Identifying spatial relationships at multiple scales: principal coordinates of neighbour matrices (PCNM) and geostatistical approaches

We compared two methodological approaches – principal coordinate analysis of neighbour matrices (PCNM) and geostatistics – that both aim at extracting several spatial scales in order to identify spatial relationships between organisms and environmental variables at multiple scales. From a statistical point of view, PCNM analysis and geostatistics come from "two different worlds"– PCNM is based on classical "data analysis" while geostatistical modelling is developed in a probabilistic context. These two methods were used to investigate the spatial relationships between defoliation caused by spruce budworm Choristoneura fumiferana and bioclimatic conditions in Ontario since 1941 through a wide range of scales. On the one hand, PCNM variables related to defoliation frequency were partitioned into four spatial submodels representing respectively four spatial scales: very broad scale (ca>300 km), broad scale (ca 180 km), fine (ca 100 km), and very fine (<80 km). On the other hand, nested variogram modelling was used to identify the relevant scales. The nested variogram model was composed of four variograms with different characteristic scales close to those of the PCNM spatial submodels. Maps of PCNM submodels and kriging components revealed similar spatial patterns of defoliation frequency at very broad and broad scales while spatial patterns at fine and very fine scales looked quite different. Both methods showed that defoliation by spruce budworm occurs at the broader spatial scales but may be explained by fluctuations at the smaller scales. Finally, results based on geostatistics using a Linear Model of Coregionalisation suggested that climatic conditions can be considered to act at the level of outbreak dynamics while the tree community of spruce budworm's principal hosts controls local population dynamics.     

Phase-dependent outbreak dynamics of geometrid moth linked to host plant phenology

Climatically driven Moran effects have often been invoked as the most likely cause of regionally synchronized outbreaks of insect herbivores without identifying the exact mechanism. However, the degree of match between host plant and larval phenology is crucial for the growth and survival of many spring-feeding pest insects, suggesting that a phenological match/mismatch-driven Moran effect may act as a synchronizing agent.We analyse the phase-dependent spatial dynamics of defoliation caused by cyclically outbreaking geometrid moths in northern boreal birch forest in Fennoscandia through the most recent massive outbreak (2000–2008). We use satellite-derived time series of the prevalence of moth defoliation and the onset of the growing season for the entire region to investigate the link between the patterns of defoliation and outbreak spread. In addition, we examine whether a phase-dependent coherence in the pattern of spatial synchrony exists between defoliation and onset of the growing season, in order to evaluate if the degree of matching phenology between the moth and their host plant could be the mechanism behind a Moran effect.The strength of regional spatial synchrony in defoliation and the pattern of defoliation spread were both highly phase-dependent. The incipient phase of the outbreak was characterized by high regional synchrony in defoliation and long spread distances, compared with the epidemic and crash phase. Defoliation spread was best described using a two-scale stratified spread model, suggesting that defoliation spread is governed by two processes operating at different spatial scale. The pattern of phase-dependent spatial synchrony was coherent in both defoliation and onset of the growing season. This suggests that the timing of spring phenology plays a role in the large-scale synchronization of birch forest moth outbreaks.     

Spatial scales in the study of reef fishes: A theoretical perspective

Abstract Theoretical models imply that spatial scale derives its greatest importance through interactions between density-dependent processes and spatial variation in population densities and environmental variables. Such interactions cause population dynamics on large spatial scales to differ in important ways from predictions based on measurements of population dynamics at smaller scales, a phenomenon called the scale transition. These differences can account for large-scale population stability and species coexistence. The interactions between density dependence and spatial variation that lead to the scale transition can be understood by the process of non-linear averaging, which shows how variance originating on various spatial scales contributes to large-scale population dynamics. Variance originating below the scale of density dependence contributes less to the scale transition as the spatial scale of the variation declines, while variation originating on or above the scale of density dependence contributes independently of the spatial scale of the variation.     

