Geographical variation in the spatial synchrony of a forest-defoliating insect: isolation of environmental and spatial drivers

Despite the pervasiveness of spatial synchrony of population fluctuations in virtually every taxon, it remains difficult to disentangle its underlying mechanisms, such as environmental perturbations and dispersal. We used multiple regression of distance matrices (MRMs) to statistically partition the importance of several factors potentially synchronizing the dynamics of the gypsy moth, an invasive species in North America, exhibiting outbreaks that are partially synchronized over long distances (approx. 900 km). The factors considered in the MRM were synchrony in weather conditions, spatial proximity and forest-type similarity. We found that the most likely driver of outbreak synchrony is synchronous precipitation. Proximity played no apparent role in influencing outbreak synchrony after accounting for precipitation, suggesting dispersal does not drive outbreak synchrony. Because a previous modelling study indicated weather might indirectly synchronize outbreaks through synchronization of oak masting and generalist predators that feed upon acorns, we also examined the influence of weather and proximity on synchrony of acorn production. As we found for outbreak synchrony, synchrony in oak masting increased with synchrony in precipitation, though it also increased with proximity. We conclude that precipitation could synchronize gypsy moth populations directly, as in a Moran effect, or indirectly, through effects on oak masting, generalist predators or diseases.     

Population and individual level of masting in a fleshy-fruited tree

Masting is usually considered as a population phenomenon but it results from individuals?? reproductive patterns. Studies of individual patterns of seed production and their synchrony are essential to an understanding of the mechanisms of masting. The aim of this study was to find the relationship between population and individual levels of masting. We examined individuals?? contribution to masting, considering their endogenous cycles, interannual variability and associated weather cues, as well as inter-individual synchrony of fruit production. We studied masting of Sorbus aucuparia L., which in Europe is one of the most common trees bearing fleshy fruits and is strongly affected by a specialized seed predator. The data are 11-year measurements of fruit production of 250 individuals distributed on a 27-ha area of subalpine forest in the Western Carpathians (Poland). Population- and individual-level interannual variability of fruit production was moderate. Synchrony among individuals was relatively high for all years, but the trees were much less synchronized in heavy crop years than in years of low fruit production. Weak synchrony among trees for heavy production years suggests that the predator satiation hypothesis does not explain the observed masting behavior. Fruit production, both at individual and at population level, was highly correlated with weather conditions. However, the presence of masting cannot be fully explained by the resource-matching hypothesis either. We suggest that adverse weather conditions effectively limit fruit production, causing high inter-individual synchrony in low crop years, whereas the unsynchronized heavy crop years seem to have been affected by individually available resources.     

Masting in ponderosa pine: comparisons of pollen and seed over space and time

Many plant species exhibit variable and synchronized reproduction, or masting, but less is known of the spatial scale of synchrony, effects of climate, or differences between patterns of pollen and seed production. We monitored pollen and seed cone production for seven Pinus ponderosa populations (607 trees) separated by up to 28?km and 1,350?m in elevation in Boulder County, Colorado, USA for periods of 4?C31?years for a mean per site of 8.7?years for pollen and 12.1 for seed cone production. We also analyzed climate data and a published dataset on 21?years of seed production for an eighth population (Manitou) 100?km away. Individual trees showed high inter-annual variation in reproduction. Synchrony was high within populations, but quickly became asynchronous among populations with a combination of increasing distance and elevational difference. Inter-annual variation in temperature and precipitation had differing influences on seed production for Boulder County and Manitou. We speculate that geographically variable effects of climate on reproduction arise from environmental heterogeneity and population genetic differentiation, which in turn result in localized synchrony. Although individual pines produce pollen and seed, only one-third of the covariation within trees was shared. As compared to seed cones, pollen had lower inter-annual variation at the level of the individual tree and was more synchronous. However, pollen and seed production were similar with respect to inter-annual variation at the population level, spatial scales of synchrony and associations with climate. Our results show that strong masting can occur at a localized scale, and that reproductive patterns can differ between pollen and seed cone production in a hermaphroditic plant.     

