A spatially explicit approach to estimating species occupancy and spatial correlation

Causal assumptions and causal inference in ecological experiments

Causal inferences from experimental data are often justified based on treatment randomization. However, inferring causality from data also requires complementary causal assumptions, which have been formalized by scholars of causality but not widely discussed in ecology. While ecologists have recognized challenges to inferring causal relationships in experiments and developed solutions, they lack a general framework to identify and address them. We review four assumptions required to infer causality from experiments and provide design-based and statistically based solutions for when these assumptions are violated. We conclude that there is no clear demarcation between experimental and non-experimental designs. This insight can help ecologists design better experiments and remove barriers between experimental and observational scholarship in ecology.

Biological control of a predator–prey system through provision of an infected predator

Epidemic transmission has a substantial effect on the dynamics and stability of the predator–prey system, in which the transmission rate plays an important role. The probabilistic cellular automaton (PCA) approach is used to investigate the spatiotemporal dynamics of a predator–prey system with the infected predator. Remarkably, it is impossible to achieve a coexistence state of prey, susceptible predators, and infected predators in a spatial population. This is different from the analysis from a non-spatial population with the mean-field approximation, where Hopf bifurcation arises and the interior equilibrium becomes unstable, and a periodic solution appears with the increasing infection rate. The results show that the introduction of the infected predator with a high transmission rate is beneficial for the persistence of the prey population in space. However, a low transmission rate will promote the coexistence state of the prey and the susceptible predator populations. In summary, it is possible to develop management strategies to manipulate the transmission rate of the infected predator for the benefit of biological control.

Spatial Segregation Facilitates the Coexistence of Tree Species in Temperate Forests

Competition between plants has an important role during the natural succession of forest communities. Niche separation between plants can reduce such interspecific competition and enable multispecies plant to achieve coexistence, although this proposition has rarely been supported in experiments. Plant competition can be captured by spatial segregation of the competing species to avoid fierce direct conflicts for nutrients and light. We investigated a site of 400 m × 1000 m in Beijing Pine Mountain National Nature Reserve that was established for protecting Chinese pine and some rare fungi. Six dominant tree species (Fraxinus chinensis Roxb., Syringa reticulata (Blume) H. Hara var. amurensis (Rupr.) J. S. Pringle, Quercus mongolica Fisch. ex Ledeb., Armeniaca sibirica (L.) Lam., Pinus tabuliformis Carrière, and Ulmus pumila L.) were individually marked. Metrics of spatial segregation, based on the theory of spatial point process, were calculated to detect spatial competition. The corresponding type (species)-specific probabilities and the p-values from a spatially implicit test revealed significant overall spatial segregation between the six tree species. We further used the cross-type L-function to check the spatial correlation between Chinese pine and the other tree species, and detected a significant spatial repulsion relationship with four other tree species. Our study shows that each of the six dominant tree species occupies a different subarea in the landscape to effectively reduce direct spatial competition. We thus argue that patchy distributions of different tree species could be common in late forest community succession, and the coexistence of plants could be maintained over a large spatial scale. Management intervention, such as thinning the densities of dominant tree species, could be used to foster species coexistence and ensure the productivity of commercial stands.

Spatial homogeneity of benthic macrofaunal biodiversity across small spatial scales

Spatial heterogeneity of biodiversity has been extensively researched, but its spatial homogeneity is virtually unstudied. An intertidal seagrass system at Knysna (South Africa) known to display spatially homogeneous macrobenthic species density at scales ≥0.0275 m² was re-investigated at four smaller spatial grains (0.0015 m² - 0.0095 m²) via a lattice of 8 × 8 stations within a 0.2 ha area. The aim was to investigate the null hypothesis that spatial homogeneity of species density is not a fixed emergent assemblage property but breaks down at small spatial grains within given spatial extents. Although assemblage abundance was significantly heterogeneous at all spatial grains investigated, both species density and functional-group density were significantly homogeneous across those same scales; observed densities not departing from those expected on the basis of independent assortment. Spatial homogeneity is therefore an emergent assemblage property within given spatial extents at Knysna and probably at equivalent sites elsewhere. Equivalent species density in South Africa, Australia and the UK at spatial grains <0.03 m², however, is a scale-related sampling artefact, as may be temporal homogeneity of species density at Knysna over a 3 year period, but close similarity in shape of their species occupancy distributions remains unexplained.

