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Int. J. Modelling, Identification and Control, Vol. 19, No. 4, 2013

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Linking and implementation of fuzzy logic control to ordinate plant strategies James Nicholas Furze* Department of Engineering, Design and Mathematics, Department of Geography and Environmental Management, Faculty of Environment and Technology, University of the West of England, Frenchay Campus, Bristol, BS16 1QY, UK E-mail: [email protected] E-mail: [email protected] *Corresponding author

Quan Min Zhu Department of Engineering, Design and Mathematics, Faculty of Environment and Technology, University of the West of England, Frenchay Campus, Bristol, BS16 1QY, UK E-mail: [email protected]

Feng Qiao Faculty of Information and Control Engineering, Shenyang JianZhu University, 9 Hunnan East Road, Hunnan New District, Shenyang, 110168, China E-mail: [email protected]

Jennifer Hill Department of Geography and Environmental Management, Faculty of Environment and Technology, University of the West of England, Frenchay Campus, Bristol, BS16 1QY, UK E-mail: [email protected] Abstract: Fuzzy control algorithms are used to give structure to the spatial categorisation of plant species by integrating digital elevation model data at increased resolution with data of selected climatic variables (mean precipitation, temperature, ground frost frequency and elevation). In previous studies, the climatic variables are obtained by minimising them to those essential for expression of the water-energy dynamic (the way in which water and energy are distributed in relation to diversity) in order to model life-history strategies of plant species. In this paper, Takagi-Sugeno-Kang fuzzy modelling is applied to infer which factors of the water energy dynamic may be used for efficient prediction of plant strategies. Implications of this paper include modelling of plant life-forms and metabolic patterning. Keywords: fuzzy control algorithm; categorisation; climatic variable; water-energy dynamic; plant-strategy. Reference to this paper should be made as follows: Furze, J.N., Zhu, Q.M., Qiao, F. and Hill, J. (2013) ‘Linking and implementation of fuzzy logic control to ordinate plant strategies’, Int. J. Modelling, Identification and Control, Vol. 19, No. 4, pp.333–342. Biographical notes: James Nicholas Furze graduated from the University of Wales Aberystwyth, UK in Botany in 1998, completed his MSc in Applied Genetics in 1999 from the University of Birmingham, UK and is currently with the Faculty of Environment and Technology, University of the West of England, Bristol, UK. His research interests include fuzzy logic, genetic algorithms, sustainability and national environmental policy formation. Quan Min Zhu is a Professor of Control Systems at the Department of Engineering Design and Mathematics, University of the West of England, Bristol, UK. He obtained his MSc in Harbin Institute of Technology, China in 1983 and PhD in Faculty of Engineering, University of

Copyright © 2013 Inderscience Enterprises Ltd.

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J.N. Furze et al. Warwick, UK in 1989. His main research interest is in the area of non-linear system modelling, identification and control. He has published over 160 papers on these topics and provided consultancy to various industries. Currently, he is acting as a member of editorial board of International Journal of Systems Science, member of editorial board of Chinese Journal of Scientific Instrument, Editor (and Founder) of International Journal of Modelling, Identification and Control, and Editor of International Journal of Computer Applications in Technology. Feng Qiao received his BEng in Electrical Engineering and MSE in Systems Engineering from the Northeastern University, Shenyang, China in 1982 and 1987, respectively, and his PhD in Intelligent Modelling and Control from the University of the West of England, UK in 2005. From 1987 to 2001, he worked at the Automation Research Institute of Metallurgical Industry, China as a Senior Engineer in Electrical and Computer Engineering. He is currently a Professor of Control Systems at the Shenyang JianZhu University, China. His research interests include fuzzy systems, neural networks, non-linear systems, stochastic systems, sliding mode control, wind energy conversion systems, structural vibration control and robotic manipulation. He is acting as an Associate Editor of the International Journal of Modelling, Identification and Control. Jennifer Hill holds an MA in Geography from the University of Oxford, UK and PhD in Biogeography from the University of Swansea, UK. She is Associate Professor and Associate Head (Research and Scholarship) in the Department of Geography and Environmental Management at the University of the West of England, Bristol, UK. She has authored close to 30 refereed journal papers, co-edited three books and published over 100 other items concerning natural resource management. She specialises in landscape ecology and biodiversity conservation. She is a Fellow of the Royal Geographical Society (with Institute of British Geographers) and is a member of the Steering Committee of the International Geographical Union Commission on Biogeography and Biodiversity. She holds a number of editorial board positions and has refereed for 26 journals.