Modeling spatial dynamics of episodic and synchronous reproduction by plant populations: the effect of small-scale pollen coupling and large-scale climate

Many plant species show masting, intermittent and synchronized reproduction at population level. In the present paper, we review the resource-based model providing a theoretically plausible physiological mechanism underlying masting. In the model, a non-linear allocation of energy reserves is considered: plants accumulate photosynthate every year, produce flowers when the energy reserve level exceeds a threshold, and set seeds at a rate limited by pollen availability. The model predicted that individual plants alter their reproductive dynamics from annual to intermittent depending on how heavily the plant invests resource in reproduction. When fruit production is limited by the availability of outcross pollen, a plant population showed diverse reproductive behavior such as completely synchronized or desynchronized reproduction. Spatial scale of reproductive synchrony tended to be a few times larger than the range of direct pollen exchange. Impact of climatic fluctuation correlated at a large spatial scale was also investigated as an alternative synchronizing factor. The variation in annual productivity and the reproductive threshold induced from climatic fluctuation was accounted for by incorporating an additional term in the model. When plants show a 2 year reproductive cycle, highly synchronized reproduction at a regional scale was induced due to correlated environmental forcing, but reproductive synchrony with long intermast periods was realized only when pollen coupling and environmental forcing were at work. These results suggest that distance-dependent processes, such as pollen exchange between nearby trees, induce synchrony at a local scale and external environmental forcing correlated at geographically large scales works to strengthen and maintain such a synchrony.     

Environmental correlates of acorn production by four species of Minnesota oaks

We measured acorn production by four species of oaks in central Minnesota over a 17-year period with the goal of understanding the proximate drivers of masting behavior. All four species exhibited significant annual variation and within-population synchrony of acorn production, although masting behavior was more pronounced in the two species that require 1 year to develop acorns (‘1-year’ species) than the two species that require 2 years (‘2-year’ species). There was also strong synchrony between species that require the same number of years to mature acorns, but not between species requiring different numbers of years. Acorn production by three of the four species correlated with spring or summer conditions, while no significant environmental correlate of acorn production was detected for the fourth species. Acorn production by none of the four species correlated significantly with variables calculated from the differences in weather conditions from 1 year to the next. These results, combined with prior studies of oaks, suggest that environmental conditions during key periods of acorn development frequently correlate with acorn production, as expected if such factors bear a direct mechanistic relationship to seed production. On the other hand, the environmental factors involve vary greatly both among species and even among populations of the same species, a result consistent with the hypothesis that environmental correlates are simply cues used by plants to synchronize reproductive investment. In either case, our results do not support the recent proposition that variables based on differences in environmental conditions from 1 year to the next serve as a general cue for masting behavior.     

Density-dependent reproductive success among sympatric dipterocarps during a major mast fruiting event

Although masting in Southeast Asia is characterized by the interspecific synchronization of reproduction, little is known about the variation in regeneration strategies among sympatric tree species during major masting events. Herein, we examined the hypothesis that non-abundant species achieve greater seed survival per seed production at the pre- and post-dispersal stages by synchronizing reproduction with abundant species. During the masting event from May to September 2010, we installed seed traps in a primary forest plot of the Deramakot Forest Reserve, Borneo. To identify the possible causes of post-dispersal seed mortality, we conducted a seed-sowing experiment from September 2010 to July 2011 in a primary forest plot with high community-level dipterocarp seed density and two surrounding secondary forests with low seed densities. An abundant species (Shorea multiflora) produced more seeds than other species and exhibited a lower survival rate during the pre-dispersal stage. The ratio of aborted seeds was greater in species with greater seed production, while the ratio of seeds predated by insects was not, suggesting that resource limitations and/or greater inbreeding frequency may explain inefficient seed production. Interspecific variation was rarely observed for post-dispersal seed survival rates. Our study highlights the density-dependent variation in reproductive success between abundant and non-abundant dipterocarp species at the pre-dispersal stage. Non-abundant species achieved greater reproductive success by synchronizing reproduction with the masting of abundant species, which might be an important mechanism for sustainability of rare species populations.     

