Factors and Mechanisms Explaining Spatial Heterogeneity: A Review of Methods for Insect Populations

Vinatier, Fabrice, Philippe Tixier, Pierre-Francois Duyck, and Francoise Lescourret. “Factors and Mechanisms Explaining Spatial Heterogeneity: A Review of Methods for Insect Populations.” Methods in Ecology and Evolution 2 (2011): 11–22. doi:10.1111/j.2041-210X.2010.00059.x.
Vinatier et al. (2011) present a review paper of the methods involved in evaluating spatial heterogeneity in insect population distributions and dynamics, with the goal of providing a framework for choosing appropriate methods in the examination of spatial patterning. This is split into three separate stages: sampling of populations, identification of spatial patterns (specifically through statistical methods), and modeling spatial patterns through mechanistic models.

Sampling methods are further divided into ‘marked point processes’, which approximate relative population size through trapping or “attack intensity”. When each individual is directly observed, and its specific location recorded, the sampling is thought to be a point pattern process, and may offer less bias than those measurements based on trapping because they are meant to represent every individual within a population. Patterns are then characterized using specific indices, many of which are specific to landscape or spatial studies. There are many indices by which to measure species aggregation, but one that I had not heard of is the SADIE collection of indices, which incorporates crowding and distance across time.

In the authors’ framework, processes that are driving this spatial patterning are then identified through conventional statistical methods such as generalized linear mixed models and regression analyses. For analysis of patterns at multiple scales, Vinatier et al. recommend the use of Generalized Linear Mixed Models, I assume for their ability to control for nested random effects across scales, although they do not explicitly mention why.

Mechanistic modeling is the third stage in the evaluation of spatial patterning, however Vinatier et al. note their use in explicitly exploring the underlying processes. Table 2 offers an excellent overview of different types of mechanistic modeling, complete with their application and example references. In general, models can incorporate space implicitly, as in Levin’s classic metapopulation model, or explicitly, many of which are multi-scale models. All spatially explicit models are described as a type of cellular automaton, in that each “cell”, regardless of its scale, is explicitly considered. The types of models differ in their complexity and method of incorporating space, however the reaction-diffusion model is able to incorporate both space and time. Vinateir et al. note that they are especially suited to the study of systems with “little or no spatial heterogeneity of resources”, an assertion that I do not fully agree with. Other studies have incorporated spatial heterogeneity into reaction-diffusion models successfully (see Riolo et al. 2015), with surprising results which may have not been evident in less complex models.

Vinatier et al. further define evaluation of a spatial pattern as inductive or deductive. Inductive reasoning may be used when the expected underlying mechanisms cannot be measured or incorporated into a model, such as learning behaviors. In this case, reasonable conclusions are drawn based on natural history and characterizing of spatial patterns. However, I would argue, that in many cases, modeling or theoretical exercises may be able to further elucidate these patterns, even if the exact parameter values are not known. Deductive procedures, on the other hand, include the statistical and mechanistic models mentioned previously. While deductive reasoning seems more conclusive than inductive, Vinatier et al. do present that caveat that a well or poorly fitted model does not necessarily confirm the confirmation or rejection of the process’s role in spatial patterning. I understand this perspective, however, many spatial patterning hypotheses are experimentally intractable because of their large spatial scale, and modeling provides a tool to test otherwise untestable hypotheses.

This framework is directed at studies of spatial patterning in insects, but I believe it is applicable to any system. The stages of spatial patterning from characterization of a pattern in the field to comparison of a simulated pattern to observed patterns are not specific to insects or pests, and offer a road map for any modeling study investigating the effects of spatial heterogeneity on population dynamics.