1

Introduction

Plant species categorisation into strategies is based on plant life history descriptions (Grime, 1979). Grime states “A plant strategy may be defined as a grouping of similar or analogous genetic characteristics which recurs widely among species or populations, such that they show similarities in ecology” [Grime et al., (1995), p.3]. The main identified categories of plant strategies are: competitor (C), stress-tolerating (S) and ruderal (R). Competitive species (C) are fast growing, often aggressive species, with rapid nutrient absorption and rapid root and leaf growth. They develop a consolidated growth form with vigorous lateral spread above and below ground, thriving in high nutrient soils. Stress-tolerating species (S) are slow growing, capturing and retaining scarce resources in a continuously hostile environment. Their leaves are long-lived and often heavily defended against predation. Ruderal species (R) have a potentially high growth rate within the seedling phase, and display early onset of the reproductive phase. The allocation of resources to flowers and seeds is suited neither to development of extensive root and shoot systems needed for dominance of habitats, nor to highly stressed environments dependent on conservative patterns of resource use. Species may combine the above described strategies (e.g., C-R, S-R, S-C and C-S-R), integrating different growth forms to suit the environment. This suggests that the environment infers the strategy and vice versa (Hodgson et al., 1999): “Understanding the distribution of plant species across environmental gradients requires bringing theories together regarding the construction of plants, as well as their interactions with the

environment, and the assembly of communities” [Craine, (2005), p.1041]. However, the principal drawback of strategies in the classical form resides in the difficulty/complexity by which plants are ordinated into different types, making categorisation time-consuming and impractical when applied to large numbers of species. For example, Grime et al. (1995) lists 20 characteristics of the three strategies that have proven useful in classifying plants. Described characteristics are morphology (including life-forms), elements of specific life history, physiological descriptions of growth rate (including photosynthetic mechanisms) and miscellaneous elements (such as litter description, palatability to unspecialised herbivores and DNA amount). Application of Grime’s strategies was made in relation to Quercus cerris L. var. cerris woodland in Samsun, northern Turkey (Kilinç et al., 2010). In the studied location habitat diversity and environmental factors were present in different combinations equating to various functional modifications in plants. It was found that plant species conformed to definite strategies, further supporting the contention that plant traits are subject to the dominant factors of competition and disturbance in their selection. The classical predictor values described (Hodgson et al., 1999) were proved, however, to be inappropriate for Ruscus aculeatus, due to the stem being the photosynthetic organ as opposed to the leaf (used in the calculation). Furthermore, it was shown that species storing large amounts of water in their leaves may be mis-classified, as the categorisation requires calculation of specific leaf area and leaf dry matter. Mis-classification also occurs in species adapted to live in very shaded conditions or high salt environments. It is