Estimating tree height-diameter models with the Bayesian method

Six candidate height-diameter models were used to analyze the height-diameter relationships. The common methods for estimating the height-diameter models have taken the classical (frequentist) approach based on the frequency interpretation of probability, for example, the nonlinear least squares method (NLS) and the maximum likelihood method (ML). The Bayesian method has an exclusive advantage compared with classical method that the parameters to be estimated are regarded as random variables. In this study, the classical and Bayesian methods were used to estimate six height-diameter models, respectively. Both the classical method and Bayesian method showed that the Weibull model was the "best" model using data1. In addition, based on the Weibull model, data2 was used for comparing Bayesian method with informative priors with uninformative priors and classical method. The results showed that the improvement in prediction accuracy with Bayesian method led to narrower confidence bands of predicted value in comparison to that for the classical method, and the credible bands of parameters with informative priors were also narrower than uninformative priors and classical method. The estimated posterior distributions for parameters can be set as new priors in estimating the parameters using data2.

Scale dependency of biocapacity and the fallacy of unsustainable development

Area-based information obtained from remote sensing and aerial photography is often used in studies on ecological footprint and sustainability, especially in calculating biocapacity. Given the importance of the modifiable areal unit problem (MAUP; i.e. the scale dependency of area-based information), a comprehensive understanding of how the changes of biocapacity across scales (i.e. the resolution of data) is pivotal for regional sustainable development. Here, we present case studies on the effect of spatial scales on the biocapacity estimated for two typical river basin and watershed in Northwest China. The analysis demonstrated that the area sizes of major land covers and subsequently biocapacity showed strong signals of scale dependency, with minor land covers in the region shrinking while major land covers expanding when using large-grain (low resolution) data. The relationship between land cover sizes and their change ratio across scales was shown to follow a logarithm function. The biocapacity estimated at 10 × 10 km resolution is 10% lower than the one estimated at 1 × 1 km resolution, casting doubts on many regional and global studies which often rely on coarse scale datasets. Our results not only suggest that fine-scale biocapacity estimates can be extrapolated from coarse-scale ones according to the specific scale-dependent patterns of land covers, but also serve as a reminder that conclusions of regional and global un-sustainability derived from low-resolution datasets could be a fallacy due to the MAUP.

On a population pathogen model incorporating species dispersal with temporal variation in dispersal rate

In the present paper, we consider a mathematical model of ecosystem population interaction where the population suffers from a susceptible-infectious-susceptible disease. Dispersal of both the susceptible and the infective is incorporated using reaction-diffusion equations. We first study the stability criteria of the basic (non-spatial) model around the disease-free and the infected steady states. We find that the loss rate of the infective species controls disease prevalence. Also without predation pressure, the disease will continue to exist among the population. Then we analyze the spatial model with species dispersal in constant as well as in time-varying form. It is observed that though constant dispersal is unable to generate diffusion-driven instability, dispersal with sinusoidal variation in dispersion rate can generate diffusive instability when the wave number of the perturbation lies within a given range. Numerical simulations are performed to illustrate analytical studies.

