Hanno Hildenbrandt

A new approach to spatially explicit modelling of forest dynamics: spacing, ageing and neighbourhood competition of mangrove trees

This paper presents a new approach to spatially explicit modelling that enables the influence of neighbourhood effects on the dynamics of forests and plant communities to be analysed. We refer to this approach as ‘field of neighbourhood’ (FON). It combines the ‘neighbourhood philosophy’ of grid-based models with the description of individual spacing in the ‘zone of influence’ (ZOI) approach. The novel feature of FON is that modelling of local competition between neighbouring trees is based on the notion of a field of neighbourhood exerted by each tree. This field is defined only on the ZOI of a tree and depends on the distance to the stemming point. For the demonstration of FONs power, a simulation model (KiWi) was implemented that focuses on the dynamic of mangrove forests. The realistic self-thinning behaviour of modelled stands of Avicennia germinans and Rhizophora mangle confirms the suitability of the FON approach for the description of intra- and inter-specific competition. In KiWi, mortality is modelled in terms of a ‘memory function’, i.e. the yearly stem increment of each tree is stored in its ‘memory’ over a certain time period and determines — as a sign of vitality — tree mortality. The results of KiWi demonstrate that this description is sufficient to keep the maximum age of the trees within a reasonable limit. The model thus manages without a description of individual tree age. This is an important feature considering the fact that a direct relationship between tree age and mortality is questioned and there is no established method as yet for determining the age of mangrove trees.

Self-organized aerial displays of thousands of starlings: a model

Aerial displays of starlings (Sturnus vulgaris) at their communal roosts are complex: thousands of individuals form multiple flocks which are continually changing shape and density, while splitting and merging. To understand these complex displays both empirical data and models are needed. Whereas detailed empirical data were recently collected through video recordings and position measurements by stereo photography of flocks of thousands of starlings, there are as yet no models that generate these complex patterns. Numerous computer models in biology, however, suggest that patterns of single groups of moving animals may emerge by self-organisation from movement and local coordination (through attraction, alignment and avoidance of collision). In this paper, we investigated whether this approach can be extended to generate patterns resembling these aerial displays of starlings. We show in a model that to generate many of the patterns measured empirically in real starlings we have to extend the usual rules of local coordination with specifics of starling behaviour, mainly 1) their aerial locomotion, 2) a low and constant number of interaction-partners and 3) preferential movement above a roosting area. Our model can be used as a tool for the study of these displays, because it provides new integrative hypotheses about the mechanisms underlying these displays and of swarming patterns in biological systems in general.

Self-organised complex aerial displays of thousands of starlings: a model

Aerial displays of starlings (Sturnus vulgaris) at their communal roosts are complex: thousands of individuals form multiple flocks which are continually changing shape and density, while splitting and merging. To understand these complex displays both empirical data and models are needed. Whereas detailed empirical data were recently collected through video recordings and position measurements by stereo photography of flocks of thousands of starlings, there are as yet no models that generate these complex patterns. Numerous computer models in biology, however, suggest that patterns of single groups of moving animals may emerge by self-organisation from movement and local coordination (through attraction, alignment and avoidance of collision). In this paper, we investigated whether this approach can be extended to generate patterns resembling these aerial displays of starlings. We show in a model that to generate many of the patterns measured empirically in real starlings we have to extend the usual rules of local coordination with specifics of starling behaviour, mainly 1) their aerial locomotion, 2) a low and constant number of interaction-partners and 3) preferential movement above a roosting area. Our model can be used as a tool for the study of these displays, because it provides new integrative hypotheses about the mechanisms underlying these displays and of swarming patterns in biological systems in general.

Schools of fish and flocks of birds: their shape and internal structure by self-organization

Models of self-organization have proved useful in revealing what processes may underlie characteristics of swarms. In this study, we review model-based explanations for aspects of the shape and internal structure of groups of fish and of birds travelling undisturbed (without predator threat). Our models attribute specific collective traits to locomotory properties. Fish slow down to avoid collisions and swim at a constant depth, whereas birds fly at low variability of speed and lose altitude during turning. In both the models of fish and birds, the ‘bearing angle’ to the nearest neighbour emerges as a side-effect of the ‘blind angle’ behind individuals and when group size becomes larger, temporary subgroups may increase the complexity of group shape and internal structure. We discuss evidence for model-based predictions and provide a list of new predictions to be tested empirically.

Some causes of the variable shape of flocks of birds.

Flocks of birds are highly variable in shape in all contexts (while travelling, avoiding predation, wheeling above the roost). Particularly amazing in this respect are the aerial displays of huge flocks of starlings (Sturnus vulgaris) above the sleeping site at dawn. The causes of this variability are hardly known, however. Here we hypothesise that variability of shape increases when there are larger local differences in movement behaviour in the flock. We investigate this hypothesis with the help of a model of the self-organisation of travelling groups, called StarDisplay, since such a model has also increased our understanding of what causes the oblong shape of schools of fish. The flocking patterns in the model prove to resemble those of real birds, in particular of starlings and rock doves. As to shape, we measure the relative proportions of the flock in several ways, which either depend on the direction of movement or do not. We confirm that flock shape is usually more variable when local differences in movement in the flock are larger. This happens when a) flock size is larger, b) interacting partners are fewer, c) the flock turnings are stronger, and d) individuals roll into the turn. In contrast to our expectations, when variability of speed in the flock is higher, flock shape and the positions of members in the flock are more static. We explain this and indicate the adaptive value of low variability of speed and spatial restriction of interaction and develop testable hypotheses.