Synchronized expression of FLOWERING LOCUS T between branches underlies mass flowering in Fagus crenata

Masting is the intermittent and synchronized production of a large amount of flower and seed in plant populations. This population-level phenomenon is caused by individual-level variability in reproduction and its synchrony between individuals. The variability at the individual level is induced by synchronized reproduction between branches within an individual because a tree is an assemblage of branches that are considered as semiautonomous units. However, there have been no empirical studies that quantify the degree of reproductive synchrony at the branch level within the same tree in masting species. Here, we evaluated the reproductive synchrony within individuals by monitoring flowering dynamics and expression level of a flowering-time gene at the branch-level in a typical masting species, Fagus crenata Blume. The 4-year census showed that the branch-level gene expression was highly variable between years and was strongly synchronized between branches. The branch-level synchrony in flowering-time gene expression was followed by coherent flowering cycle at the whole individual. To examine the causal relationship between gene expression and climatic factors, we performed a nonlinear statistical analysis called convergent cross-mapping using the time course data of gene expression and environmental variables. Our results indicated that the observed gene expression pattern was well cross-mapped by temperature or precipitation. However, this cross-mapping skill was lower than that of randomly generated seasonal dynamics, implying a combination of internal and external environmental signals is more likely to regulate gene expression dynamics in F. crenata. Our results provide the first empirical evidence that synchronized expression of a flowering-time gene between branches underlies integrated flowering behavior at the individual level.     

Prior reproduction and weather affect berry crops in central Ontario, Canada

Populations of many perennial plants intermittently produce large seed crops—a phenomenon referred to as mast seeding or masting. Masting may be a response to spatially correlated environmental conditions (the Moran effect), an adaptive reproductive strategy reflecting economies of scale, or a consequence of the internal resource budgets of individual plants. Fruit production by endozoochorous plants representing eight genera varied synchronously over much of central Ontario, Canada, 1998–2009. We tested for effects of weather and prior reproduction on fruit production by comparing AIC_c values among regression models fit to time series of fruit production scores and partitioning contributions by different predictors to multiple R ² into independent and joint contributions. Fruit production by mountain ash (Sorbus spp.), juneberry (Amelanchier spp.), dogwoods (Cornus spp.), nannyberry (Viburnum lentago), and possibly cherries (Prunus spp.) was inversely related to production in the previous year. These effects were independent of weather conditions, suggesting that intrinsic factors such as internal resource budgets or an adaptive strategy of variable reproductive output influenced fruit production. To our knowledge, this is the first evidence of masting in members of the genera Cornus, Viburnum, and Amelanchier, and in members of Prunus and Sorbus in North America. All species produced fewer fruits when weather conditions were dry, so the Moran effect could have synchronized fruit production both within and among species. Patterns and causes of variation in berry crops have implications for ecosystem dynamics, particularly in boreal and subArctic environments where berry crops are important wildlife foods.     

Environmental colour intensifies the Moran effect when population dynamics are spatially heterogeneous

Evidence for synchronous fluctuations of spatially separated populations is ubiquitous in the literature, including accounts within and across taxa. Among the few mechanisms explaining this phenomenon is the Moran effect, whereby independent populations are synchronized by spatially correlated environmental disturbances. The body of research on the Moran effect predominantly assumes that environmental disturbances within a local site are serially uncorrelated; that is, successive observations in time at a particular local site are independent. Yet, many environmental variables are known to possess strong temporal autocorrelation – a character which has often been described as 'colour'. The omission of environmental colour from research on the Moran effect may be due in part to the lack of methods capable of generating sets of time series with a desired colour and spatial correlation. Here I present a novel and simple method designated as 'phase partnering' to generate such sets of time series and I investigate the combined impact of spatial correlation and environmental colour on population synchrony in two common models of population dynamics. For linear population dynamics, and for a subset of nonlinear population dynamics, coloured environments intensify the Moran effect when population dynamics are spatially heterogeneous; in coloured environments the spatial correlation between populations more closely mimics the spatial correlation between their respective environments. Given that most environmental variables are coloured, these results imply that the Moran effect may be a far more significant driver of regional-scale population and interspecific synchrony than is currently believed.     

Does the pattern of population synchrony through space reveal if the Moran effect is acting?