Downscaling species occupancy from coarse spatial scales

The measurement and prediction of species' populations at different spatial scales is crucial to spatial ecology as well as conservation biology. An efficient yet challenging goal to achieve such population estimates consists of recording empirical species' presence and absence at a specific regional scale and then trying to predict occupancies at finer scales. So far the majority of the methods have been based on particular species' distributional features deemed to be crucial for downscaling occupancy. However, only a minority of them have dealt explicitly with specific spatial features. Here we employ a wide class of spatial point processes, the shot noise Cox processes (SNCP), to model species occupancies at different spatial scales and show that species' spatial aggregation is crucial for predicting population estimates at fine scales starting from coarser ones. These models are formulated in continuous space and locate points regardless of the arbitrary resolution that one employs to study the spatial pattern. We compare the performances of nine models, calibrated at regional scales and demonstrate that a very simple class of SNCP, the Thomas process, is able to outperform other published models in predicting occupancies down to areas four orders of magnitude smaller than the ones employed for the parameterization. We conclude by explaining the ability of the approach to infer spatially explicit information from spatially implicit measures, the potential of the framework to combine niche and spatial models, and the possibility of reversing the method to allow upscaling.

A point-process model for variance-occupancy-abundance relationships

The relationship between species abundance, the variance of the number of individuals, and species occupancy is a fundamental ecological characteristic of a community. Moreover, this relationship varies across scales, and any model for the variance-occupancy-abundance (VOA) relationship has to address its scale dependency in a consistent way. In this study, point-process theory was used to define a multiscale model that jointly predicts the VOA relationship across scales in a consistent way. This provides a tool to jointly analyze data sets collected at different scales and to give insights into the biological processes underlying the VOA relationship. This model can also account for different types of individual spatial pattern (clustered, random, or regular). Three stand-mapping data sets of tree species in tropical rain forests were used to assess the relevance of this model. When compared with four existing models, the model based on point-process theory provided the best fit to the data and was the most often ranked as the model with the best predictive performance.

Extrapolating population size from the occupancy-abundance relationship and the scaling pattern of occupancy

The estimation of species abundances at regional scales requires a cost-efficient method that can be applied to existing broadscale data. We compared the performance of eight models for estimating species abundance and community structure from presence-absence maps of the southern African avifauna. Six models were based on the intraspecific occupancy-abundance relationship (OAR); the other two on the scaling pattern of species occupancy (SPO), which quantifies the decline in species range size when measured across progressively finer scales. The performance of these models was examined using five tests: the first three compared the predicted community structure against well-documented macroecological patterns; the final two compared published abundance estimates for rare species and the total regional abundance estimate against predicted abundances. Approximately two billion birds were estimated as occurring in South Africa, Lesotho, and Swaziland. SPO models outperformed the OAR models, due to OAR models assuming environmental homogeneity and yielding scale-dependent estimates. Therefore, OAR models should only be applied across small, homogenous areas. By contrast, SPO models are suitable for data at larger spatial scales because they are based on the scale dependence of species range size and incorporate environmental heterogeneity (assuming fractal habitat structure or performing a Bayesian estimate of occupancy). Therefore, SPO models are recommended for assemblage-scale regional abundance estimation based on spatially explicit presence-absence data.

Patch-occupancy modeling as a method for monitoring changes in forest floristics: a case study in southeastern Australia

The ability to monitor changes in biodiversity is fundamental to demonstrating sustainable management practices of natural resources. Disturbance studies generally focus on responses at the plot scale, whereas landscape-scale responses are directly relevant to the development of sustainable forest management. Modeling changes in occupancy is one way to monitor landscape-scale responses. We used understory vegetation data collected over 16 years from a long-term study site in southeastern Australia. The site was subject to timber harvesting and frequent prescribed burning. We used occupancy models to examine the impacts of these disturbances on the distribution of 50 species of plants during the study. Timber harvesting influenced the distribution of 9 species, but these effects of harvesting were generally lost within 14 years. Repeated prescribed fire affected 22 species, but the heterogeneity of the burns reduced the predicted negative effects. Twenty-two species decreased over time independent of treatment, and only 5 species increased over time. These changes probably represent a natural response to a wildfire that occurred in 1973, 13 years before the study began. Occupancy modeling is a useful and flexible technique for analyzing monitoring data and it may also be suitable for inclusion within an adaptive-management framework for forest management.

