An implicit approach to model plant infestation by insect pests

Various spatial approaches were developed to study the effect of spatial heterogeneities on population dynamics. We present in this paper a flux-based model to describe an aphid-parasitoid system in a closed and spatially structured environment, i.e. a greenhouse. Derived from previous work and adapted to host-parasitoid interactions, our model represents the level of plant infestation as a continuous variable corresponding to the number of plants bearing a given density of pests at a given time. The variation of this variable is described by a partial differential equation. It is coupled to an ordinary differential equation and a delay-differential equation that describe the parasitized host population and the parasitoid population, respectively. We have applied our approach to the pest Aphis gossypii and to one of its parasitoids, Lysiphlebus testaceipes, in a melon greenhouse. Numerical simulations showed that, regardless of the number and distribution of hosts in the greenhouse, the aphid population is slightly larger if parasitoids display a type III rather than a type II functional response. However, the population dynamics depend on the initial distribution of hosts and the initial density of parasitoids released, which is interesting for biological control strategies. Sensitivity analysis showed that the delay in the parasitoid equation and the growth rate of the pest population are crucial parameters for predicting the dynamics. We demonstrate here that such a flux-based approach generates relevant predictions with a more synthetic formalism than a common plant-by-plant model. We also explain how this approach can be better adapted to test different management strategies and to manage crops of several greenhouses.     

Spatially Explicit Modeling in Ecology: A Review

The use of spatially explicit models (SEMs) in ecology has grown enormously in the past two decades. One major advancement has been that fine-scale details of landscapes, and of spatially dependent biological processes, such as dispersal and invasion, can now be simulated with great precision, due to improvements in computer technology. Many areas of modeling have shifted toward a focus on capturing these fine-scale details, to improve mechanistic understanding of ecosystems. However, spatially implicit models (SIMs) have played a dominant role in ecology, and arguments have been made that SIMs, which account for the effects of space without specifying spatial positions, have an advantage of being simpler and more broadly applicable, perhaps contributing more to understanding. We address this debate by comparing SEMs and SIMs in examples from the past few decades of modeling research. We argue that, although SIMs have been the dominant approach in the incorporation of space in theoretical ecology, SEMs have unique advantages for addressing pragmatic questions concerning species populations or communities in specific places, because local conditions, such as spatial heterogeneities, organism behaviors, and other contingencies, produce dynamics and patterns that usually cannot be incorporated into simpler SIMs. SEMs are also able to describe mechanisms at the local scale that can create amplifying positive feedbacks at that scale, creating emergent patterns at larger scales, and therefore are important to basic ecological theory. We review the use of SEMs at the level of populations, interacting populations, food webs, and ecosystems and argue that SEMs are not only essential in pragmatic issues, but must play a role in the understanding of causal relationships on landscapes.     

Aggregate statistical measures and metapopulation dynamics

There are two main types of metapopulation models. Spatially implicit models are analytically tractable but neglect spatial heterogeneities. Spatially explicit models are more realistic but too complex. In this paper, I build a bridge between both approximations. I derive a new metapopulation model using a well-known technique in population genetics. Spatial heterogeneities are captured by an aggregate statistical measure of spatial correlation. When this correlation is zero, i.e., space is homogeneous, the model becomes the well-known Levins' model. As spatial correlation increases, equilibrium patch occupancy decreases from what would be expected under the spatially homogeneous assumption. I proceed by testing how well spatial complexities from a spatially explicit simulation can be encapsulated by such an aggregate statistical measure.     

Effects of perceptual and movement ranges on joint predator–prey distributions

We developed a spatially‐explicit individual‐based model to study how limited perceptual and movement ranges affect spatial predator–prey interactions. Earlier models of ‘predator–prey space games’ were often developed by modifying ideal free distribution models, which are spatially‐implicit and also assume that individuals are omniscient, although some more recent models have relaxed these assumptions. We found that under some conditions, the spatially‐explicit model generated similar predictions to previous models. However, the model showed that limited range in a spatially‐explicit context generated different predictions when 1) predator density and range are both small, and 2) when the predator movement range varied while the prey range was small. The model suggests that the differences were the result of 1) movement range changing the value of information sources and thus changing the behavior of individual predators and prey and 2) movement range limiting the ability of individuals to exploit the environment.     