Emergent Patterns of Social Affiliation in Primates, a Model

Many patterns of affiliative behaviour have been described for primates, for instance: reciprocation and exchange of grooming, grooming others of similar rank, reconciliation of fights, and preferential reconciliation with more valuable partners. For these patterns several functions and underlying cognitive processes have been suggested. It is, however, difficult to imagine how animals may combine these diverse considerations in their mind. Although the co-variation hypothesis, by limiting the social possibilities an individual has, constrains the number of cognitive considerations an individual has to take, it does not present an integrated theory of affiliative patterns either. In the present paper, after surveying patterns of affiliation in egalitarian and despotic macaques, we use an individual-based model with a high potential for self-organisation as a starting point for such an integrative approach. In our model, called GrooFiWorld, individuals group and, upon meeting each other, may perform a dominance interaction of which the outcomes of winning and losing are self-reinforcing. Besides, if individuals think they will be defeated, they consider grooming others. Here, the greater their anxiety is, the greater their “motivation” to groom others. Our model generates patterns similar to many affiliative patterns of empirical data. By merely increasing the intensity of aggression, affiliative patterns in the model change from those resembling egalitarian macaques to those resembling despotic ones. Our model produces such patterns without assuming in the mind of the individual the specific cognitive processes that are usually thought to underlie these patterns (such as recordkeeping of the acts given and received, a tendency to exchange, memory of the former fight, selective attraction to the former opponent, and estimation of the value of a relationship). Our model can be used as a null model to increase our understanding of affiliative behaviour among primates, in particular macaques.

Asymmetric competition as a natural outcome of neighbour interactions among plants: results from the field-of-neighbourhood modelling approach

Numerous attempts have been made to infer the mode of competition from size or biomass distributions of plant cohorts. However, since the relationship between mode of competition and size distributions may be obscured by a variety of factors such as spatial configuration, density or resource level, empirical investigations often produce ambiguous results. Likewise, the findings of theoretical analyses of asymmetric competition are equivocal. In this paper, we analyse the mode of competition in an individual-based model which is based on the new field-of-neighbourhood approach. In this approach, plants have a zone of influence that determines the distance up to which neighbours are influenced. Additionally, a superimposed field within the zone of influence defines phenomenologically the strength of influence of an individual on neighbouring plants. We investigated competition at both individual and population level and characterised the influence of density and of the shape of the field-of-neighbourhood on occurrence and degree of competitive asymmetry. After finding asymmetric competition emerging in all scenarios, we argue that asymmetric competition is a natural consequence of local competition among neighbouring plants.

Cyclic dynamics in simulated plant populations

Despite the general interest in nonlinear dynamics in animal populations, plant populations are supposed to show a stable equilibrium that is attributed to fundamental differences compared with animals. Some studies find more complex dynamics, but empirical studies usually are too short and most modelling studies ignore important spatial aspects of local competition and establishment. Therefore, we used a spatially explicit individual–based model of a hypothetical, non–clonal perennial to explore which mechanisms might generate complex dynamics, i.e. cycles. The model is based on the field–of–neighbourhood approach that describes local competition and establishment in a phenomenological manner. We found cyclic population dynamics for a wide spectrum of model variants, provided that mortality is determined by local competition and recruitment is virtually completely suppressed within the zone of influence of established plants. This destabilizing effect of local processes within plant populations might have wide–ranging implications for the understanding of plant community dynamics and coexistence.

Testing the intermediate disturbance hypothesis in species-poor systems: A simulation experiment for mangrove forests

Abstract Questions: What factors influence tree species diversity of mangrove forests, an example of species-poor systems? What are the respective importance and interactions of these factors? Is the intermediate disturbance hypothesis applicable to such systems? Methods: We used the spatially explicit individual-based model KiWi to investigate the effects on species diversity of perturbation frequency and intensity, different abiotic conditions, and interspecific competition simulated at the individual level. The simulation system considered the three dominant Caribbean mangrove species: Rhizophora mangle, Avicennia germinans and Laguncularia racemosa, applying species-specific growth and mortality characteristics. Firstly, effects on species dominance of the abiotic conditions nutrient availability and porewater salinity were tested with two competition scenarios. Secondly, the effect of perturbation frequency and intensity were investigated with selected abiotic conditions. Results: Abiotic conditions influenced species dominance and, in extreme cases, excluded one or two species. Abiotic and competition settings controlled the successional dynamics and the response of species dominance to perturbation regimes. A response consistent with the intermediate disturbance hypothesis was observed only with a configuration of plant interaction in which one species behaved as a pioneer so that succession occurred by competitive exclusion. Conclusions: We suggest that successional dynamics interact with the intensity and timing of perturbations and determine whether or not mangrove tree diversity conforms to predictions of the intermediate disturbance hypothesis. For mangroves, these successional dynamics are site-specific depending on abiotic conditions and species configurations.

The confusion effect when attacking simulated three-dimensional starling flocks

The confusion effect describes the phenomenon of decreasing predator attack success with increasing prey group size. However, there is a paucity of research into the influence of this effect in coherent groups, such as flocks of European starlings (Sturnus vulgaris). Here, for the first time, we use a computer game style experiment to investigate the confusion effect in three dimensions. To date, computerized studies on the confusion effect have used two-dimensional simulations with simplistic prey movement and dynamics. Our experiment is the first investigation of the effects of flock size and density on the ability of a (human) predator to track and capture a target starling in a realistically simulated three-dimensional flock of starlings. In line with the predictions of the confusion effect, modelled starlings appear to be safer from predation in larger and denser flocks. This finding lends credence to previous suggestions that starling flocks have anti-predator benefits and, more generally, it suggests that active increases in density in animal groups in response to predation may increase the effectiveness of the confusion effect.