Anomalous outbreaks of an invasive defoliator and native bark beetle facilitated by warm temperatures,changes in precipitation and interspecific interactions

Biotic disturbance agents such as insects can be highly responsive to climatic change and have widespread ecological and economic impacts on forests. Quantifying the responses of introduced and native insects to climate, including how dynamics of one agent may mediate those of another, is important for forecasting disturbance and associated impacts on forest structure and function. We investigated drivers of outbreaks by larch casebearer Coleophora laricella, an invasive defoliator, and eastern larch beetle Dendroctonus simplex, a native, tree‐killing bark beetle, on tamarack Larix laricina from 2000 to in Minnesota, USA. We evaluated the utility of temporal, spatial and climatic variables in predicting the presence/absence of outbreaks of each insect in cells of rasterized aerial survey data. The role of defoliation by larch casebearer in outbreaks of eastern larch beetle was also investigated. For both species, the most important predictors of outbreak occurrence were proximity of conspecific outbreaks in space and time. For larch casebearer, outbreak occurrence was positively associated with spring precipitation and warmer growing seasons. Outbreak occurrence of eastern larch beetle was positively associated with warmer and dryer years and was more likely in cells with prior defoliation by larch casebearer. Our results demonstrate that climate can drive large scale outbreaks of introduced and non‐native disturbance agents on a single host species, and that interactions at the tree level between such agents may scale up to manifest across large temporal and spatial scales.     

Can hyperparasitoids cause large‐scale outbreaks of insect herbivores?

Synchronous population fluctuations occur in many species and have large economic impacts, but remain poorly understood. Dispersal, climate and natural enemies have been hypothesized to cause synchronous population fluctuations across large areas. For example, insect herbivores cause extensive forest defoliation and have many natural enemies, such as parasitoids, that may cause landscape‐scale changes in density. Between outbreaks, parasitoid‐caused mortality of hosts/herbivores is high, but it drops substantially during outbreak episodes. Because of their essential role in regulating herbivore populations, we need to include parasitoids in spatial modelling approaches to more effectively manage insect defoliation. However, classic host‐parasitoid population models predict parasitoid density, and parasitoid density is difficult to relate to host‐level observations of parasitoid‐caused mortality. We constructed a novel model to study how parasitoids affect insect outbreaks at the landscape scale. The model represents metacommunity dynamics, in which herbivore regulation, colonisation and extinction are driven by interactions with the forest, primary parasitoids and hyperparasitoids. The model suggests that parasitoid spatial dynamics can produce landscape‐scale outbreaks. Our results propose the testable prediction that hyperparasitoid prevalence should increase just before the onset of an outbreak because of hyperparasitoid overexploitation. If verified empirically, hyperparasitoid distribution could provide a biotic indicator that an outbreak will occur.     

Extensive gypsy moth defoliation in Southern New England characterized using Landsat satellite observations

Southern New England is currently experiencing the first major gypsy moth (Lymantria dispar) defoliation event in nearly 30 years. Using a novel approach based on time series of Landsat satellite observations, we generated consistent maps of gypsy moth defoliation for 2015 (first year of the outbreak), 2016 (second year of outbreak), and 2017 (third year of outbreak). Our mapped results demonstrate that the defoliation event continued through the 2017 growing season. Moreover, the affected area more than doubled in extent each year and expanded radially to encompass 4386 km² of forested area in Rhode Island, eastern Connecticut, and central Massachusetts. The current gypsy moth outbreak is believed to be the result of a series of unusually dry springs in 2014, 2015, and 2016, which suppressed Entomophaga maimaiga, a fungal mortality agent that has historically reduced gypsy moth impacts in this region. The continuation and marked expansion of the outbreak in 2017 despite average spring rainfall suggests that caterpillars were active early in the growing season, and mortality from the fungus likely peaked after significant defoliation had already occurred. Our Landsat time series approach represents an important new source of data on spatial and temporal patterns in gypsy moth defoliation, and continued satellite-based monitoring will be essential for tracking the progress of this and other gypsy moth outbreaks.     

Landscape host abundance and configuration regulate periodic outbreak behavior in spruce budworm Choristoneura fumiferana

