A large number of methods for the analysis of point pattern data have been developed in a wide range of scientific fields. First-order statistics describe large-scale variation in the intensity of points in a study region, whereas second-order characteristics are summary statistics of all point-to-point distances in a mapped area and offer the potential for detecting both different types and scales of patterns. Second-order analysis based on Ripley's K-function is increasingly used in ecology to characterize spatial patterns and to develop hypothesis on underlying processes; however, the full range of available methods has seldomly been applied by ecologists. The aim of this paper is to provide guidance to ecologists with limited experience in second-order analysis to help in the choice of appropriate methods and to point to practical difficulties and pitfalls. We review (1) methods for analytical and numerical implementation of two complementary second-order statistics, Ripley's K and the Oring statistic, (2) methods for edge correction, (3) methods to account for first-order effects (i.e. heterogeneity) of univariate patterns, and (4) a variety of useful standard and non-standard null models for univariate and bivariate patterns. For illustrative purpose, we analyze examples that deal with non-homogeneous univariate point patterns. We demonstrate that large-scale heterogeneity of a point-pattern biases Ripley's K-function at smaller scales. This bias is difficult to detect without explicitly testing for homogeneity, but we show that it can be removed when applying methods that account for first-order effects. We synthesize our review in a number of step-bystep recommendations that guide the reader through the selection of appropriate methods and we provide a software program that implements most of the methods reviewed and developed here.

Agent-based complex systems are dynamic networks of many interacting agents; examples include ecosystems, financial markets, and cities. The search for general principles underlying the internal organization of such systems often uses bottom-up simulation models such as cellular automata and agent-based models. No general framework for designing, testing, and analyzing bottom-up models has yet been established, but recent advances in ecological modeling have come together in a general strategy we call patternoriented modeling. This strategy provides a unifying framework for decoding the internal organization of agent-based complex systems and may lead toward unifying algorithmic theories of the relation between adaptive behavior and system complexity. What makes James Bond an agent? He has a clear goal, he is autonomous in his decisions about achieving the goal, and he adapts these decisions to his rapidly changing situation. We are surrounded by such autonomous, adaptive agents: cells of the immune system, plants, citizens, stock market investors, businesses, etc. The agent-based complex systems (1) (ACSs) around us are made up of myriad interacting agents. One of the most important challenges confronting modern science is to understand and predict such systems. Bottom-up simulation modeling is one tool for doing so: We compile relevant information about entities at a lower level of the system (in Bagent-based models,[ these are individual agents), formulate theories about their behavior, implement these theories in a computer simulation, and observe the emergence of system-level properties related to particular questions (2, 3).Bottom-up models have been developed for many types of ACSs (4), but the identification of general principles underlying the organization of ACSs has been hampered by the lack of an explicit strategy for coping with the two main challenges of bottom-up modeling: complexity and uncertainty (5, 6). Consequently, model structure often is chosen ad hoc, and the focus is often on how to represent agents without sufficient emphasis on analyzing and validating the applicability of models to real problems (5, 7).A strategy called pattern-oriented modeling (POM) attempts to make bottom-up modeling more rigorous and comprehensive (6,(8)(9)(10). In POM, we explicitly follow the basic research program of science: the explanation of observed patterns (11). Patterns are defining characteristics of a system and often, therefore, indicators of essential underlying processes and structures. Patterns contain information on the internal organization of a system, but in a Bcoded[ form. The purpose of POM is to Bdecode[ this information (10).The motivation for POM is that, for complex systems, a single pattern observed at a specific scale and hierarchical level is not sufficient to reduce uncertainty in model structure and parameters. This has long been known in science. For example, Chargaff_s rule of DNA base pairing was not sufficient to decode the structure of DNA-until combined with patterns from x-ray...

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Summary Fundamental ecological research is both intrinsically interesting and provides the basic knowledge required to answer applied questions of importance to the management of the natural world. The 100th anniversary of the British Ecological Society in 2013 is an opportune moment to reflect on the current status of ecology as a science and look forward to high‐light priorities for future work. To do this, we identified 100 important questions of fundamental importance in pure ecology. We elicited questions from ecologists working across a wide range of systems and disciplines. The 754 questions submitted (listed in the online appendix) from 388 participants were narrowed down to the final 100 through a process of discussion, rewording and repeated rounds of voting. This was done during a two‐day workshop and thereafter. The questions reflect many of the important current conceptual and technical pre‐occupations of ecology. For example, many questions concerned the dynamics of environmental change and complex ecosystem interactions, as well as the interaction between ecology and evolution. The questions reveal a dynamic science with novel subfields emerging. For example, a group of questions was dedicated to disease and micro‐organisms and another on human impacts and global change reflecting the emergence of new subdisciplines that would not have been foreseen a few decades ago. The list also contained a number of questions that have perplexed ecologists for decades and are still seen as crucial to answer, such as the link between population dynamics and life‐history evolution. Synthesis. These 100 questions identified reflect the state of ecology today. Using them as an agenda for further research would lead to a substantial enhancement in understanding of the discipline, with practical relevance for the conservation of biodiversity and ecosystem function.

