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Pubblicazione N°9
 
 

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Pubblicazione N° 9

 

THE MANAGEMENT OF POPULATIONS IN HIERARCHICALLY ORGANIZED SYSTEMS. 

Atti delle II Giornate di Studio su 'Metodi Numerici, Statistici e Informatici nella Difesa delle Colture Agrarie e delle Foreste: Ricerca e Applicazioni' - Pisa, Scuola Superiore Sant'Anna, Maggio 2002.

JOHANN BAUMGÄRTNER(1), GIANNI GILIOLI(2), DAVID SCHNEIDER(3) AND MAURIZIO SEVERINI(4)

1 International Centre of Insect Physiology and Ecology (ICIPE), Nairobi, Kenya
2 Dipartimento di Agrochimica e Agrobiologia, Universitā di Reggio di Calabria,
Gallina di Reggio di Calabria, Italy
3 Memorial University of Newfoundland, St. John's, Newfoundland, Canada
4 Istituto di Scienze dell'Atmosfera e del Clima (ISAC-CNR). Sezione di Roma. Area di Ricerca 'Tor Vergata', Via del Fosso del Cavaliere, 100. I-00133 Roma.

ABSTRACT

Ecological research on populations, communities and ecosystems is guided, among others, by principles originating from social sciences including economics, informatics, biochemistry and biophysics. In our work, however, we primarily rely on biophysical approaches and use mathematics to formalize a coherent and concise framework for the analysis of structure and function of ecological systems as well as for the design of management schemes. 
Hierarchy refers to discrete levels in organized systems, whereas scale denotes the spatial or temporal dimension of an object or process characterized by both grain and extent. Examples of scale-dependencies in time, space and biomass dimensions are presented. In general, scaling dependencies are not considered in population model development. Population ecologists should also be aware that measurements are taken in observational windows of time, space and biomass, and conclusions are specific to these windows.


LA GESTIONE DELLE POPOLAZIONI IN SISTEMI ORGANIZZATI GERARCHICAMENTE

RIASSUNTO

La ricerca ecologica su popolazioni, comunitā ed ecosistemi č guidata, tra gli altri, da principi tratti dalle scienze sociali, dall'economia, dall'informatica, dalla biochimica e dalla biofisica. Nel nostro lavoro noi ci basiamo soprattutto su approcci biofisici ed usiamo la matematica per formalizzare una base coerente e concisa per l'analisi della struttura e della funzione dei sistemi ecologici cosė come per il progetto di schemi di gestione. 
La gerarchia si riferisce a livelli discreti in sistemi organizzati, mentre la scala denota la dimensione spaziale o temporale di un oggetto o processo ed č caratterizzata sia dalla risoluzione che dall'estensione. Vengono presentati esempi di dipendenza dalla scala nelle dimensioni di tempo, spazio e biomassa. Generalmente, la dipendenza dalla scala non viene considerata nello sviluppo dei modelli di popolazione. Gli ecologi delle popolazioni debbono anche avere la coscienza che le misure sono prese all'interno di 'finestre' di tempo, spazio e biomassa e che le conclusioni sono specifiche per queste finestre. 

INTRODUCTION

Ecology is a branch of science concerned with the interrelationships of organisms and their environment and relies on principles derived from many different disciplines. In our work, biophysical elements related to matter and energy applied to biological systems are very important (CURRY & FELDMAN, 1987; GUTIERREZ, 1996; JØRGENSEN, 2001). Mathematics provides a coherent and concise framework for the analysis of structure and function of ecological systems as well as for the design of management schemes. Biochemistry deals with the composition, properties and transformation of substances relevant to biological systems. Of interest to us are not the substances but their effects on organism behaviour and physiology including nutritional influences on population development . For example, the demand for energy depends on the ratio of nitrogen supply to demand (WERMELINGER et al., 1991). This is a substantial aspect in resource-based functions used for representing population interactions (GUTIERREZ, 1996). The combination of biophysical and biochemical elements has been referred to as physiological based approach to populations system study (GUTIERREZ & BAUMGÄRTNER, 2002). Informatics deals with the collection, storage, retrieval and dissemination of recorded knowledge and has found wide applications in information dissemination (XIA & BAUMGÄRTNER, 1999), had a profound influence on ecological concepts and methods of ecological investigations. Moreover, it is an important tool for the analyses of biological systems at the cellular level (KITANO, 2002), However, in our work, we are primarily interested in information dissemination technologies (XIA & BAUMGÄRTNER, 1999; BAUMGÄRTNER et al., 2002). 

