we strive for clean models that produce simulations without dead ends. These are said to occur in behaviour paths in the state-graph when the last state, in a sequence of states, does not reach a valid successor state despite having potential transitions. In the case of such a dead end there exists at least one quantity that is moving in the direction of the next value in its quantity space, but that does not reach this value (often due to inconsistencies in the model). Contrary, in a ‘clean end state’ each quantity has one of the following options: (i) stable (∂Q = 0), (ii) increase in highest interval, or (iii) decrease in lowest interval. Notice that, in each of these three cases no transitions will be found for a quantity. The reason for dismissing models with dead ends is that such a model must be incorrect or at least be incomplete at this point. Its behaviour with

infinite movement on a bounded interval does not comply with the limit analysis (e.g. Forbus, 1984) that is used. For an intuitive explanation of this concept consider Zeno's paradox of the arrow that never reaches its target because it always has the remaining half of the distance to travel. This is of course an infinite but converging series with a therefore finite outcome. All our scenarios have been assessed for the presence of such end states. And in development these have been present, always indicating problematic modelling decisions. In our final implementation all the produced simulations are free of dead ends. 4.2. Model implementation discussion Our use of the concept Carrying capacity seems to match the concept of Population potential used by (Noble et al., 2009). This model differs

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however both because of the functions used to determine Carrying capacity and because in the related work the growth process is not included in the model scope. Other work on qualitative population dynamics has been dealing with growth processes as well (e.g. Nuttle et al., 2009; Salles and Bredeweg, 2006), but this work does not explicitly incorporate the Carrying capacity concept to the extent that we have used it. For future work, it will be interesting to see how the inequality used for determining the balance in the growth dynamics (Carrying capacity − Biomass = Production rate − Mortality rate) can be adapted for use with yet more complex models of growth processes in open populations using quantities such as birth, death, immigration and emigration. As noted in Section 1.1, a second pollutant in the DDBR (next to nutrients) is heavy metals. This factor has been dealt with in Cioaca et al. (2006a). Even so the reader may wonder why this factor has not been included in this DDBR model. A strong reason for this is that this factor seems to behave uncorrelated with the nutrients factor. Including

two unrelated driving variables is absolutely possible in Qualitative Reasoning, but it has the downside of producing large state-graph only because all possible combinations of quantity behaviour will be generated. We feel that such a model (incorporating two independent phenomena) has no advantages over two separate models. One could even argue that the explanatory power of the combined model is less in such a case. To cope with the fact that the causal model determining Carrying capacity changes when an optimum temperature is reached, we have not included a maximum magnitude in the Carrying capacity quantity space. This illustrates the need for a renewed analysis of the treatment of immediate transitions and points in the Garp3 reasoning engine. Currently a point may be reached with a steady derivative and then left when the derivative becomes unequal to zero, meaning the quantity is at the point for two states. This conflicts with the temperature being in the optimum value only during a single state. In a way, our model suggests that the maximum should be only reached during a

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single instant. This is similar to other physical examples such as spring and mass system where maximum deflection reached exactly in the instant that velocity is zero (Blickhan, 1989). It also follows Fermat's theorem that states that maxima and minima in a continuous function have a zero derivative. A solution may be to regard states with immediate transitions as a single one, or to allow a quantity with a steady derivative to leave a point, leading to a state with a non-zero derivative. 4.2.1. Qualitative functions and conditional mechanisms The implemented functionalities for determining Carrying capacity all exhibit some ambiguity. The functionality to determine Cover does so too. Ideally a function does not have this property, as this leads to large state-graphs, but ambiguity is unavoidable in Qualitative Reasoning. Some functions that may be implemented in an ecological context are functions such as: • • • •

Qualitative Addition/Subtraction Qualitative Multiplication Qualitative Minimum/Maximum Other custom qualitative functions