Landscape‐level forest management has long been hypothesized to affect forest insect outbreak dynamics, but empirical evidence remains elusive. We hypothesized that the combination of increased hardwood relative to host tree species, prevalence of younger forests, and fragmentation of those forests due to forest harvesting legacies would reduce outbreak intensity, increase outbreak frequency, and decrease spatial synchrony in spruce budworm Choristoneura fumiferana outbreaks. We investigated these hypotheses using tree ring samples collected across 51 sites pooled into 16 subareas distributed across a large ecoregion spanning the international border between Ontario (Canada), and Minnesota (USA). This ecoregion contains contrasting land management zones with clear differences in forest landscape structure (i.e. forest composition and spatial configuration) while minimizing the confounding influence of climate. Cluster analyses of the 76‐yr time‐series generally grouped by subareas found within the same land management zone. Spatial nonparametric covariance analysis indicated that the highest and lowest degree of spatial synchrony of spruce budworm outbreaks were found within unmanaged wilderness and lands managed at fine spatial scales in Minnesota, respectively. Using multivariate analysis, we also found that forest composition, configuration, and climate together accounted for a total of 40% of the variance in outbreak chronologies, with a high level of shared variance between composition and configuration (13%) and between composition and climate (9%). At the scale of our study, climate on its own did not explain any of the spatial variation in outbreaks. Outbreaks were of higher frequency, lower intensity, and less spatially synchronized in more fragmented, younger forests with a lower proportion of host species, with opposing outbreak characteristics observed in regions characterised by older forests with more concentrated host species. Our study is the first quantitative evaluation of the long‐standing ‘silvicultural hypothesis’ of spruce budworm management specifically conducted at a spatio‐temporal scale for which it was intended.     

Multiple scales and the relationship between density and spatial aggregation in littoral zone communities

Understanding the constraints on community composition at multiple spatial scales is an immense challenge to community and ecosystem ecologists. As community composition is basically the composite result of species’ spatial patterning, studying this spatial patterning across scales may yield clues as to which scales of environmental heterogeneity influence communities. The now widely documented positive interspecific relationship between ‘regional’ range and mean ‘local’ abundance has become a generalisation describing the spatial patterning of species at coarse scales. We address some of the shortcomings of this generalisation, as well as examine the cross‐scale spatial patterning (aggregation and density levels) of littoral‐benthic invertebrates in very large lakes. Specifically, we (a) determine whether the positive range‐abundance relationship can be reinterpreted in terms of the actual spatial structure of species distributions, (b) examine the relationship between aggregation and density across different spatial scales, and (c) determine whether the spatial patterning of species (e.g. low density/aggregated distribution) is constant across scales, that is, whether our interpretation of a species spatial pattern is dependent on the scale at which we choose to observe the system. Spatial aggregation of littoral invertebrates was generally a negative function of mean density across all spatial scales and seasons (autumn and spring). This relationship may underlie positive range‐abundance relationships. Species that were uncommon and highly aggregated at coarse spatial scales can be abundant and approach random distributions at finer spatial scales. Also, the change in spatial aggregation of closely related taxa across spatial scales was idiosyncratic. The idiosyncratic cross‐scale spatial patterning of species implies that multiple scales of environmental heterogeneity may influence the assembly of littoral communities. Due to the multi‐scale, species‐specific spatial patterning of invertebrates, littoral zone communities form a complex spatial mosaic, and a ‘spatially explicit’ approach will be required by limnologists in order to link littoral‐benthic community patterns with ecosystem processes in large oligotrophic lakes.     

The effect of spatial scale on interactions between two weevils and their parasitoid

1. The effect of spatial scale on the interactions between three hymenopteran parasitoids and their weevil hosts was investigated. The parasitoid Mesopolobus incultus (Walker) parasitised Gymnetron pascuorum Gyll.; the parasitoids Entodon sparetus (Walker) and Bracon sp. parasitised Mecinus pyraster Herbst. Both of these weevils develop inside the seedhead of Plantago lanceolata L. but occupy different niches. Seedheads were sampled annually from 162 plants at each of two experimental sites consisting of a series of habitat patches of two distinct sizes. Data were analysed from three site‐years. 2. Parasitoid densities at each site‐year were closely related to the abundance of their respective weevil hosts. The overall proportion of hosts parasitised was more variable for M. incultus than for E. sparetus and Bracon sp. 3. Changes in spatial scale affected the variability of parasitoid densities. For M. incultus, there was generally a greater degree of additional heterogeneity for all increases of scale; for E. sparetus, this was true only at the largest scales; for Bracon sp., all components of variance were negative. 4. The rate of parasitism was related to host density in different ways at different spatial scales. Mesopolobus incultus exhibited inverse density dependence at the finest (seedhead) scale, direct density dependence at the intermediate (plant) scale, and density independence at the large (habitat area 729 m²) scale. Entodon sparetus showed no response to variation in host density at any spatial scale. Bracon sp. showed direct density dependence only at the intermediate and largest scales. 5. Parasitoids E. sparetus and Bracon sp. seemed able to detect more than one M. pyraster individual in seedheads with multiple host occupancy; a greater incidence of conspecific parasitoids than expected emerged from such seedheads.     