Linking and implementation of fuzzy logic control to ordinate plant strategies recommended that future applications of strategies should be done through more robust calculation (Kilinç et al., 2010). In a study of the evolution of model plant populations in computer simulated environments, where nitrogen availability and disturbance frequency alone were used as variables, the evolution of expected plant strategies and patterns proved consistent with described theoretical and field evidence (Grime, 1979; Mustard et al., 2003). The illustration of plant strategies in computer simulated systems supports the existence of patterns on all scales, which may be modelled in real space and time. Plant species were linearly spaced using simulation techniques to obtain the rK (‘Kp’) continuum, with seven definite partitions (Barreto, 2008), from low to high Kp value: plants of ruderal (R) strategy were isolated in places of high disturbance and productivity; stress tolerant-ruderal plants (S-R) were seen in lightly disturbed habitats with low productivity; competitive-ruderal plants (C-R) were present in habitats where disturbance brought moderated competition by a relatively low level of stress; competitive plants (C or r = K) were found in environments with low disturbance and high productivity; competitive-stress tolerant-ruderal plants (C-S-R) were found in environments where there was a moderate intensity of stress and disturbance; competitive-stress tolerating plants (C-S) were found in environments where a moderate intensity of stress and a situation of relative non-disturbance existed; stress tolerating plants (S) were found in environments where there was low productivity and low disturbance. An algorithm was combined with the technique for order preference and similarity to ideal situation (Barreto, 2008; Hung and Chen, 2009), which effectively reconciled both the rk and C-S-R theories (Grime et al., 1995; Raunkier, 1934). Once again computer simulated systems were efficiently used to illustrate plant strategy with a more complex suite of input variables (Barreto, 2008; Bornhofen et al., 2011). Considering large numbers of species in virtual or real-life situations, there are various methods that can be used to show clustering or grouping patterns. The recent work discussed on L-systems (Bornhofen et al., 2011), for example, makes use of multi-variate principle component analysis. However, it is possible to use alternative, simpler methods. In practice, the use of ‘principal component analysis’ and ‘detrended correspondance analysis’ may be difficult due to the nature of data being analysed and/or to the arching effect of continuous variables. Basic clustering methods used in modelling and algorithm development could be more pertinent in these cases (Bornhofen et al., 2011). In this context, ‘fuzzy logic’ is one method by which algorithms may be constructed. Fuzzy logic is a process of approximate reasoning which gives mathematical strength to perceptual and linguistic elements of patterns. An inference mechanism is provided under uncertainty, allowing networks to be learnt and adapted with tolerance to errors or changes in the variables

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(Akmeliawati et al., 2012; El-Metawal et al., 2006; Sivanandam et al., 2007). Fuzzy sets are often founded in Gaussian or ‘normal distribution’ models and the use of this and other weighted distributions has been discussed (Silvert, 2000; Sivanandam et al., 2007; Yang and Zhao, 2012) Gaussian distribution is used when using fuzzy logic in biological data (Taheriyoun et al., 2010). The latter paper considers reservoir water quality evaluation, in such a way that three different classes of water body are implicated, using four different indicators. The objectives of the present paper are to construct maps of chosen global locations showing topographical details available through publicly accessible internet files, (e.g., United States Geological Survey, http://www.http://eros.usgs.gov/#/Find_Data/Products_and_ Data_Available/GTOPO30) and to subsequently display climatic data [e.g., Intergovernmental Panel on Climate Change (IPCC), http://www.ipcc-data.org) of chosen parameters to show the conditions where plant life history strategies are present. This is achieved by implementing novel fuzzy rule-based algorithms designed to quantify plant strategies of plant species, and to describe their spatial distribution. Furthermore a Takagi-Sugeno-Kang (Alimi and Chtourou, 2007; Mohan and Ghosh, 2012; Omizegba and Monikang, 2009; Wang and Yang, 2010) modelling structure will be shown to verify the chosen example and the appropriate use of a fuzzy controller. Objectives were chosen in order to query the distribution of plant strategies amongst more than 300,000 plant species and their individual occurrence. This paper is organised as follows. Section 2 introduces the data sources, the reasoning behind the choices and details the steps for fuzzy modelling of plant strategies. Section 3 discusses the T-S-K modelling of plant strategies and lays out steps for differentiation. Section 4 presents locational climatic and digital elevation data, gives the algorithm by which the data is quantified and numerical data translating the algorithm. Section 5 details the implementation of the earlier presented algorithm and gives steps through which any such algorithm may be processed and culminates in the rule structure of the exemplified algorithm. Section 6 presents the node structure of the adaptive neuro-fuzzy interface and shows the efficiency of the algorithm. Lastly, conclusions are provided in Section 7.