Universal scaling of species‐abundance distributions across multiple scales

The scale‐dependent species abundance distribution (SAD) is fundamental in ecology, but few spatially explicit models of this pattern have thus far been studied. Here we show spatially explicit neutral model predictions for SADs over a wide range of spatial scales, which appear to match empirical patterns qualitatively. We find that the assumption of a log‐series SAD in the metacommunity made by spatially implicit neutral models can be justified with a spatially explicit model in the large area limit. Furthermore, our model predicts that SADs on multiple scales are characterized by a single, compound parameter that represents the ratio of the survey area to the species’ average biogeographic range (which is in turn set by the speciation rate and the dispersal distance). This intriguing prediction is in line with recent empirical evidence for a universal scaling of the species‐area curve. Hence we hypothesize that empirical SAD patterns will show a similar universal scaling for many different taxa and across multiple spatial scales.     

Local variation in plant quality influences large‐scale population dynamics

Spatial variation in ecological systems can arise both as a consequence of variation in the quality and availability of resources and as an emergent property of spatially structured interactions. We used a spatially explicit model to simulate populations of herbivore hosts and their parasitoids in landscapes with different levels of variance in plant patch quality and different spatial arrangements of high‐ and low‐quality plant patches. We found that even small variation in patch quality at a fine spatial scale decreased overall herbivore populations, as parasitoid populations on low‐quality plant patches were subsidized by those from high‐quality neighbors. On landscapes with large, homogeneous regions of high‐ and low‐quality plant patches, herbivore populations increased with variation in patch quality. Overall, our results demonstrate that local variation in resource quality profoundly influences global population dynamics. In particular, fine‐scale variation in plant patch quality enhanced biological control of herbivores by parasitoids, suggesting that adding back plant genetic variation into perennial production systems may enhance the biological control of herbivores by their natural enemies.     

Coevolution across landscapes: a spatially explicit model of parasitoid-host coevolution

The geographic mosaic theory of coevolution suggests that population spatial structure may have a strong impact on coevolutionary dynamics. Therefore, coevolution must be studied across geographic scales, not just in single populations. To examine the impact of movement rate on coevolutionary dynamics, we developed a spatially explicit model of host–parasitoid coevolution. We described space as a coupled-map lattice and assumed that resistance (defined as the ability of a host to encapsulate a parasitoid egg) and virulence (defined as the successful parasitization of a host) traits were graded and costly. The model explicitly detailed population and evolutionary dynamics. When holding all parameters constant and varying only the movement rate of the host and parasitoid, profoundly different dynamics were observed. We found that fluctuations in the mean levels of resistance and virulence in the global population were greatest when the movement rate of the host and parasitoid was high. In addition, we found that the variation in resistance and virulence levels among neighboring patches was greatest when the movement rates of the host and parasitoid was low. However, as the distance among patches increased, so did the variation in resistance and virulence levels regardless of movement rate. These generalizations did not hold when spatial patterns in the distribution of resistance and virulence traits, such as spirals, were observed. Finally, we found that the evolution of resistance and virulence caused the abundance of hosts to increase and the abundance of parasitoids to decrease. As a result, the spatial distribution of hosts and parasitoids was influenced.     

A simulation study of population interaction between the greenhouse whitefly,Trialeurodes vaporariorum Westwood (Homoptera: Aleyrodidae), and the parasitoidEncarsia formosa gahan (Hymenoptera: Aphelinidae) I. Description of the model

A simple simulation model was developed to simulate the population dynamics of the system of the greenhouse whitefly (Trialeurodes vaporariorumWestwood ) and the parasitoid Encarsia formosaGahan . On the assumption that temperature is constant, the whitefly population was described as theLeslie Matrix model. Parasitization and host feeding by the parasitoid population were modelled by means of a modified disc equation. The validity of the model was demonstrated by comparing the predictions of the model with the observed values obtained in greenhouse experiments.     