Qualitative addition, subtraction and multiplication have been covered before and ambiguity is an inherent property of these qualitative functions (Kuipers, 1994). Qualitative addition and subtraction are available in Garp3. Multiplication can be obtained by creating a dedicated set of model fragments. A strict implementation of a qualitative minimum function is not trivial, since minimum functions can behave discontinuous with regard to their derivative (Noble et al., 2009). Such discontinuity is currently not allowed in Garp3. Other custom functions are functions that are not directly related to a single specific mathematical function as this relation may be unknown and the modeller wants to capture his qualitative knowledge about the system. In our model for example a soft ‘weakest link’ function is used, where any low value will limit the behaviour of the resulting quantity, but unlike a strict minimum function, the bigger quantities still have some effect on the movement of the quantity. It has taken some effort to get the behaviour of this and other custom functions right with respect to dead ends (see Section 4.1.2). In the next section we will analyse the implementation of conditional functions in general. 4.2.2. Analysis and recommendations Dead ends occur when all transitions fail because all successor states are contradictory. Custom conditional functions may cause these contradictions by imposing contradictory constraints as their consequences. The activation of such contradictory constraints is a crucial point, since the current state is of course not contradictory. In our modelling efforts, the epsilon principle (de Kleer and Brown, 1984) has always been involved in these problematic activations of contradictory constraints. This principle states that transitions from a point to an interval are immediate, and transitions from an interval to a point are non-immediate. The solution to these modelling issues lies in the recognition of the problem that any immediate transition leading to a contradictory state takes precedence over all other non-immediate transitions. And these non-immediate transitions may in fact lead to valid states. A contradictory state for any custom conditional function may be reached in two ways: • Conditions become true, whilst consequences remain (or become) false. • Consequences become false, whilst conditions remain (or become) true. This leads us to the following two general guidelines: • The activation of the custom function should be a non-immediate event. • The imposed constraint should be of such nature that its invalidation is a non-immediate event.

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Quantity A A4 A3 |

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A2 A1 | zero Quantity B B4 B3 |

P+

Quantity C C4 | C3 C2 | C1 zero

B2 B1 | zero Fig. 19. Example relations between quantity space values for a hypothetical conditional qualitative function. The values of A and B are conditional for the value of C.

These guidelines ensure that transitions into contradictory states never take precedence over transitions that allow the right behaviour to occur first or remain in place. The specific application of these guidelines is done by recognizing the conditional and consequential mechanisms of the custom function in question and then analysing and adjusting their behaviour with respect to the epsilon principle. As a concrete example we will consider a function with conditions and consequences that are values or regions on the quantity spaces of the involved quantities. A transition into the conditional region activates the constraint and if this transition is forced by the epsilon principle, then problems may occur. Similarly a transition out of the consequential region invalidates the constraint and if this transition is forced by the epsilon principle, then problems may occur. Consider the quantities A and B determining quantity C by means of a hypothetical custom conditional function (Fig. 19). This function may implement the idea that C has a low magnitude if either A or B has a low magnitude (or both). In this example the conditional low regions may include the adjacent landmarks A2 and B2 as indicated by the arrows in the figure or the conditional regions may only consist of the intervals A1 and B1. If the second option is taken: C must be in C1 when A = A1 or B = B1. Then a problem occurs when A = A2, B = B3, and C = C3, and all are moving downwards. The transition from A = A2 to A = A1 is immediate, but its consequences (C= C1) are contradictory with the current state (C = C3). Therefore the landmarks delimiting the conditional region need to be included and before the regions are reached other events may take place. On a similar note, the consequences of conditional function must not include the landmark delimiting the region. Take for example a model similar to Fig. 19 where C should be in {C1, C2} if B = {B1, B2}, and the current state is that B = B1 and C = C1 and both are increasing, then C may reach the landmark C2 before B reaches landmark B2, which is a valid state. The immediate and therefore mandatory successor of this state is contradictory however (B= B1, C = C3). This path becomes a dead end and the model is incorrect. In practice the guideline for the described type of functions therefore is: Include boundary landmarks3 for conditional quantity space regions and exclude boundary landmarks for consequential quantity space regions. The abovementioned guidelines are not sufficient however. A final example will illustrate the broader problem. This example concerns a hypothetical conditional function that results in a single point (landmark). Consider the situation for the topmost landmarks of Fig. 19. Here a mechanism where both A and B can independently trigger C to be in its topmost landmark is not possible.4 For example, if 3 Note that this example covers landmarks, but the idea can be directly extended to inequalities in general (b versus ≤ and N versus ≥). 4 Note that an ad hoc solution might be constructed by dynamically changing the causal model, but one may wonder if this is an elegant or even sound modelling approach.