Human ecology deals with human communities and populations as concerned with the preservation of environmental qualities. Of interest to us is the valuation of ecological system performance in the framework of ecosystem services that are conditions and processes through which natural ecosystems sustain and fulfill human life (DAILY, 1997). Sociology is the systematic study of the development, structure, interaction, and collective behavior of organized groups of human beings. It is the basis for hierarchy theory with a profound influence on ecology (AHL & ALLEN, 1996) and the provision of a framework for our research activities. In a hierarchical organization, discrete levels emerge as a result of the interaction between the observer and the part of the universe observed (ALLAN & HOEKSTRA, 1992). When striving for management schemes of sustainable ecological systems, we agree with GOODLAND (1995) who linked environmental and social sustainability to economic sustainability but considered environmental sustainability as a basis for social sustainability (BAUMGÄRTNER et al., 2002). Environmental sustainability is achieved by holding the scale of the human economic system within the biophysical limits of the ecosystem.

This is a brief overview on hierarchy and scale theory elements with particular reference to population study as well as management with references to the relevant modern literature (e.g. GARDNER et al., 2001). LEVIN (1992) stated that problems of patterns and scale are the central problem in ecology, unifying population biology and ecosystem science, and marrying basic and applied ecology. When presenting examples, we primarily rely on our work because of familiarity with both objectives and explicit as well as implicit assumptions of relevance to methodology selection. The selection of case studies, however, does not imply comparisons and evaluations of population models constructed and implemented by different researchers or research teams. The work focus on populations, but their place within the biological system of individuals, cohorts, communities and ecosystems (Fig. 1) as well as the implications for study and management are recognized. Populations studies are based on methods outlined by GILBERT et al. (1976), CURRY & FELDMAN (1987), SEVERINI et al. (1990, 1996), GUTIERREZ (1996), DI COLA et al. (1998, 1999) and GUTIERREZ & BAUMGÄRTNER (2002), while population control is sought by means of Integrated Pest Management (IPM) systems (FLINT & VAN DEN BOSCH, 1981; KOGAN, 1998; KOGAN et al., 1999, BAUMGÄRTNER et al., 2002).

HIERARCHY THEORY IN POPULATION ECOLOGY

Brief hierarchy theory review

The hierarchical organization of nature has been referred to as a basic presumption in modern ecology (NAVEH & LIEBERMAN, 1984). Hierarchically organized systems have levels that are distinguished by rates that differ by one or more orders of magnitude (O'NEILL & KING, 1989). Hence, in order to describe adequately a complex system several levels should be addressed simultaneously (AHL & ALLAN, 1996). Levels are a system characteristic that depends on the system's internal structure and complexity. This feature emerges from observation (AHL & ALLAN, 1996), or in ALLAN & HOEKSTRA's (1992) words, results from the interaction between decisions of the observer and the part of the universe observed. Thus, hierarchy theory is also a theory on the observer's role in any formal study of complex systems (ALLAN & STARR, 1982, ULANOWICS, 1997, O'NEILL & KING, 1998, ULANOWICS, 2000) and takes into account the problem of aggregation errors by identifying levels of nested systems within larger systems (SCHNEIDER, 1994). Hence, the passage from a level to a succeeding one is not a simple aggregation of subsystems (AGENO, 1994). Hierarchical organization means that higher level processes can steer and constrain lower level processes, while, at the same time, high level features might emerge from low level dynamics (ANONYM, 2001). At each level of organization phenomena exist that requires new laws and principles, that cannot be predicted just from those at more fundamental levels (WILSON, 1998).

There are two principal ways to characterize a hierarchical system. At any pre-defined levels of organization, elements that bear a certain set of common structural and/or process features may be treated as functional groups (KÖRNER, 1993). Alternatively, levels of organizations are occupied by entities, and those entities are responsible for the characteristics of the level in question (ALLAN & HOEKSTRA, 1992). Accordingly, populations can be considered as entities or functional groups that operate within hierarchically organized biological, spatial, temporal and organizational systems (Fig. 1). 

Fig. 1 The hierarchical organization of ecological and decision-making systems of relevance to population study and integrated management. 

As an aside, several levels of explanation may similarly be required for an abstract system (AHL & ALLEN, 1996). In population ecology, we may seek a deep level of understanding as obtained by thermodynamics principles (CURRY & FELDMAN, 1987; JØRGENSEN, 2001) or statistical relationship may provide an adequate understanding (BAUMGÄRTNER & GUTIERREZ, 1989). 

Applications

Hierarchically organized systems can easily be recognized in Integrated Pest Management (IPM) research and implementation work (CONWAY, 1984; KOGAN, 1998; KOGAN et al., 1999; BAUMGÄRTNER et al. 2002; Fig. 2). The organizational structure of the systems, resulting from human activities (BAUMGÄRTNER & SCHNEIDER, 2001), may be represented by fields, farms, communities and regions well as decision making levels are represented by farmers, extensionists, administrators and policy makers (Fig. 2). The subject of this work is population study and management. Nevertheless, IPM should not be restricted to a population but consider communities and ecosystem levels as well (Fig. 2). 

Fig. 2 The hierarchical organization of systems relevant to Integrated Pest Management (IPM) as identified by Conway (1984), Kogan (1999), Kogan et al., 1999) and Baumgärtner et al. (2002). The roman numbers refer to different integration categories.