We used point pattern analysis to examine the spatial distribution of 46 common tree species (diameter at breast height >10 cm) in a fully mapped 500x500-m tropical forest plot in Sinharaja, Sri Lanka. We aimed to disentangle the effect of species interactions (second-order effects) and environment (first-order effects) on the species' spatial distributions. To characterize first-order associations (segregation, overlap), we developed a classification scheme based on Ripley's K and nearest-neighbor statistics. We subsequently used heterogeneous Poisson null models, accounting for possible environmental heterogeneity, to reveal significant uni- and bivariate second-order interactions (regularity, aggregation and repulsion, attraction). First-order effects were strong; overall, 53% of all species pairs occupied largely disjoint areas (segregation), 40% showed partial overlap, and 6% overlapped. Only 5% of all species pairs showed significant second-order effects, but about half of the species showed significant intraspecific effects. Significant plant-plant interactions occurred mostly within 2-4 m and disappeared within 15-20 m of the focal plant. While lack of significant species interactions suggests support for the unified neutral theory, species' observed spatial segregation does not support the assumptions of the neutral theory. The strong observed tendency of species to segregate may have supplementary effects on other processes promoting species coexistence.

Statistical models are the traditional choice to test scientific theories when observations, processes or boundary conditions are subject to stochasticity. Many important systems in ecology and biology, however, are difficult to capture with statistical models. Stochastic simulation models offer an alternative, but they were hitherto associated with a major disadvantage: their likelihood functions can usually not be calculated explicitly, and thus it is difficult to couple them to well-established statistical theory such as maximum likelihood and Bayesian statistics. A number of new methods, among them Approximate Bayesian Computing and Pattern-Oriented Modelling, bypass this limitation. These methods share three main principles: aggregation of simulated and observed data via summary statistics, likelihood approximation based on the summary statistics, and efficient sampling. We discuss principles as well as advantages and caveats of these methods, and demonstrate their potential for integrating stochastic simulation models into a unified framework for statistical modelling.

Summary 1.The spatial pattern of tree species retains signatures of factors and processes such as dispersal, available resource patches for establishment, competition and demographics. Comparison of the spatial pattern of different size classes can thus help to reveal the importance and characteristics of the underlying processes. However, tree dynamics may be masked by large-scale heterogeneous site conditions, e.g. when the restricting size of regeneration sites superimposes emergent patterns. 2.Here we ask how environmental heterogeneity may influence the spatial dynamics of plant communities. We compared the spatial patterns and demographics of western hemlock in a homogeneous and a heterogeneous site of old-growth Douglas-fir forests on Vancouver Island using recent techniques of point pattern analysis. We used homogeneous and inhomogeneous K -and pair-correlation functions, and case-control studies to quantify the change in spatial distribution for different size classes of western hemlock. 3. Our comparative analyses show that biological processes interacted with spatial heterogeneity, leading to qualitatively different population dynamics at the two sites. Population structure, survival and size structure of western hemlock were different in the heterogeneous stand in such a way that, compared to the homogeneous stand, seedlings were more clustered, seedling densities higher, seedling mortality lower, adult growth faster and adult mortality higher. Under homogeneous site conditions, seedling survival was mainly abiotically determined by random arrival in small gaps with limiting light. At the heterogeneous site, seedling densities and initial survival were much higher, leading to strong density-dependent mortality and selection for faster growing individuals in larger size classes. We hypothesise that the dynamics of the heterogeneous stand were faster due to asymmetric competition with disproportionate benefit to taller plants. 4. Synthesis . Our study supports the hypothesis that successional dynamics are intensified in heterogeneous forest stands with strong spatial structures and outlines the importance of spatial heterogeneity as a determinant of plant population dynamics and pattern formation.

Remote sensing enables the quantification of tropical deforestation with high spatial resolution. This in-depth mapping has led to substantial advances in the analysis of continent-wide fragmentation of tropical forests. Here we identified approximately 130 million forest fragments in three continents that show surprisingly similar power-law size and perimeter distributions as well as fractal dimensions. Power-law distributions have been observed in many natural phenomena such as wildfires, landslides and earthquakes. The principles of percolation theory provide one explanation for the observed patterns, and suggest that forest fragmentation is close to the critical point of percolation; simulation modelling also supports this hypothesis. The observed patterns emerge not only from random deforestation, which can be described by percolation theory, but also from a wide range of deforestation and forest-recovery regimes. Our models predict that additional forest loss will result in a large increase in the total number of forest fragments-at maximum by a factor of 33 over 50 years-as well as a decrease in their size, and that these consequences could be partly mitigated by reforestation and forest protection.