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C must be in C4 if A is in A4 or B is in B4, then the state where A = A4 and steady, B = B3 and increasing, leads to C = C4 and increasing. This is contradictory not only because C cannot be increasing in a maximum point, but also because it must leave the C4 value immediately because of the epsilon principle and if there were an interval above C4 this successor state would still be invalid because of our conditional mechanism remaining active. Therefore in such a case a function is needed that places the resulting consequence if and only if all conditional quantities are at the conditional magnitude. 5. Conclusion In this paper we have presented an elaborate Qualitative Reasoning model of the Danube Delta Biosphere Reserve (DDBR) ecosystem using the Garp3 workbench. The model includes a detailed mechanism explaining the phenomenon of algal bloom, covering the difference in temperature ranges for different species as well as the effects of different nutrient levels. The latter largely being determined by pollution from upstream farming activities. The propagation of bloom effects through cover, food, toxins, oxygen and light is also modelled, thereby illustrating the food chain. The model is specifically tuned to the situation of the DDBR but the implemented mechanisms are generic and applicable to systems with similar characteristics. Furthermore, this work has proposed new ways of modelling growth processes thereby making progress in the effort of constructing qualitative models of population dynamics. We have also presented an analysis of modelling custom qualitative functions. In this context, generally applicable qualitative modelling principles were established regarding the conditional implementation of such functions. The model produces valid simulations without dead ends. The simulation results illustrate especially how the combination of human related changes (temperature and nutrient pollution) can seriously affect the ecosystem as a whole because of the nature of their interaction and the propagation of their effects through the food chain. Acknowledgements The research presented in this paper is co-funded by the EC within FP6 (2002–2006) (project NaturNet-Redime, number 004074, http://www.NaturNet.org), and FP7 (2009–2012) (project DynaLearn, 231526, http://www.DynaLearn.eu). We like to thank the Flash Meeting Project of the UK Open University for providing an online platform on which we could have our model discussions (http://flashmeeting.open.ac.uk/home.html). Special thanks are directed to our fellow project members who have contributed valuable insights with their case studies. References Beven, K.J., Freer, J. (2001). Equifinality, data assimilation, and uncertainty estimation in mechanistic modelling of complex environmental systems. Journal of Hydrology 249, 11–29. Bouwer, A., 2005. Explaining behaviour: using qualitative simulation in interactive learning environments. PhD Thesis. Faculty of Science, University of Amsterdam, Amsterdam.