Spatial and temporal heterogeneity explain disease dynamics in a spatially explicit network model

There is an increasing recognition that individual-level spatial and temporal heterogeneity may play an important role in metapopulation dynamics and persistence. In particular, the patterns of contact within and between aggregates (e.g., demes) at different spatial and temporal scales may reveal important mechanisms governing metapopulation dynamics. Using 7 years of data on the interaction between the anther smut fungus (Microbotryum violaceum) and fire pink (Silene virginica), we show how the application of spatially explicit and implicit network models can be used to make accurate predictions of infection dynamics in spatially structured populations. Explicit consideration of both spatial and temporal organization reveals the role of each in spreading risk for both the host and the pathogen. This work suggests that the application of spatially explicit network models can yield important insights into how heterogeneous structure can promote the persistence of species in natural landscapes.     

Modelling forest dynamics: a perspective from point process methods

This paper reviews the main applications of (marked) point process theory in forestry including functions to analyse spatial variability and the main (marked) point process models. Although correlation functions do describe spatial variability at distinct range of scale, they are clearly restricted to the analysis of few dominant species since they are based on pairwise analysis. This has over-simplified the spatial analysis of complex forest dynamics involving "large" number of species. Moreover, although process models can reproduce, to some extent, real forest spatial patterns of trees, the biological forest-ecological interpretation of the resulting spatial structures is difficult since these models usually lack of biological realism. This problem gains in strength as usually most of these point process models are defined in terms of purely spatial relationships, though in real life, forest develop through time. We thus aim to discuss the applicability of such formulations to analyse and simulate "real" forest dynamics and unwrap their shortcomes. We present a unified approach of modern spatially explicit forest growth models. Finally, we focus on a continuous space-time stochastic process as an alternative approach to generate marked point patterns evolving through space and time.     

Generalizing Levins metapopulation model in explicit space: models of intermediate complexity

A recent study [Harding and McNamara, 2002. A unifying framework for metapopulation dynamics. Am. Nat. 160, 173-185] presented a unifying framework for the classic Levins metapopulation model by incorporating several realistic biological processes, such as the Allee effect, the Rescue effect and the Anti-rescue effect, via appropriate modifications of the two basic functions of colonization and extinction rates. Here we embed these model extensions on a spatially explicit framework. We consider population dynamics on a regular grid, each site of which represents a patch that is either occupied or empty, and with spatial coupling by neighborhood dispersal. While broad qualitative similarities exist between the spatially explicit models and their spatially implicit (mean-field) counterparts, there are also important differences that result from the details of local processes. Because of localized dispersal, spatial correlation develops among the dynamics of neighboring populations that decays with distance between patches. The extent of this correlation at equilibrium differs among the metapopulation types, depending on which processes prevail in the colonization and extinction dynamics. These differences among dynamical processes become manifest in the spatial pattern and distribution of “clusters” of occupied patches. Moreover, metapopulation dynamics along a smooth gradient of habitat availability show significant differences in the spatial pattern at the range limit. The relevance of these results to the dynamics of disease spread in metapopulations is discussed.     

The effects of spatial and temporal environmental heterogeneities on persistence in a laboratory experimental community

Among many stabilizing factors for community dynamics, spatial and temporal heterogeneities have been widely considered in recent years as two of the most important properties. However, the difference between the two types of heterogeneities have not been studied, except for Clark and Yoshimura (1993). We evaluated experimentally the effect of temporal and spatial heterogeneities on the persistence of a biological community. The experimental communities consisted of one parasitic wasp species, one bean weevil species, and two kinds of bean. Temporal and spatial heterogeneities of experimental communities were generated by kinds and timing of bean supply. Of all the experimental communities, the most persistent community was a temporally and spatially homogeneous community with Red Kidney bean as primary resource. Compared to spatially heterogeneous communities, temporally heterogeneous communities were more persistent. These results were easily explained by considering the attack rate of parasitic wasps and the difference between arithmetic and geometric means. In order to discuss the relative importance of environmental heterogeneity and the mode of biological interaction on community persistence, we have to measure the degree of environmental heterogeneity as the rate of change of the strength of interspecific interactions.     