In the next sections, we disregard IPM scheme implementation and focus on demographic models as the appropriate instrument to study population dynamics at predefined hierarchical levels. In general, a population is pragmatically defined as a collection of individuals of the same species occupying a spatial interval. When seeking a mechanistic representation of population development, the VON FÖRSTER (1959) model and its discretized and stochastic variants (SEVERINI et al., 1990, 1996; DI COLA et al., 1998, 1999), accounting for time varying population age-structures, are often appropriate

[1a]

with the boundary condition

[1b]

where N(t,a) = population density, t = time, a = age, m(t,a) = specificmortality rate, l(t,a) = specific fecundity rate.

For poikilothermic organisms, chronological age should be replaced by physiological age, and aging is expressed by a temperature-dependent rate function r(.) 

[2] 

At the organizational levels of fields and farms, eqs. 1a, 1b have been used to model the dynamics of thrips and ticks (TAMŌ & BAUMGÄRTNER, 1993; TAMŌ et al. 1993; MWAMBI et al., 2000a,b). These models represent the temporal dynamics of arthropod populations and have been developed for strategic and policy purposes (CONWAY, 1984).

In many cases, the consideration of population changes relative to biomass is required. This is done by the modified SINKO-STREIFER (1967) model and its discrete and stochastic variants (GUTIERREZ, 1996; DI COLA et al. 1998, 1999) 

[3a]with boundary conditions

[3b]

where = rate of development, wo = initial biomass of the newly born individuals (note that in this model the initial weight is the same for all individuals), g = growth rate with reference to the biomass and w = biomass and other variables defined above. In the case of poikilothermic organisms, the rate of development is expressed as a function of temperature GILBERT et al., 1976).

At the organizational level of a field, eqs. 3a,b have been used to model the dynamics of maize crop yield formation (BONATO et al., 1999), of cassava including the crop and an arthropod community (GUTIERREZ et al., 1988), and of other systems (GUTIERREZ & BAUMGÄRTNER, 2002). The models have been developed for research and population management purposes including for demonstrating the impact of classical biological control to policy makers and administrators.



Some limitations

The population models discussed so far operate at the predefined hierarchical level of the field, and little attempt has apparently been made so far to develop multi-level approaches according to hierarchy theory (AHL & ALLAN, 1996). Moreover, the consideration of ecological processes, such as reproduction, in the definition of populations (ALLAN & HOEKSTRA, 1992) might improve the understanding of population dynamics and lead to new management strategies.

Hierarchy theory was adopted by ecologists because of familiarity with phenomena segregated into discrete levels and the belief they could be named a priori, and interactions would occur at specific levels only (O'NEILL & KING, 1998). However, we agree with O'NEILL & KING (1998) who state that in general, levels of explanation must be extracted from data, not pre-imposed. They added that to date, empirical evidence shows that the levels extracted from data do correspond in any simple way to traditional levels of biological organization. For example, the population is assigned to a lower level than the ecosystem (Fig. 1). However, the foraging strategy of large herbivores depends on moving across spatial scales usually identified with ecosystems. If levels in hierarchy are distinguished by rates that differ by one or more orders of magnitude, O'NEILL & KING (1998) can easily cite additional examples of ambiguity. 

Probably, the use of pre-imposed levels is valid and useful for man-made ecological and socio-economic systems such as the levels of fields, farms, social communities and decision-making bodies (BAUMGÄRTNER & SCHNEIDER, 2001). Nevertheless, the identity of at least some levels might require verification by data analysis, while other levels should be obtained from data (O'NEILL & KING, 1998) or might be derived from thermodynamics theory (JØRGENSEN , 2001). WIENS (1989, 2001) for example, expects that there are discontinuities in trajectories from small to large spatial scales (see below). These discontinuities and plateaus (Fig. 3) may reveal hierarchical levels and the boundaries separating them (WIENS, 1989, 2001; KEMP et al. (2001). This provides a link between hierarchy and scale theories.

Fig. 3 Conceptual relationship between scale of observation and ecological variance, including scale grain (a) and scale extent (b) influences. Dashed lines indicate discontinuities in the trajectory from small to large scales. With kind permissions from editors and authors, this figure has been reproduced from Kemp et al. (2001), who adapted it from Wiens (1989).

SCALE THEORY AND POPULATION ECOLOGY

Brief scale theory review

The spatio-temporal framework for the explanation of natural phenomena can be traced back to the philosopher Kant (HONDRICH, 1995). In population ecology, numbers and biomass have long been treated as state variables in models on spatio-temporal dynamics. Disregarding the spatial dimension, this is exemplified by the aforementioned von FÖRSTER (1959) model and its variants. To our knowledge, the biomass dimension has been added to the time and space dimension in the recent past only (SCHNEIDER, 1994). The widely used SINKO & STREIFER (1967) model and its variants disregard spatial processes but consider changes in population densities in both time and biomass dimensions (DI COLA et al., 1998, 1999). 