Blickhan, R. (1989). The spring-mass model for running and hopping. Journal of Biomechanics 22–11, 1217–1227. Bredeweg, B., Salles, P. (2009). Mediating conceptual knowledge using qualitative reasoning. In: Jørgensen, S.V., Chon, T.-S., Recknagel, F.A. (Eds.), Handbook of Ecological Modelling and Informatics. Wit Press, Southampton, UK, pp. 351–398. Bredeweg, B., Salles, P., Nuttle, T. (2007). Using exogenous quantities in qualitative models about environmental sustainability. AI Communications 20 (1), 49–58. Bredeweg, B., Salles, P., Bouwer, A., Liem, J., Nuttle, T., Cioaca, E., Nakova, E., Noble, R.A.A., Caldas, A.L.R., Uzunov, Y., Varadinova, E., Zitek, A. (2008). Towards a structured approach to building qualitative reasoning models and simulations. Ecological Informatics 3 (1), 1–12. Chorus, I., Bartram, J. (Eds.), 1999. Toxic Cyanobacteria in Water: A Guide to Their Public Health Consequences, Monitoring and Management. World Health Organization — Routledge, London, p. 416. Cioaca, E., Covaliov, S., David, C., Tudor, M., Torok, L., Ibram, O., 2006a. Textual description of the Danube Delta Biosphere Reserve case study focusing on basic biological, physical, and chemical processes related to the environment. Naturnet-Redime, STREP FP6, no. 004074, D6.2.1. Cioaca, E., Bredeweg, B., Salles, P., 2006b. Qualitative Reasoning Model and documentation for learning about sustainable development focusing on basic biological, physical, and chemical processes related to the environment in the Danube Delta Biosphere Reserve, Naturnet-Redime, STREP FP6 no. 004074, D6.2.2. De Kleer, J., Brown, J.S. (1984). A qualitative physics based on confluences. Artificial Intelligence 24 (1–3), 7–83. Forbus, K. (1984). Qualitative process theory. Artificial Intelligence 24, 85–168. Gils, J.van, Behrendt, H., Constantinescou, A., Laszio, F., Popescu, L. (2005). Impact of the Danube River on the pollution of the Black Sea — changes of the nutrient loads of the Danube since the late eighties: an analysis based on long term changes along the whole Danube River and its main tributaries. Water Science and Technology 51 (11), 205–212. Hooper, D.U., Chapin III, F.S., Ewel, J.J., Hector, A., Inchausti, P., Lavorel, S., Lawton, J.H., Lodge, D.M., Loreau, M., Naeem, S., Schmid, B., Setala, H., Symstad, A.J., Vandermeer, J., e Wardle, D.A. (2005). Effects of biodiversity on ecosystem functioning: a consensus of current knowledge. Ecological Monographs 75, 3–35. Irwin Keating, K. (1978). Blue–green algal inhibition of diatom growth: transition from mesotrophic to eutrophic community structure. Science 199 (4332), 971–973. Kuipers, B.J. (1994). Qualitative Reasoning: Modeling and Simulation with Incomplete Knowledge. MIT Press, Cambridge, Massachusetts. Noble, R.A.A., Bredeweg, B., Linnebank, F.E., Salles, P., Cowx, I.G., 2009. A qualitative model of limiting factors for a salmon life cycle in the context of river rehabilitation. Ecological informatics 4, 299–319. Nuttle, T., Salles, P., Bredeweg, B., Neumann, M., 2009. Representing and managing uncertainty in qualitative ecological models. Ecological informatics 4, 358–366. Odum, E.P., Barrett, G.W. (Eds.), 2005. Fundamentals of Ecology, 5th ed. Brooks Cole, Belmont, CA. 624 pp. Oosterberg, W., Staras, M., Buijse, A.D., Bogdan, L., Coops, H., Constantinescu, A., Ibelings, B.W., Hanganu, J., Menting, G.A.M., Navodaru, I. and Torok, L., 2000. Ecological gradients in the Danube Delta lakes — present state and man-induced changes. Technical report. In: RIZA rapport 2000.015, ISBN 90.369.5309x, Institute for Inland Water Management and Waste Water Treatment (the Netherlands), and the Danube Delta National Institute (Romania). Padovesi-Fonseca, C., Philomeno, M.G. (2004). Effects of algicide (copper sulfate) application on short-term fluctuations of phytoplankton in lake Paranoá, central Brazil. Brazilian Journal of Biology 64 (4), 819–826. Petschel-Held, P. (2005). Qualitative reasoning and global change research: experiences from modeling human–environment systems for policy advice. Proceedings of the 19th International Workshop on Qualitative Reasoning, May 18–20, Graz, Austria. Salles, P., Bredeweg, B. (2006a). Modelling population and community dynamics with qualitative reasoning. Ecological Modelling 195 (1–2), 114–128. Salles, P., Bredeweg, B., Bensusan, N. (2006b). The Ants' Garden: qualitative models of complex interactions between populations. Ecological Modelling 194 (1–3), 90–101. Suzuki, Y., Takahashi, M. (1995). Growth responses of several diatom species isolated from various environments to temperature. Journal of Phycology 31 (6), 880–888. Teodorof, L., David, C., Tudor, D., Năstase, C. (2007). Surface water quality indicators of Danube Delta lakes between 2003–2005. Scientific Annals of DDNI 13, 145–154. Wachs, B. (2000). Heavy metal content in Danubian fish. Archiv für Hydrobiologie. Supplement 115 (4), 533–566.