Can inverse density dependence at small spatial scales produce dynamic instability in animal populations?

All else being equal, inversely density-dependent (IDD) mortality destabilizes population dynamics. However, stability has not been investigated for cases in which multiple types of density dependence act simultaneously. To determine whether IDD mortality can destabilize populations that are otherwise regulated by directly density-dependent (DDD) mortality, I used scale transition approximations to model populations with IDD mortality at smaller “aggregation” scales and DDD mortality at larger “landscape” scales, a pattern observed in some reef fish and insect populations. I evaluated dynamic stability for a range of demographic parameter values, including the degree of compensation in DDD mortality and the degree of spatial aggregation, which together determine the relative importance of DDD and IDD processes. When aggregation-scale survival was a monotonically increasing function of density (a “dilution” effect), dynamics were stable except for extremely high levels of aggregation combined with either undercompensatory landscape-scale density dependence or certain values of adult fecundity. When aggregation-scale survival was a unimodal function of density (representing both “dilution” and predator “detection” effects), instability occurred with lower levels of aggregation and also depended on the values of fecundity, survivorship, detection effect, and DDD compensation parameters. These results suggest that only in extreme circumstances will IDD mortality destabilize dynamics when DDD mortality is also present, so IDD processes may not affect the stability of many populations in which they are observed. Model results were evaluated in the context of reef fish, but a similar framework may be appropriate for a diverse range of species that experience opposing patterns of density dependence across spatial scales.     

The frequency of detection of density dependence in insect orders

Abstract.

• 1 A priori, there are no obvious reasons why patterns should exist in the frequency of density dependence across insect orders. However, orders may reflect related factors which influence population regulation (e.g. life-history patterns and ecology) and are difficult to quantify. The frequency of occurrence of density dependence is compared in 171 time series (of ten or more generations) from Lepidoptera, Hemiptera, Diptera, Odonata, Hymenoptera and Coleoptera. A posteriori attempts are made to identify the cause of observed patterns.
• 2 Buhner's (1975) test found non-delayed density dependence more frequently in Odonata than Lepidoptera and Hymenoptera, which in turn showed non-delayed density dependence more frequently than Diptera, Hemiptera and Coleoptera. Similarly, detection was greater for Odonata than other orders using Dennis & Taper's (1993) test for density dependence and Crowley's (1992) test for attraction. Varley & Gradwell's (1960) test found density dependence less frequently in Hemiptera than other orders. These differences were independent of time series length, temporal trends and numbers of generations per year.
• 3 The reasons for observed patterns in detection of density dependence (and attraction) in insect orders are not clear; however, plausible explanations are differences in: (i) intrinsic growth rate, which is correlated with body size (although evidence to support this hypothesis is weak); (ii) the sampling method used; or (iii) whether individuals come from a single population or many populations.
• 4 Using Turchin's (1990) test, delayed (lag 2) density dependence was detected most frequently in Hymenoptera, which often show delayed diapause or are parasitoids.

     

Detection of density dependence from annual censuses of bracken-feeding insects

Summary A variety of techniques were used to test for density dependence in 32 time series from bracken-feeding insects. Seventeen taxa (primarily species, but including some pooled data from two or more closely related species whose larvae could not be distinguished in frond surveys) occurred on an open site; a woodland site held 15 taxa. For series of 12 years, collected on the open habitat, direct density dependence was detected by one or more of the techniques in 10 (58.8%) of 17 taxa, compared to only 5 (33.3%) of 15 taxa with time series of 8 years in length from the woodland habitat. Delayed density dependence was detected in 6 cases for the open site and in no cases at the woodland site. Either direct or delayed density dependence was found in 13 (76.5%) of 17 taxa for the open site and 13 (86.7%) of the 15 taxa which occurred on both sites. Although these results suggest a high frequency of density dependence in the species making up the bracken insect community, results from individual tests were extremely variable. Density dependence was detected least often by Vickery and Nudds' (1984) test, and most frequently by Varley and Gradwell's (1960) test, although the latter is prone to high rates of detecting spurious density dependence. Direct density dependence was detected most frequently in taxa that were univoltine and did not have delayed diapause, i.e. in those taxa whose life-histories conform most closely to the assumptions of the models underlying the analyses. Delayed density dependence occurred more frequently in species with more complex life-histories at the open site (taxa that were either bivoltine or multivoltine, or had delayed diapause). The results are consistent with the view that that the bracken herbivore assemblage consists of populations which are independently regulated by density dependent processes, although the present analyses suggest that we cannot rely on these tests to firmly show whether density dependence is present or not in an individual time series of the lengths considered here.     

