Which spatial heterogeneity framework? Consequences for conclusions about patchy population distributions.

Patches, gradients, and hierarchies are three common organizational frameworks for assessing the effects of spatial heterogeneity on species distributions. Since these frameworks are often chosen a priori, without knowledge of study systems, they may not correspond to the empirical heterogeneity present and may result in partial or erroneous conclusions about the forces structuring species distributions. I tested the consequences of choosing particular frameworks and whether patch heterogeneity structured patchily distributed populations of the valley elderberry longhorn beetle (Desmocerus californicus dimorphus) along four rivers in California's Central Valley (USA). A comparison of the three approaches revealed that each led to incomplete conclusions about controls on the beetle's distribution and populations. Patch analysis revealed weak effects of patch size and quality, and high unexplained variance, which likely reveals large amounts of stochasticity since replication was high. The patch analysis therefore concluded that distributions consistent with patch dynamic structures like classic metapopulation, source-sink, and mainland-island models existed in the different rivers. Conversely, gradient analyses revealed a gradient-distribution pattern responding to continuous and often large-scale variables, such as host-plant age or size, water availability, and the presence of an invasive leguminous tree; again most variance in beetle occurrence remained unexplained. Hierarchical analysis identified the natural spatial patterns of the system but gave no indication of causal processes. The combination of all three approaches explained the maximum variance in beetle occurrence, through inclusion of a comprehensive list of explanatory variables, multiple spatial scales, various types of heterogeneity, and a focus on the scales at which beetle-environment interactions were strongest. Surprisingly, these results still supported the notion that the beetle exists as a metapopulation, a structure thought to be rare because it ignores habitat quality and landscape conditions. These analyses exemplify the simultaneous importance of local patch attributes and broad-scale and/or gradient variables that are commonly overlooked in patch studies. Importantly, some patch attributes acted over inter-patch scales, affecting the perception of patch distances and distributional extents. Only through the integration of frameworks was I able to decipher the system's complexity and see that all three types of heterogeneity were acting in the system, sometimes over unexpected scales.