BARENBLATT (1996) states that physical laws do not depend on an arbitrarily chosen basic unit of measurement, such as the ones taken here in the time, space and biomass dimension. He draws a simple conclusion from this observation: the functions that express physical laws must possess a certain fundamental property, which in mathematics is called generalized homogeneity or symmetry. 

TURNER & GARDNER (1991) define scale as the spatial or temporal dimension of an object or process characterized by both grain and extent. Grain is the spatial and temporal resolution chosen to analyze a given data set, whereas extent is the size of the study and the total duration over which measurements are made. To the commonly used space and time dimensions SCHNEIDER (1994) adds the biomass dimension. Accordingly, the concept of scale is different from the aforementioned concept of hierarchy; scale is recorded as a quantity and involves (or at least implies) measurements and measurement units (O'NEILL & KING, 1998).
Scale dependent patterns can be defined as a change in some measure of patterns with a change in either the resolution (grain) or the range (extent) of measurement (WIENS, 1989, 2001). For both observation and experimentation, a particular property is said to be scale dependent if the magnitude (or variability) of that property changes with a change in either the grain or the extent of the measurement (SCHNEIDER 1994).
Specifically, a quantity Q may scale with another measured quantity Y (e.g. area, duration, mass) as follows 

[4a]

Hence         [4b]

The exponent of these power laws can sometimes be obtained by dimensional analysis. In ecology, power laws are typically obtained empirically, by regressing the logarithm of Q against the logarithm of Y. Examples of power law scaling in ecology include body size allometry (Y= mass), species area curves (Y = area), and Taylor's Power Law (TAYLOR, 1961)(Y = mean density) and are presented below.
Scale theory applications

Rather than hierarchical levels, we consider spatial as measurable quantities in the spatial dimension and explore the dynamics of populations in the spatio-temporal dimension. It is often assumed that natural or man-made pest population control occurs at a particular local scale such as a mosquito breeding site (FOUQUE & BAUMGÄRTNER, 1996). This is the case in weed, but not necessarily in arthropod control (FIRBANK, 1993). For example, AEBISCHER (1991) found that many arthropods showed few differences between fields and farms and seemed to respond to large scale factors. Nevertheless, many population models such as the one for cowpea infesting thrips (TAMŌ & BAUMGÄRTNER, 1993; TAMŌ et al. 1993) and cassava infesting mealybugs (GUTIERREZ et al., 1988) have been developed for a micro or local scale. Ticks are moving at a micro-scale, but their occurrence depends on the movement of their mammal hosts and hence, control operations should be undertaken at a larger scale (MWAMBI et al., 2000a, 2000b). Highly mobile tsetse fly populations are operating over large geographical areas and herd- or farm-specific control operations are less efficient than measures undertaken at a meso-scale (SAINI et al., 1999; ODULAJA et al., 2001). The African Bollworm Helicoverpa armigera (HÜBNER) is a pest in fields of vegetables and cotton. Field-specific control systems such as the inundative releases of virus and egg parasitoids are combined with naturally occurring control. However, population movement occurs over waste geographical areas requiring wide scale extents to be considered in population study and management. Pest control methods have been developed for farms (placement of crops in space and time), for communities (autodissemination of pathogens) as well as for regional (or meso) scales (pest prediction and early warning systems). For this purpose, a multi-scale control system has been proposed (SITHANANTHAM et al., 2001). Such a system may also be required for study and management of Plum Moth Cydia funebrana TR. populations (SCIARRETTA et al., 2001) as well as for many other pests. In these examples, reference has been implicitly or explicitly made to scale, but little attempt has been made to consider scale dependencies in model development. 
In population ecology, scale dependent patterns can be identified in the spatial, temporal and, according to Schneider (1994), biomass dimension. Here, we examine some scale dependencies and draw some conclusions regarding the relationship between measurements, population dynamics and management.
Spatial dimension. In a homogeneous habitat, the sample variance d2 can be related to the mean u according to Taylor's power law (TAYLOR, 1961) that can be derived empirically from sample data or analytically from models on population movements (SAWYER, 1989) 

. [5]

A single b describes a consistent relationship between sample variance and sample means over a range of densities, on a spatial scale related to the size of the sample unit (SAWYER, 1989). KENDAL (1995) derived eq. 5 from diffusion-limited aggregation and discovered therein an inherent symmetry 

. [6]

That is, for obtaining the variance d2 of quadrat size q, the variance for a unit size quadrate is scaled up by a facto fb when the quadrate size is increased by the factor f. KENDAL (1995) also observed that the exponent b can be interpreted as a fractal dimension and hence, showed the link between scaling and fractal geometry (see GARDNER, 1998). In conclusion, different sample unit sizes detect different spatial distributions. The grain effect is important in demographic studies and has implications in population management strategies. The effect of extent on the other hand, was studied by SAWYER AND HAYNES (1978). They observed that the parameter a of eq. 5 was extent-dependent, but recognized the need to validate the inherent assumption of density invariant distribution within the strata. KEMP et al. (2001) refer to WIENS (1989, 2001) when discussing the effect of both grain and extent to spatial distributions (Fig. 3). 