Landscape level analysis of mountain pine beetle in British Columbia, Canada: spatiotemporal development and spatial synchrony within the present outbreak

Eruptive herbivores can exert profound landscape level influences. For example, the ongoing mountain pine beetle outbreak in British Columbia, Canada, has resulted in mortality of mature lodgepole pine over >7 million ha. Analysis of the spatio‐temporal pattern of spread can lend insights into the processes initiating and/or sustaining such phenomena. We present a landscape level analysis of the development of the current outbreak. Aerial survey assessments of tree mortality, projected onto discrete 12×12 km cells, were used as a proxy for insect population density. We examined whether the outbreak potentially originated from an epicenter and spread, or whether multiple localized populations erupted simultaneously at spatially disjunct locations. An aspatial cluster analysis of time series from 1990 to 2003 revealed four distinct time series patterns. Each time series demonstrated a general progression of increasing mountain pine beetle populations. Plotting the geographical locations of each temporal pattern revealed that the outbreak occurred first in an area of west‐central British Columbia, and then in an area to the east. The plot further revealed many localized infestations erupted in geographically disjunct areas, especially in the southern portion of the province. Autologistic regression analyses indicated a significant, positive association between areas where the outbreak first occurred and conservation lands. For example, the delineated area of west‐central British Columbia is comprised of three conservation parks and adjacent working forest. We further examined how population synchrony declines with distance at different population levels. Examination of the spatial dependence of temporal synchrony in population fluctuations during early, incipient years (i.e. 1990–1996) suggested that outbreaking mountain pine beetle populations are largely independent at scales >200 km during non‐epidemic periods. However, during epidemic years (i.e. 1999–2003), populations were clearly synchronous across the entire province, even at distances of up to 900 km. The epicentral pattern of population development can be used to identify and prioritize adjacent landscape units for both reactive and proactive management strategies intended to minimize mountain pine beetle impacts.     

Interactions Across Spatial Scales among Forest Dieback,Fire, and Erosion in Northern New Mexico Landscapes

Abstract Ecosystem patterns and disturbance processes at one spatial scale often interact with processes at another scale, and the result of such cross-scale interactions can be nonlinear dynamics with thresholds. Examples of cross-scale pattern-process relationships and interactions among forest dieback, fire, and erosion are illustrated from northern New Mexico (USA) landscapes, where long-term studies have recently documented all of these disturbance processes. For example, environmental stress, operating on individual trees, can cause tree death that is amplified by insect mortality agents to propagate to patch and then landscape or even regional-scale forest dieback. Severe drought and unusual warmth in the southwestern USA since the late 1990s apparently exceeded species-specific physiological thresholds for multiple tree species, resulting in substantial vegetation mortality across millions of hectares of woodlands and forests in recent years. Predictions of forest dieback across spatial scales are constrained by uncertainties associated with: limited knowledge of species-specific physiological thresholds; individual and site-specific variation in these mortality thresholds; and positive feedback loops between rapidly-responding insect herbivore populations and their stressed plant hosts, sometimes resulting in nonlinear “pest” outbreak dynamics. Fire behavior also exhibits nonlinearities across spatial scales, illustrated by changes in historic fire regimes where patch-scale grazing disturbance led to regional-scale collapse of surface fire activity and subsequent recent increases in the scale of extreme fire events in New Mexico. Vegetation dieback interacts with fire activity by modifying fuel amounts and configurations at multiple spatial scales. Runoff and erosion processes are also subject to scale-dependent threshold behaviors, exemplified by ecohydrological work in semiarid New Mexico watersheds showing how declines in ground surface cover lead to non-linear increases in bare patch connectivity and thereby accelerated runoff and erosion at hillslope and watershed scales. Vegetation dieback, grazing, and fire can change land surface properties and cross-scale hydrologic connectivities, directly altering ecohydrological patterns of runoff and erosion. The interactions among disturbance processes across spatial scales can be key drivers in ecosystem dynamics, as illustrated by these studies of recent landscape changes in northern New Mexico. To better anticipate and mitigate accelerating human impacts to the planetary ecosystem at all spatial scales, improvements are needed in our conceptual and quantitative understanding of cross-scale interactions among disturbance processes.     