Optimal control of the spatial allocation of COVID-19 vaccines: Italy as a case study

While campaigns of vaccination against SARS-CoV-2 are underway across the world, communities face the challenge of a fair and effective distribution of a limited supply of doses. Current vaccine allocation strategies are based on criteria such as age or risk. In the light of strong spatial heterogeneities in disease history and transmission, we explore spatial allocation strategies as a complement to existing approaches. Given the practical constraints and complex epidemiological dynamics, designing effective vaccination strategies at a country scale is an intricate task. We propose a novel optimal control framework to derive the best possible vaccine allocation for given disease transmission projections and constraints on vaccine supply and distribution logistics. As a proof-of-concept, we couple our framework with an existing spatially explicit compartmental COVID-19 model tailored to the Italian geographic and epidemiological context. We optimize the vaccine allocation on scenarios of unfolding disease transmission across the 107 provinces of Italy, from January to April 2021. For each scenario, the optimal solution significantly outperforms alternative strategies that prioritize provinces based on incidence, population distribution, or prevalence of susceptibles. Our results suggest that the complex interplay between the mobility network and the spatial heterogeneities implies highly non-trivial prioritization strategies for effective vaccination campaigns. Our work demonstrates the potential of optimal control for complex and heterogeneous epidemiological landscapes at country, and possibly global, scales.     

Roots in space: a spatially explicit model for below-ground competition in plants

Game theory provides an untapped framework for predicting how below-ground competition will influence root proliferation in a spatially explicit environment. We model root competition for space as an evolutionary game. In response to nutrient competition between plants, an individual's optimal strategy (the spatial distribution of root proliferation) depends on the rooting strategies of neighbouring plants. The model defines and predicts the fundamental (in the absence of competition) and realized (in the presence of competition) root space of an individual plant. Overlapping fundamental root spaces guarantee smaller, yet still overlapping, realized root spaces as individuals concede some but not all space to a neighbour's roots. Root overlap becomes an intentional consequence of the neighbouring plants playing a nutrient foraging game. Root proliferation and regions of root overlap should increase with soil fertility, decline with the distance cost of root production (e.g. soil compactness) and shift with competitive asymmetries. Seemingly erratic patterns of root proliferation and root overlap become the expected outcome of nutrient foraging games played in soils with small-scale heterogeneities in nutrient availability.     

Mechanistic home range models capture spatial patterns and dynamics of coyote territories in Yellowstone

Patterns of space-use by individuals are fundamental to the ecology of animal populations influencing their social organization, mating systems, demography and the spatial distribution of prey and competitors. To date, the principal method used to analyse the underlying determinants of animal home range patterns has been resource selection analysis (RSA), a spatially implicit approach that examines the relative frequencies of animal relocations in relation to landscape attributes. In this analysis, we adopt an alternative approach, using a series of mechanistic home range models to analyse observed patterns of territorial space-use by coyote packs in the heterogeneous landscape of Yellowstone National Park. Unlike RSAs, mechanistic home range models are derived from underlying correlated random walk models of individual movement behaviour, and yield spatially explicit predictions for patterns of space-use by individuals. As we show here, mechanistic home range models can be used to determine the underlying determinants of animal home range patterns, incorporating both movement responses to underlying landscape heterogeneities and the effects of behavioural interactions between individuals. Our analysis indicates that the spatial arrangement of coyote territories in Yellowstone is determined by the spatial distribution of prey resources and an avoidance response to the presence of neighbouring packs. We then show how the fitted mechanistic home range model can be used to correctly predict observed shifts in the patterns of coyote space-use in response to perturbation.     