Temporal dimension. Scale grain appears as time step length in simulation models, but detailed considerations go beyond the scope of this paper. For example, FIRBANK (1993) cites a study on the temporal coincidence of weed-crop interactions, where a scale of more than 12 hours affects yield predictions. Moreover, spectral analyses the measure of association between measurements taken through time depends on the grain of scale used (SCHNEIDER, 1994). WIENS (1989) describes scale extent influence as represented in Fig. 3 (KEMP et al., 2001).

Mass dimension. Respiration rates are related to body weight m according to

[7]

that is, to obtain the respiration rate z of body weight m, the respiration rate for a unit mass z(1) organism is scaled up by a factor mc. The scaling relationship between the breathing rate of animals and their mass reflects the fractality of respiratory organs (BARENBLATT, 1996). In a narrow range of arthropod body mass, biomass consumption rates may be approximately proportional to biomass (GUTIERREZ, 1996). For a wider range, however, scaling functions may be required for both respiration and consumption rates. This is important in the development of resource-based functional and numerical response models for representing population interactions (GUTIERREZ, 1996; GUTIERREZ & BAUMGÄRTNER, 2002).

Spatio-temporal dimensions. In ecological processes there is a connection between temporal and spatial scales (O'NEILL & KING, 1998; SCHNEIDER, 1998). SCHNEIDER et al. (1999) and SCHNEIDER (2001) analysed scaling effects in

. [8]
where a = birth rate, d = death rate and F = net movement rate

They relied on dimensional analyses and studied scaling effects on movement and death processes. For the case of a bivalve under study, they concluded that the changes in density are controlled by movement at low spatio-temporal scales, while mortality becomes the predominant factor at high spatio-temporal scales (Fig. 4). 


CONCLUDING REMARKS

According to hierarchy theory, populations as subjects of study and management are placed in a system comprising individual, cohort, community and ecosystem levels (Fig. 1). Moreover, organizational systems provide additional levels for study and management (Fig. 1). When relying on hierarchy theory, population studies and IPM schemes might benefit from approaches in that the levels are simultaneously addressed and receive more attention than until now.

The population can be defined as a collection of individuals belonging to the same species. However, the definition says nothing about the time frame over which populations might exist, and nothing about the spatial coherence of the population on the landscape (ALLAN & HOEKSTRA, 1992). In the aforementioned examples, the appropriate levels were identified according to pragmatic criteria. For example, the populations were studied as collections of individuals inhabiting specified habitats, fields, farms or regions. However, if populations are delimited in space and time by coherent internal processes (AGENO, 1994),

Fig. 4 Biological effects of spatial and temporal scales. Scales where mortality prevails over lateral movement and where lateral movement prevails over mortality for adult stages of the bivalve Macoma liliana, indicated by dashed lines. Solid lines have been obtained by Monte Carlo simulation methods (Schneider et al., 1999; Schneider, 2001). With kind permissions from editors and authors, this figure has been reproduced from Schneider (2001) in the book edited by Gardner et al. (2001).

or in ALLAN & HOEKSTRA's (1992) words, if spatially aggregated and historically defined populations are seen as arising from ecological processes such as reproduction, than spatially aggregated and historically defined populations may arise . The study of so defined populations may provide new insight into the dynamics and open new possibilities for management.
From a theoretical standpoint, in most of the population models under consideration, scale dependencies remain to be investigated. From a practical and theoretical standpoint, population ecologists should be aware that measurements are taken in observational windows of time, space and biomass and that conclusions are specific to these windows.

Scaling theory suggest that hierarchical levels occur at distinct breaks in the scale continuum (Fig. 3), i.e. that levels can be recognized by discontinuities (O'NEILL & KING, 1989; KEMP et al., 2001; WIENS, 1989, 2001). This provides a link between hierarchy and scale theories and might open a way to derive hierarchical levels from field data. If possible, the application of hierarchy theory in ecology would be strengthened. Very likely, the combination of hierarchy theory and scale theory elements will profoundly influence the methodology in population ecology, provide new insights in population systems and result to new management solutions.
REFERENCES