The biogeography of kin discrimination across microbial neighbourhoods

The spatial distribution of potential interactants is critical to social evolution in all cooperative organisms. Yet the biogeography of microbial kin discrimination at the scales most relevant to social interactions is poorly understood. Here we resolve the microbiogeography of social identity and genetic relatedness in local populations of the model cooperative bacterium Myxococcus xanthus at small spatial scales, across which the potential for dispersal is high. Using two criteria of relatedness—colony‐merger compatibility during cooperative motility and DNA‐sequence similarity at highly polymorphic loci—we find that relatedness decreases greatly with spatial distance even across the smallest scale transition. Both social relatedness and genetic relatedness are maximal within individual fruiting bodies at the micrometre scale but are much lower already across adjacent fruiting bodies at the millimetre scale. Genetic relatedness was found to be yet lower among centimetre‐scale samples, whereas social allotype relatedness decreased further only at the metre scale, at and beyond which the probability of social or genetic identity among randomly sampled isolates is effectively zero. Thus, in M. xanthus, high‐relatedness patches form a rich mosaic of diverse social allotypes across fruiting body neighbourhoods at the millimetre scale and beyond. Individuals that migrate even short distances across adjacent groups will frequently encounter allotypic conspecifics and territorial kin discrimination may profoundly influence the spatial dynamics of local migration. Finally, we also found that the phylogenetic scope of intraspecific biogeographic analysis can affect the detection of spatial structure, as some patterns evident in clade‐specific analysis were masked by simultaneous analysis of all strains.     

Density dependence,spatial scale and patterning in sessile biota

Sessile biota can compete with or facilitate each other, and the interaction of facilitation and competition at different spatial scales is key to developing spatial patchiness and patterning. We examined density and scale dependence in a patterned, soft sediment mussel bed. We followed mussel growth and density at two spatial scales separated by four orders of magnitude. In summer, competition was important at both scales. In winter, there was net facilitation at the small scale with no evidence of density dependence at the large scale. The mechanism for facilitation is probably density dependent protection from wave dislodgement. Intraspecific interactions in soft sediment mussel beds thus vary both temporally and spatially. Our data support the idea that pattern formation in ecological systems arises from competition at large scales and facilitation at smaller scales, so far only shown in vegetation systems. The data, and a simple, heuristic model, also suggest that facilitative interactions in sessile biota are mediated by physical stress, and that interactions change in strength and sign along a spatial or temporal gradient of physical stress.     

Optimal configurations of spatial scale for grid cell firing under noise and uncertainty

We examined the accuracy with which the location of an agent moving within an environment could be decoded from the simulated firing of systems of grid cells. Grid cells were modelled with Poisson spiking dynamics and organized into multiple ‘modules’ of cells, with firing patterns of similar spatial scale within modules and a wide range of spatial scales across modules. The number of grid cells per module, the spatial scaling factor between modules and the size of the environment were varied. Errors in decoded location can take two forms: small errors of precision and larger errors resulting from ambiguity in decoding periodic firing patterns. With enough cells per module (e.g. eight modules of 100 cells each) grid systems are highly robust to ambiguity errors, even over ranges much larger than the largest grid scale (e.g. over a 500 m range when the maximum grid scale is 264 cm). Results did not depend strongly on the precise organization of scales across modules (geometric, co-prime or random). However, independent spatial noise across modules, which would occur if modules receive independent spatial inputs and might increase with spatial uncertainty, dramatically degrades the performance of the grid system. This effect of spatial uncertainty can be mitigated by uniform expansion of grid scales. Thus, in the realistic regimes simulated here, the optimal overall scale for a grid system represents a trade-off between minimizing spatial uncertainty (requiring large scales) and maximizing precision (requiring small scales). Within this view, the temporary expansion of grid scales observed in novel environments may be an optimal response to increased spatial uncertainty induced by the unfamiliarity of the available spatial cues.     