The ecology of predispersal insect herbivory on tree reproductive structures in natural forest ecosystems

Plant-insect interactions are key model systems to assess how some species affect the distribution, the abundance, and the evolution of others. Tree reproductive structures represent a critical resource for many insect species, which can be likely drivers of demography, spatial distribution, and trait diversification of plants. In this review, we present the ecological implications of predispersal herbivory on tree reproductive structures by insects (PIHR) in forest ecosystems. Both insect's and tree's perspectives are addressed with an emphasis on how spatiotemporal variation and unpredictability in seed availability can shape such particular plant-animal interactions. Reproductive structure insects show strong trophic specialization and guild diversification. Insects evolved host selection and spatiotemporal dispersal strategies in response to variable and unpredictable abundance of reproductive structures in both space and time. If PIHR patterns have been well documented in numerous systems, evidences of the subsequent demographic and evolutionary impacts on tree populations are still constrained by time-scale challenges of experimenting on such long-lived organisms, and modeling approaches of tree dynamics rarely consider PIHR when including biotic interactions in their processes. We suggest that spatially explicit and mechanistic approaches of the interactions between individual tree fecundity and in sect dynamics will clarify predictions of the demogenetic implications of PIHR in tree populations. In a global change context, further experimental and theoretical contributions to the likelihood of life-cycle disruptions between plants and their specialized herbivores, and to how these changes may gen erate novel dynamic patterns in each partner of the interaction are increasingly critical.     

The highs and lows of dispersal: how connectivity and initial population size jointly shape establishment dynamics in discrete landscapes

Identifying the main factors driving introduced populations to establishment is a major challenge of invasion biology. Due to their small initial size, introduced populations are most vulnerable to extinction because of demographic stochasticity or Allee effects. While an increase in initial population size is known to increase establishment success, much remains to be understood regarding its interplay with connectivity in spatially structured environments. In order to better understand how demographic mechanisms interact at such spatial scale, we developed a stochastic model of population dynamics in discrete space to investigate the effect of connectivity and initial population size on establishment. The predictions derived from the model were then tested using experimental introductions of an insect parasitoid (Trichogramma chilonis) in spatially structured laboratory microcosms. Both theoretical and experimental results demonstrated that the connectivity of the introduction site had 1) a deleterious effect in the first generation when the introduced population was small and 2) a beneficial impact brought about by metapopulation effects in the subsequent generations. Interestingly, populations displayed a weakly pushed invasion pattern promoting early establishment, which was mainly underpinned by dispersal stochasticity and the discrete nature of the landscape. These results shed light on the critical influence of landscape connectivity on establishment dynamics.     

Estimating and interpreting migration of Amazonian forests using spatially implicit and semi‐explicit neutral models

With many sophisticated methods available for estimating migration, ecologists face the difficult decision of choosing for their specific line of work. Here we test and compare several methods, performing sanity and robustness tests, applying to large‐scale data and discussing the results and interpretation. Five methods were selected to compare for their ability to estimate migration from spatially implicit and semi‐explicit simulations based on three large‐scale field datasets from South America (Guyana, Suriname, French Guiana and Ecuador). Space was incorporated semi‐explicitly by a discrete probability mass function for local recruitment, migration from adjacent plots or from a metacommunity. Most methods were able to accurately estimate migration from spatially implicit simulations. For spatially semi‐explicit simulations, estimation was shown to be the additive effect of migration from adjacent plots and the metacommunity. It was only accurate when migration from the metacommunity outweighed that of adjacent plots, discrimination, however, proved to be impossible. We show that migration should be considered more an approximation of the resemblance between communities and the summed regional species pool. Application of migration estimates to simulate field datasets did show reasonably good fits and indicated consistent differences between sets in comparison with earlier studies. We conclude that estimates of migration using these methods are more an approximation of the homogenization among local communities over time rather than a direct measurement of migration and hence have a direct relationship with beta diversity. As betadiversity is the result of many (non)‐neutral processes, we have to admit that migration as estimated in a spatial explicit world encompasses not only direct migration but is an ecological aggregate of these processes. The parameter m of neutral models then appears more as an emerging property revealed by neutral theory instead of being an effective mechanistic parameter and spatially implicit models should be rejected as an approximation of forest dynamics.