2

Data sourcing and fuzzy partitioning

In this section, the background of data types and sources is given along with their subsequent categorisation. Biodiversity data, being the digitised data of individual plant occurrences identified to species level, was sourced from the Global Biodiversity Information Facility (GBIF, http://www.gbif.org). The total number of occurrences was then summed. Seven locations were chosen at random from Barthlott’s description of diversity zones 8–10. The zones were documented as containing more than 3,000 plant species/10,000 km2 (Barthlott et al., 2005). The data have been validated (Yesson et al., 2007) and their quality proved

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sufficient to allow analysis using fuzzy techniques in classification (Zadeh, 1965). Previous studies (Furze et al., 2011, 2012) have made use of ranges of topographical measures based on publicly available broad-scale digital elevation model (DEM) data. In the current study, topographical data (1 km resolution) was sourced from the United States Geological Survey (USGS) DEM (USGS http://www.http://eros.usgs.gov/#/ Find_Data/Products_and_Data_Available/GTOPO30), being 33 tiles with global coverage. The chosen areas were identified. Files were downloaded in compressed format. Data were extracted and processed using MATLAB (Version R2010a ©) and topographical maps were produced using the same platform. Data of climate variables (mean precipitation; mean temperature; mean ground frost frequency) at monthly intervals 1961-90 were sourced from the IPCC (http://www.ipcc-data.org) The geographical location (i.e., latitude, longitude) of the chosen area(s) was defined from the display of the DEM in step 2 above. Graphical images displaying quarterly data of 1961-90 (Mitchell and Jones, 2005; New et al., 1999) were obtained for the three required climate variables. The four images displaying the variables were processed in MATLAB in order to obtain the variables that express the image. The range of each variable was obtained from the data sources using the units of each source. These were then converted into percentage values and the percentages broken into five quintiles. The linguistic expressions, quantification and notations used to describe the data are shown in Table 1. The numerical data for each of the variables was considered in each of seven example environments. Using the maximum and minimum inference of each variable’s linguistic definition (A1,…,n), the fuzzy rule-based algorithms were constructed so that each variable was expressed in terms of the number of species (B1,…,n) of each geographic location (E1, …, E7). Mean temperature was noted as A1(1,…,n), precipitation was noted as A2(1,…,n), ground frost frequency was given as A3(1,…,n), altitude was noted as A4(1,…,n), the number of species was noted as B(1,…,n). The linguistic connections ‘IF’, ‘AND’ and ‘THEN’ were used to construct the conditional fuzzy rule base. The basic framework of the fuzzy algorithms was:

Table 1

IF A1(n) – A1(n) AND A2(n) − A2(n) AND A3(n) – A3(n) AND A4(n) – A4(n) THEN B(n) = E1, ..., E7

Expression (1) was constructed as the variables were the constituent singletons of A, and may be formed using precise structure of Zadeh (1973): A=

∫

U

(2)

μ A ( y) / y

∫ stands for the union of the fuzzy singletons (A1, A2, A3, A4), µ is the grade of membership of A (or y), (according to notation seen in Table 1).

3

Implementation of the T-S-K modelling system for differentiation of strategies using the water-energy dynamic

In order to build the fuzzy inference engine which may predict the structure of seven strategy-based environments of plant species occurrence the following steps were taken: 1

define fuzzy inference system type (Sugeno for defined output type) variable names

2

define membership functions of each variable

3

define rules, weights according to algorithm

4

examine (adaptive neuro fuzzy/Sugeno) logic structure, modify as necessary

5

test rules through data input

6

display 2D and 3D views of resultant surface in order to graphically display the algorithm (efficiency).

The modelling system may also be used as a ‘stand alone’ engine. This was carried out by saving the fuzzy inference system in MATLAB workspace and to file. The code is available from the first author.