Scaling effects of grazing in a semi-arid grassland

Abstract. Previous studies have demonstrated relationships between spatial scale and spatial pattern and developed general hypotheses of scaling effects. Few studies, however, have examined the interactive relationship between scale and pattern-driving processes such as grazing. The goal of this study is to evaluate scale-dependent patterns across three spatial scales for three grazing intensities over 45 yr and to identify some mechanisms that may be associated with scale related differences. Correlation analysis and analysis of the coefficients of variation indicate that the relationships between units are dependent upon spatial scale and treatment. Across all grazing treatments, the relationship between units of the same scale becomes stronger as the spatial scale is increased. However, the rate of increase in the correlation coefficient is different for each treatment. The coefficient of variation responded inversely across scales with the greatest variation between small-scale units and little difference between the intermediate- and large scales. In addition to different relationships between units at each scale, differences in heterogeneity within treatments over time is illustrated by the relationship between small-scale units within each treatment and their associated larger scale units. The strongest relationship occurred in the heavily grazed treatments where correlation coefficients of small-scale units with intermediate- and large-scale units were ca. 0.60, indicating similar dynamics across scales. For the moderately grazed and ungrazed treatments this relationship varied from 0.40 to 0.47. Results from this study suggest that grazing alters scaling effects. Variability between small-scale units was greatest in the ungrazed treatment which had greater heterogeneity and less predictability than grazed treatments because of the influence of grazing on plant morphology, demography and composition. At the intermediate scale, relationships between units were fairly similar with the least variation occurring in the moderately grazed treatment. Alternatively, variation between large-scale units was greatest in the moderately grazed treatment because of the relationship between rest cycles, weather patterns, and patch grazing. Therefore, grazing can have a positive, a negative, or no influence on heterogeneity between units depending upon the scale of observation. Evaluation of long-term dynamics across these treatments at the same small spatial scale results in different variances within each treatment which may violate assumptions of some statistical and experimental designs. Therefore, evaluations of temporal dynamics should consider scale relative to the relationship between plant size, density and longevity (relative scale).     

Spatially explicit analyses unveil density dependence

Density-dependent processes are fundamental in the understanding of species population dynamics. Whereas the benefits of considering the spatial dimension in population biology are widely acknowledged, the implications of doing so for the statistical detection of spatial density dependence have not been examined. The outcome of traditional tests may therefore differ from those that include ecologically relevant locational information on both the prey species and natural enemy. Here, we explicitly incorporate spatial information on individual counts when testing for density dependence between an insect herbivore and its parasitoids. The spatially explicit approach used identified significant density dependence more frequently and in different instances than traditional methods. The form of density dependence detected also differed between methods. These results demonstrate that the explicit consideration of patch location in density-dependence analyses is likely to significantly alter current understanding of the prevalence and form of spatial density dependence in natural populations.     

The importance of spatial scale for trait–abundance relations

The concept of community assembly through trait‐based environmental filtering has played a key role in our understanding of how communities change over space and time, however, the importance of spatial scale in the filtering process remains unclear. We propose that different environmental filters may operate at different spatial scales, and that filters at finer scales would be nested within those acting at coarser scales. We tested for the existence of spatially nested sets of trait‐based filters in a temperate native grassland by applying the recently proposed maximum entropy (MaxEnt) approach to trait‐based community assembly, which we extend through a trait selection procedure. We found that different traits were important in influencing the abundances of species at the three different spatial scales examined (micro‐habitat, habitat, landscape), supporting the idea that trait based filtering processes operating at coarse spatial scales can be quite distinct from those operating at fine scales. Despite this result, we identified several traits which were frequently related to abundance at all spatial scales. Taken together, our results support the proposition that trait‐based environmental filters at finer spatial scales are nested within those operating at coarser scales. We compared our results to those obtained using a simpler trait‐by‐trait analytical approach (correlation analysis and MaxEnt on individual traits). The capacity for MaxEnt to incorporate multiple traits simultaneously provided unique insights into the important traits at each spatial scale and presents significant advantages over existing univariate and multivariate approaches.