AEBISCHER N.J., 1991 - Twenty years of monitoring invertebrates and weeds in cereal fields of Sussex. Pp: 305-331. In FIRBANK L.G., CARTER N., DARBYSHIRE J.F. & G.R. POTTS (eds.), The Ecology of Temperate Cereal Fields. Blackwell Scientific Publications, Oxford 241 p. 
AGENO M., 1994 - Che cos'č la vita ? In occasione del cinquantenario di What is Life ? di Erwin Schrödinger. Lombardo Editore, Rome, 159 p.. 
AHL V. & ALLAN, T.F.H., 1996 - Hierarchy Theory. Columbia University Press, New York, 206 p..
ALLAN T.F.H. & T. HOEKSTRA, 1992 - Toward a Unified Ecology. Columbia University Press, New York, 384 p.
ALLEN T.F.H. & T.B. STARR, 1982 - Hierarchy. University of Chicago Press, Chicago, 310 p. .
ANONYM, 2001- The CLUE project. Spatially explicit modelling of the multi-scale dynamics of land use. Land use and Land Cover Change (LUCC) Newsletters No. 6: 25-26.
BARENBLATT G.I., 1996 - Scaling, Self-similarity, and Intermediate Asymptotics. Cambridge University Press, Cambridge, 386 p.
BAUMGÄRTNER J. & A.P. GUTIERREZ, 1989 - Simulation techniques applied to crops and pest models. Pp. 175-214. In CAVALLORO R. & V. DELUCCHI (eds.), Parasitis 88. Proceedings of a Scientific Congress, Barcelona, October 25-28. Boletėn de Sanidad Vegetal, fuera de serie, 17, 549 p.
BAUMGÄRTNER J. & D.C. SCHNEIDER, 2001 - Scale and Hierarchy in Integrated Pest Management. Encyclopaedia of Entomology (submitted 2001).
BAUMGÄRTNER J., SEVERINI M. & M. TAMŌ, 1991 - Modelli matematici demografici per la fenologia e l'interazione fra specie nella gestione di sistemi agricoli. Pp. 19-40. Atti del convegno 'modelli euristici e operativi per la difesa integarta in agricoltura. Caserta, 27-29 Settembre 1990. Edizione curata da Cittā Studi scrl., Milano.
BAUMGÄRTNER J., XIA Y. & F. SCHULTHESS, 2002 - Integrated arthropod pest management systems for human health improvement in Africa. Insect Science & its Application (submitted 2002).
BONATO O., SCHULTHESS F. & J. BAUMGÄRTNER, 1999 - Simulation model for maize crop growth based on acquisition and allocation functions for carbohydrate and nitrogen. Ecological Modelling 124: 13-28.
CONWAY G.R., 1984 - Introduction. Pp. 1-11. In CONWAY G. (ed.), Pest and Pathogen Control. Strategic, Tactical and Policy models. Wiley, New York, 488 p.
CURRY G.L. & R.M. FELDMAN, 1987 - Mathematical Foundations of Population Dynamics. Texas A&M University Press, College Station, 246 p.
DAILY G.C. (ed.). 1997 - Nature's Services. Societal Dependence on Natural Ecosystems. Island Press, Washington, 392 p.
DI COLA G., GILIOLI G. & J. BAUMGÄRTNER, 1998 - Mathematical models for age-structured population dynamics: An overview. Pp. 45-61. In BAUMGÄRTNER J., BRANDMAYR P.& B. F. J. MANLY (eds.), Population and Community Ecology for Insect Management and Conservation. Balkema Publishers, Rotterdam, 253 p.
DI COLA G., GILIOLI G. & J. BAUMGÄRTNER, 1999 - Mathematical models for age-structured population dynamics. Pp. 503-536 In HUFFAKER, C. B. & A. P. GUTIERREZ (eds.), Ecological Entomology, 2nd edition. Wiley, New York, 756 p.
FIRBANK L.G., 1993 - Implications of scale on the ecology and management of weeds. Pp. 91-104. In: Landscape Ecology and Ecosystems. In BUNCE R.G.H, RYSKOWSKI L.& M. G. PAOLETTI (eds), Landscape Ecology and Ecosystems. CRC Press, Boca Raton, 241 p.
FLINT M.L. & R. VAN DEN BOSCH, 1981 - Introduction to Integrated Pest Management. Plenum Press, New York, 240 p. 
FOUQUE F. & J. BAUMGÄRTNER, 1996 - Simulating development and survival of Aedes vexans (Diptera: Culicidae) praeimaginal stages under field conditions. J. Med. Entomol. 33: 32-38.
GARDNER R.H., 1998 - Pattern, process and the analysis of spatial scales. Pp. 17-34. In PETERSEN D.L. & V. T. PARKER (eds.), Ecological Scale: Theory and Applications. Columbia University Press, New York, 615 p.
GARDNER R.H., KEMP W.M., KENNEDY V.S. & J.E. PETERSEN (eds.), 2001 - Scaling Relations in Experimental Ecology. Complexity in Ecological Systems. Columbia University Press , New York, 373 p.
GILBERT N.A. GUTIERREZ A.P., FRAZER B.D. & R.E. JONES, 1976. - Ecological Relationships. Freeman, San Francisco, 148 p.