Beta-diversity of geometrid moths from northern Borneo: effects of habitat, time and space

1. Spatial patterns of beta-diversity, an important property of species communities, are less well-studied than those of local species richness, particularly in insects from tropical rainforests. 2. We use geometrid moth samples from northern Borneo to quantify ensemble turnover across distances of > 700 km, consider habitat- and sampling-related impacts on their composition, and evaluate remaining spatial patterns in the data. 3. Geometrid moth ensembles from Borneo are shaped by environmental parameters such as elevation and habitat disturbance, by temporal factors acting at small (mediated by weather) and large scales (i.e. changes over decades), and by methodological differences of sampling (related to the nightly flight times of species). 4. These parameters explain a large portion of the spatial structure of ensemble composition, but residual variation still contains a pattern that is tentatively best explained by geographical distance, particularly at distances < 20 km. 5. Patterns of species turnover indicate no evidence for biotic homogenization due to human-caused degradation of habitats. Beta-diversity plays a crucial part in mediating the regional diversity of geometrids on Borneo.

A self-similarity model for the occupancy frequency distribution

The shapes of interspecific range-size distributions at scales finer than the geographic range are highly variable. However, no numerical model has been developed as a basis for understanding this variation. Using self-similarity conditions, we present an occupancy probability transition (OPT) model to investigate the effect of sampling scale (i.e. sample grain) and species saturation (strongly positively correlated with the fractal dimension) on the shape of occupancy frequency distributions (fine scale expression of range-size distributions). In accordance with empirical observations, the model showed that core-modes are likely to be rare in occupancy frequency distributions. The modal occupancy shifted from core to satellite with an increase in sample grain (from coarse scale to fine scale) at a linear rate after log-transformation of occupancy. Saturation coefficients above a particular threshold generated multimodality. Bimodal distributions arose from a combination of different occupancy probability distributions (OPDs), with species-specific saturation coefficients generating occupancy frequency distributions of the shape commonly observed empirically, i.e. bimodal with a dominant satellite mode. This is a consequence of the statistical properties of the OPD, and is also largely insensitive to species richness. The OPT model thus provides a null model for the shape of occupancy frequency distributions. Furthermore, it demonstrates that the sample grain of a study, sampling adequacy (based on a linear sampling assumption) and the distribution of species saturation coefficients in a community are together largely able to explain the patterns observed in empirical occupancy frequency distributions.

Spatial Patterns of Prisoner’s Dilemma Game in Metapopulations

Because to defect is the evolutionary stable strategy in the prisoner's dilemma game (PDG), understanding the mechanism generating and maintaining cooperation in PDG, i.e. the paradox of cooperation, has intrinsic significance for understanding social altruism behaviors. Spatial structure serves as the key to this dilemma. Here, we build the model of spatial PDG under a metapopulation framework: the sub-populations of cooperators and defectors obey the rules in spatial PDG as well as the colonization-extinction process of metapopulations. Using the mean-field approximation and the pair approximation, we obtain the differential equations for the dynamics of occupancy and spatial correlation. Cellular automaton is also built to simulate the spatiotemporal dynamics of the spatial PDG in metapopulations. Join-count statistics are used to measure the spatial correlation as well as the spatial association of the metapopulation. Simulation results show that the distribution is self-organized and that it converges to a static boundary due to the boycotting of cooperators to defectors. Metapopulations can survive even when the colonization rate is lower than the extinction rate due to the compensation of cooperation rewards for extinction debt. With a change of parameters in the model, a metapopulation can consist of pure cooperators, pure defectors, or cooperator-defector coexistence. The necessary condition of cooperation evolution is the local colonization of a metapopulation. The spatial correlation between the cooperators tends to be weaker with the increase in the temptation to defect and the habitat connectivity; yet the spatial correlation between defectors becomes stronger. The relationship between spatial structure and the colonization rate is complicated, especially for cooperators. The metapopulation may undergo a temporary period of prosperity just before the extinction, even while the colonization rate is declining.