4

Climatic and elevational modelling data and algorithmic application

In this part, climatic data is shown which underlies the algorithmic structure employed based on set theory (Zadeh, 1965).

Variable partitioning

Ling exp Low Low-medium Medium Medium-high High

% Quant/Not’n 0–20/(1) 20–40/(2) 40–60/(3) 60–80/(4) 80–100/(5)

Range MT (°C) –75 to –51 –51 to –27 –27 to –3 –3 to 21 21 to 45

(1)

2

MP (kg m )

MGFF (days)

Alt (m)

0–100 100–200 200–300 300–400 400–500

0–6 6–12 12–18 18–24 24–30

0–600 600–1,200 1,200–1,800 1,800–2,400 2,400–3,000

Notes: Ling exp = linguistic expression, Quant’ = quantification, Not’n = notation, % = percentage, MT = mean temperature, °C = degrees Celsius, MP = mean precipitation, kg m2 = kilogram per square metre, MGFF = mean ground frost frequency, Alt = altitude, m = metre.

Linking and implementation of fuzzy logic control to ordinate plant strategies Figure 1

Guyana quarterly precipitation 1961-90 mean at 10-minute (18.5 km) resolution (see online version for colours)

Figure 2

Guyana digital elevation data/topography at 30-second (1 km) resolution (see online version for colours)

Figure 1 shows example data, where Guyana mean precipitation is 0.75 (January, April, July) 0–100 kg m2 to 200–300 kg m2, and 0.25 (October) 0–100 kg m2 to 300–400 kg m2. The quantity of precipitation is shown in colours from low (dark blue) to high (dark red).

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Figure 2 is a representation of Guyana, situated between latitude 60°–55° West, longitude 0°–7.5° North with an elevation from 0–1,500 metres above sea level. Sea level is shown in blue, low elevation is in dark green and low-medium elevation in lighter green to white.

338 Figure 3

J.N. Furze et al. Fuzzy control algorithm integrating climate variables and DEM data for Guyana

IF A1(5)≤ A1(5) AND 0.75A2(1) A2(3), 0.25A2(1) A2(4) AND A3(1) IS ≤ A3(1) AND A4(1) to A4(2) THEN B(51847)=E2

Figure 3 shows the control algorithm applicable for categorisation of the example location chosen at random. The dominant strategy of individuals in this location was stress tolerating-ruderal species (E2). Numerical quantification of the algorithm is as follows: IF Variables A = • Temperature = 80–100% to 80–100% (A1(5)) • Precipitation = 0.75 × 0–100 kg m2 (A2(1)) to 200–300 kg m2 (A2(3)), 0.25 × 0–100 kg m2 (A2(1)) to 300–400 kg m2 (A2(4)) • Ground Frost frequency = 0–6 days to 0–6 days (A3(1)) • Altitude = –30–1,366 m (A4(1)) to 1,366–1,500 m (A4(2)) THEN B(51847) = E2

Temperature and ground frost frequency were not shown in this paper; however, they can be found on the IPCC web site. Example locations of environments E1, E2, E3, E5, E6, and E7 were defined using the algorithmic control structure above (as shown in Table 2). Table 2

Categorisation of environments and plant life history strategies

1 2 3 4

Plant life history strategy R S-R S-R/C-R C-R/C

5 6 7

C-S-R/C-S C-S S

Environment

Figure 4

Example location/number of individuals Mexico/51847-65535 Guyana/50700-51847 Cuba/33356-50700 Democratic Republic of the Congo/11355-33356 Georgia/8805-11355 Guinea/2203-8805 Macedonia/0-2203