GOODLAND R., 1995 - The concept of environmental sustainability. Annual Review of Ecology and Systematics 26:1-24.
GUTIERREZ A.P., 1996 - Applied Population Ecology: A Supply-Demand Approach. Wiley, New York, 300 p.
GUTIERREZ A.P. & J. BAUMGÄRTNER, 2002 - Modeling the dynamics of tritrophic interactions. (in prep).
GUTIERREZ A.P., WERMELINGER B, SCHULTHESS F., BAUMGÄRTNER J., YANINEK J.S.. HERREN H.R.. NEUENSCHWANDER P., LÖHR B., HAMMOND W.N.O. & C.K. ELLIS, 1988 - An overview of a systems model of cassava and cassava pests in Africa. Insect Science & its Application 8: 919-924.
HONDRICH T., 1995 - The Oxford Companion to Philosopy. Oxford University Press, Oxford, 1009 p.
JØRGENSEN S.E., 2001 (ed.) - Thermodynamics and Ecological Modelling. Lewis Publishers, Boca Raton, 373 p.
KEMP W.M., PETERSEN J.E. & R.H. GARDNER, 2001 - Scale-dependence and the problem of extrapolation: implications for experimental and natural coastal ecosystems. Pp. 3:47. In GARDNER R.H., KEMP W.M., KENNEDY V. S. & J.E. PETERSEN (eds.), Scaling Relations in Experimental Ecology. Columbia University Press, New York, 373 p.
KENDAL W.S., 1995 - A probabilistic model for the variance to mean power law in ecology. Ecological Modelling 80: 293-297.
KITANO H., 2002 - Systems biology: a brief review. Science, 295: 1662-1664.
KOGAN M., .1998 - Integrated pest management: Historical perspectives and contemporary development. Annual Review of Entomology 43: 243-270.
KOGAN M. CROFT B.A. & R.F. SUTHERST, 1999 - Applications of Ecology for Integrated Pest Management. Chapter 20, pp. 681- 736. In HUFFAKER C.B. & A.P. GUTIERREZ (eds.), Ecological Entomology, 2nd ed. Wiley, New York, 756 p.
KÖRNER Ch., 1993 - Scaling from species to vegetation; the usefulness of functional groups. Pp. 118-137. In SCHULZE E. D. & H.A. MOONEY (eds.), Biodiversity and Ecosystem Function. Ecological Studies, Vol. 99. Springer-Verlag, Berlin, 525 p.
LEVIN S.A., 1992 - Multiple scales and the maintenance of biodiversity. Ecosystems 3: 498-506.
MWAMBI H.G., BAUMGÄRTNER J. & K.P. HADELER, 2000a.- Ticks and tick-borne diseases: a vector-host interaction model for the brown ear tick (Rhipicephalus appendiculatus). Statistical Methods in Medical Research 9: 279-301.
MWAMBI H.G., BAUMGÄRTNER J. & K.P. HADELER, 2000b - Development of a stage-structured analytical population model for strategic decision making: the case of ticks and tick-borne diseases. Rivista Matematica della Universitā di Parma 3: 157-169.
NAVEH Z. & A. LIEBERMAN, 1984 - Landscape Ecology. Theory and Praxis. 2nd edition. Springer, New York, 356 p.
ODULAJA A., BAUMGÄRTNER J., MIHOK S., & I. ABU-ZINID, 2001 - Geostatistical analysis of tsetse fly (Diptera: Glossinidae) catch distribution and spread at Nguruman, southwestern Kenya. Bull. Ent. Res.91: 213-220.
O'NEILL R.V. & A. W. KING, 1998 - Homage to St. Michael; or why are there so many books on scale ? Pp. 3-15. In PETERSON D.L. & V. T. PARKER (eds.), Ecological Scale: Theory and Applications. Columbia University Press, New York.
SAINI R.K, NG'ENY-MENGECH A. & J. OGENDO, 1999b - Fighting Africa's deadly fly - new ecofriendly solutions for tsetse management. Accomplishments of the European Union-funded project on interactive development and application of sustainable tsetse management technologies for agropastoral communities in Africa. International Centre of Insect Physiology and Ecology (ICIPE), Nairobi, Keyna.
SAWYER A.J., 1989 - Inconstancy of Taylor's b: simulated sampling with different quadrat sizes and spatial distributions. Res. Popul. Ecol. 31: 11-24.
SAWYER A.J.& D.L. HAYNES, 1978 - Allocating limited sampling resources for estimating regional populations of overwintering cereal leaf beetles. Environmental Entomology 7: 63-66
SCHIARRETTA A., TREMATERRA P. & BAUMGÄRTNER J, 2001 - Geostatistical analysis of Plum Moth Cydia funebrana (Treitschke) (Lepidoptera, Tortricidae) pheromone trap catches at two spatial scales. American Entomologist 47: 174-184.
SCHNEIDER D.C., 1994 - Quantitative Ecology, Spatial and Temporal Scaling. Academic Press, San Diego, 395 p.