5

Implementing fuzzy control algorithms to ordinate plant life history strategies

The choice of fuzzy inference system is presented here by which plant life history strategies are mathematically ordinated according to the data presented in the previous section. The above engine was applied over the input vectors temperature, precipitation, ground frost frequency and altitude and the output vector of strategy as in the control algorithm of Figure 3. Membership functions of each of the variables were defined as shown in Figure 5, making use of triangular functions to discretely define each partition. Each inferential variable membership function was defined with use of the graphical user interface within the fuzzy toolbox of MATLAB, each vector function operated together under the instruction of the root algorithm of Figure 3 which was expressed with the use of ten separately weighted rules as follows: 1

if (temperature is high) and (GFF is low) then (strategy is S-R) (1)

2

if (precipitation is low) then (strategy is S-R) (0.75)

3

if (precipitation is low-medium) then (strategy is S-R) (0.75)

4

if (precipitation is medium) then (strategy is S-R) (0.75)

5

if (precipitation is low) then (strategy is S-R) (0.25)

6

if (precipitation is low-medium) then (strategy is S-R) (0.25)

7

if (precipitation is medium) then (strategy is S-R) (0.25)

8

If (precipitation is medium-high) then (strategy is S-R) (0.25)

9

if (altitude is low) then (strategy is S-R) (1)

10 if (altitude is low-medium) then (strategy is S-R) (1).

Design of fuzzy inference engine to differentiate strategies from the water energy dynamic (see online version for colours)

Linking and implementation of fuzzy logic control to ordinate plant strategies Figure 5

Definition of membership functions (see online version for colours)

Figure 6

Node structure of the T-S-K model for differentiation of strategies (see online version for colours)

6

Adaptive neuro fuzzy interface and algorithmic efficiency

The structure of the adaptive neuro fuzzy interface for stress tolerant-ruderal plants is as shown in Figure 6. Within the node structure it follows that the input variables (A11, A2, …, An) may be stated as vectors x = [ x1 , x2 , ..., xn ] and y = [ y1 , y2 , ..., yn ]. The model was tested by inputting the data within the ranges of Figure 3 for Guyana into the engine shown in Figure 4. The resultant strategy was S-R, the 2nd of the seven possible strategies. The result was also displayed in graphical form in two-dimensional and three-dimensional formats in order to

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monitor the efficiency of the algorithm when considering different variables of the dynamic. Combinations of single factors led to incorrect strategy (z) output. It was found that combining any two variables other than precipitation and temperature resulted in the correct measurement with the 1st (x) variable, but too high a measurement with the 2nd (y) variable. The three-dimensional diagram of Figure 7 shows the maximum efficiency obtained from the algorithm. It is imperative that at least two of the driving dynamic vectors are used – both altitude and ground frost frequency show static responses. This relationship is consistent with previous work (Omizegba and Monikang, 2009) which suggests that transference of variables into vector structure

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such as that shown in Figure 3 may provide a relational index (R) which may also be determined by expert knowledge or alternatively via genetic algorithm (Zadeh, 1973). Such a relational algorithm index may be used to quantify the cooperative link between the number of individuals and climatic modelling structure in different locations, since y = [ x * R ].

7

Conclusions

The patterning of plant species presence can be broken down into the seven life-history based strategies as follows: The occurrence of a high water-energy dynamic results in the highest level of plant species diversity, reflected in the greatest numbers of plant species presence. The highest numbers of plant species presence reflect the dominance of ruderal plant species. Decreasing numbers of individuals in each of the algorithmically described environments reflect the transition through competitive to stress tolerant species, which are present in more extreme environments. Environment 1 contains ruderal plants, i.e., herbaceous and bryophyte species. These are of relatively small stature and have limited lateral spread; leaf forms show great variation and are often mesophytic; roots formed are short in length. The canopy layers of these species may be of various types. Each phase of the ruderal plants’ life cycle is short. They have a short phase of production in periods of high potential productivity. In moderate to high temperature and water availability, flowers are formed early in the life history and there is a high frequency of flowering. The proportion of production devoted to seeds is high in annual growth cycles. In response to adverse conditions for growth (e.g., presence of competitive species, resource depletion), the plants show a rapid decrease in vegetative growth and re-allocation of resources into flowering. Consequently, Figure 7

photosynthesis may be described as opportunistic: it is optimal in environments with high temperatures and water availability. The total number of individuals present in environment 1 (e.g., Mexico) is very high. Environment 2 contains plants with elements of both ruderal and stress tolerant species, i.e., herbaceous, bryophyte, shrubs and trees. Species and conditions are intermediate between environments 1 and 7; hence, the number of species is consistently high. Temperature and water availability are also high, although there is a moderate intensity of disturbance/stress shown in the example produced by variable altitudes across the location and low ground frost frequency (e.g., Guyana). Environments 3, 4, 5, and 6 contain either stress tolerant and/or ruderal species, as well as increasing numbers of competitive species (i.e., herbaceous, shrubs and trees). Competitive species have dense canopies of leaves around prominent, rapidly growing shoots. The leaf form is robust and exists in rapidly ascending monolayers. Phases of life cycle may be short or long, flexibly matching the optimal growth for the environmental conditions. Leaf production is well defined and coincides with periods of maximum potential productivity. Root length is relatively short; flowers are most often produced after periods of maximum productivity on an annual basis. A small proportion of annual production is devoted to seeds. Resource depletion is addressed by great morphogenetic redistribution of leaf and root form. Optimal conditions of photosynthesis align with periods of vegetative growth during wetter and/or warmer seasonal months. Alternative strategies are out-competed given that the environmental conditions become more suited to competitors; only the stress tolerant species survive against competitors in the extreme environments, e.g., Macedonia.

Three-dimensional surface view of control algorithm for differentiation of plant strategy environment 2 (see online version for colours)

Linking and implementation of fuzzy logic control to ordinate plant strategies Environment 7 contains stress tolerant plants, i.e., lichens, bryophytes, shrubs and trees. These show a very wide range of shoot growth forms; the leaf form is small, leathery or needle-like. The canopy formed by these species often forms many layers; however, if it develops in one layer the ascension is slow. Roots formed are long and efficient in resource capture. Each phase of growth is long, being suited to the conditions of the environment. Stress tolerant plants are often evergreen across the annual term and have variable patterns of leaf production. There is generally no relationship between flowering time and seasonal variation. These plants flower gradually over long life histories. The proportion of annual production devoted to seed production is low and individuals have low potential growth rates. Adverse conditions lead to little response in these species. Environment 7 species are suited to more severe conditions, e.g., Macedonia, which has high temperatures, low precipitation and extensive periods of stress (medium and high frequency of ground frost). The total number of individuals present in this environment is the lowest of all environments. The information rich ordering of plant strategies shows the least severe environments to contain the highest numbers of individuals (ruderal plants), moving gradually through competitive, and reaching the lowest number of individuals (stress tolerant plants) in the most severe environments. Future work based on the findings of this paper will make use of the increased application of mathematical methods. In order to detail more precisely, the characterisation of plant species in terms of finer spatial and temporal resolutions, it is proposed that categorisation is carried out further with use of field based species data and climatic/topographic data. Such work will place plant species within categories of life form, groups of metabolism, and through to various morphologies, reflected in the variation of the primary producers and their adaptive radiation (Raunkier, 1934; Silvera et al., 2009). It is believed that this will significantly enhance the modelling of available climatic scenarios and will provide valuable understanding of diversity patterns of local and national importance under ongoing changing climate. Preserving the relationship between plant species presence and climatic and topographic variability requires the application of cooperatively controlled multi-agent systems (Yang and Zhao, 2012). The use of a fuzzy-logic rule base is considered to be especially appropriate with respect to species presence, as numbers of the latter involve mathematical dispersion based on the values of singletons with fuzzy relations (water, energy and topographic dynamics). Further elaboration will be carried out in future work in order to facilitate fuzzy consequential categorisation of plant species in terms of life-form and metabolic patterning. The use of generational algorithms is envisaged to be a method of great potential in biological systems research (Gao et al., 2012; Omizegba and Monikang, 2009; Zadeh, 1973).

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