SCHNEIDER D.C., 1998- Applied scaling theory. Pp. 253-269. In: PETERSON, D.L. & PARKER, V.T. (eds.), Ecological Scale: Theory and Applications. Columbia University Press, New York
SCHNEIDER D.C., 2001- Spatial allometry. Theory and application to experimental and natural aquatic ecosystems. Pp. 113:148. In GARDNER R.H. KEMP W.M., KENNEDY V.S. & J.E. PETERSEN (eds.). Scaling Relations in Experimental Ecology. Columbia University Press, New York.
SCHNEIDER D.C., BULT T., GREGORY R.S., METVEN D.A., INGS D.W. & V. GOTCEITAS, 1999- Mortality, movement, and body size: critical scales for Atlantic cod (Gadus morha) in the Northwest Atlantic. Can. J. Fish. Aquat. Sci. 56 (Suppl. 1): 180-187.
SEVERINI M., BAUMGÄRTNER J., SEIFERT M. & M. RICCI, 1996 - The analysis of poikilothermic development by means of time distributed delay models. Proc. Intern. Workshop 'Computer Science and Mathematical Methods in Plant Protection', Parma, November 7-9, 1990. DI COLA G. & GILIOLI, G. (eds.). Quaderni del Dipartimento di Matematica, Universitā di Parma, 135: 159-176. 
SEVERINI M., BAUMGÄRTNER J. & M. RICCI, 1990 - Theory and practice of parameter estimation of distributed delay models for insect and plant phenologies. Pp. 674-719. In GUZZI R., NAVARRA A. & SHUKLA J. (eds), Physical Climatology and Meteorology for Environmental Application. World Scientific Publishing, Singapore, 809 p.
SINKO J.W. & W. STREIFER, 1967 - A new model for age-structure of a population. Ecology 48: 910-918.
SITHANANTHAM S., BAUMGÄRTNER J., MINJA E., MANJANIA N., OSIR E., LÖHR B, & SENESHAW A., 2001 - Evolving an ecosystem approach for sustainable management of African Bollworm: vision for strategies and partnership in Africa. Proceedings 14th African Association of Insect Scientists and the 9th Crop Protection Society of Ethiopia Joint Conference, Addis Ababa, Ethiopia, June 4 to 8, 2001.
TAMŌ M. & J. BAUMGÄRTNER, 1993 - Analysis of the cowpea agro-ecosystem in West Africa. I. A demographic model for carbon acquisition and allocation in cowpea Vigna unguiculata (L.) Walp. Ecological Modelling 65: 95-121.
TAMŌ M., BAUMGÄRTNER J.& A.P. GUTIERREZ, 1993 - Analysis of the cowpea agro-ecosystem in West Africa. II. Modelling the interactions between cowpea and the bean flower thrips Megalurothrips sjostedti (Trybom) (Thysanoptera, Thripidae). Ecological Modelling 70: 89-113.
TAYLOR, L.R., 1961 - Aggregation, variance and the mean. Nature 189: 732.
TURNER M. G. & R. H. GARDNER, 1991 - Quantitative methods in landscape ecology: an introduction. Pp. 4-14. In TURNER M.G. & R.H. GARDNER (eds.), Quantitative Methods in Landscape Ecology. Springer, New York, 536 p.
ULANOWICZ R.E., 1997 - Ecology, the Ascendent Perspective. Complexity in Ecological Systems Series. Columbia University Press, New York, 201 p.
ULANOWICZ R.E., 2000. Ontic closures and the hierarchy of scale. Pp. 266-271. In CHANDLER, J.L.R. & VAN DE VIJER, G (eds.), Closure, Emergent Organizations and Their Dynamics (.), Annals of the New York Academy of Sciences, Vol. 901, New York.
VON FÖRSTER H., 1959. Some remarks on changing populations. Pp. 387-407. In: The Kinetics of Cellular Proliferation (F. STOHLMAN, Jr., ed.). Grune & Stratton, New York.
WERMELINGER B., BAUMGÄRTNER J. & A.P. GUTIERREZ, 1991. A demographic model of assimilation and allocation of carbon and nitrogen in grapevines. Ecological Modelling 53: 1:26.
WIENS J.A., 1989. Spatial scaling in ecology. Functional Ecology 3: 385-397. 
WIENS J.A., 2001. Understanding the problem of scale in experimental ecology. Pp. 61-80. In GARDNER R.H., KEMP W.M., KENNEDY V.S. & J.E. PETERSEN (eds.). Scaling Relations in Experimental Ecology. Columbia University Press, New York.
WILSON E.O., 1998. Consilience, the Unity of Knowledge. Vintage books, New York.
XIA Y. & J. BAUMGÄRTNER, 1999. ICIPE Insect Informatics Initiative: An Integrated Approach for Insect Information Generation, Processing and Dissemination. EFITA 99. Second European Conference of the European Federation for Information Technology in Agriculture, Food and Environment, September 27-30, 1999, University of Bonn.

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