The populations of many species fluctuate in synchrony across large geographical areas. This synchrony is often attributed to the Moran effect, that is, shared environmental fluctuations across the region. In this article, I use a series of simple metapopulation models to show that the degree of synchrony among populations separated by different distances is strongly affected by the particular way that environmental stochasticity is represented in the models. Furthermore, when multiple types of stochasticity are acting simultaneously, the synchronizing effect of any one type is difficult to discern from the resulting pattern of population synchrony. These effects can be exacerbated under certain demographic conditions or if population dynamics are affected by interspecific interactions. In general, it should be extremely difficult to determine if synchrony is caused by the Moran effect using only the synchrony–distance relationship of natural populations.     

Population synchrony within and among Lepidoptera species in relation to weather, phylogeny, and larval phenology

Abstract.  1. The population dynamics of native herbivore species in central Appalachian deciduous forests were studied by analysing patterns of synchrony among intra- and interspecific populations and weather.
2. Spatial synchrony of 10 Lepidoptera species and three weather variables (minimum temperature, maximum temperature, precipitation) from 12 sites was measured using cross-correlation functions relating levels of synchrony to the distance separating each set of populations. Based on both the pattern of synchrony and the region-wide cross-correlation coefficients, Lepidoptera species appear to be synchronised, at least in part, by local weather conditions.
3. Interspecific cross-correlations were calculated for all sympatric species pairs and trends in interspecific synchrony were related to phylogenetic relatedness, life-history timing, and weather. Interspecific synchrony was highest among species whose larvae were present during the same time of the season, but there was no relationship between interspecific synchrony and phylogenetic affinity.
4. Spatial synchrony of weather variables was significantly related to both species of some interspecific pairs, indicating weather as a potential mechanism involved in synchronising populations of different species.     

Weather and regional crop composition variation drive spatial synchrony of lepidopteran agricultural pests

1. Spatial synchrony, the tendency for temporal population fluctuations to be correlated across multiple locations at regional scales, is common and contributes to the severity of outbreaks and epidemics, but is little studied in agricultural pests. 2. This study analysed spatial synchrony from 1974 to 2008 in 16 lepidopteran agricultural pests in Maryland, U.S.A., and investigated whether pest synchrony is driven by interannual variability in seasonal weather and the areas planted in different crop types. 3. Lepidopteran pests exhibited high degrees of spatial synchrony, which was driven by environmental variation, a phenomenon known as the Moran effect. Region-wide variation in the areas planted in major crops drove spatially synchronous abundance fluctuations in more than half of studied species. The combination of weather and crop composition explained large fractions of synchrony in black cutworm, corn earworm, European corn borer, and spotted cutworm populations. Other pests, including forage looper and variegated cutworm, displayed a high degree of spatial synchrony, but without dependence on the tested drivers. 4. The study finding that synchronous variation in the area planted in different crop types contributed to synchronous pest abundance fluctuations suggests that strategies to reduce synchrony in changes in crop type across a region could reduce the severity of pest outbreaks and enhance the stability of agricultural systems.     

Spatial dynamics of Norwegian tetraonid populations

Different species in a given site or population of a given species in different sites may fluctuate in synchrony if they are affected similarly by factors such as spatially autocorrelated climate, predation, or by dispersal between populations of one species. We used county wise time series of hunting bag records of four Norwegian tetraonid species covering 24 years to examine patterns of interspecific and intraspecific synchrony. We estimated synchrony at three spatial scales; national, regional (consisting of counties with similar climate), and county level. Ecologically related species with overlapping distributions exhibited strong synchrony across Norway, but there was much variation between the different regions and counties. Regions with a long coastline to both the North Sea and the Norwegian Ocean exhibited an overall stronger synchrony than those consisting of more continental areas. Intraspecific synchrony was generally low across all counties, but stronger synchrony between counties within regions defined by climatic conditions. Synchrony was negatively related to distance between populations in three of four species. Only the synchrony in willow ptarmigan showed a clear negative relationship with distance, while the other species had both strong positive and negative correlations at short distances. Strong interspecific synchrony between some species pairs within regions and weak intraspecific synchrony across counties within regions suggest a stronger synchronizing effect from environmental factors such as weather or predation and less effect from dispersal. Our results suggest that the complete tetraonid community is structured by environmental factors affecting the different species similarly and causes widespread interspecific synchrony. Local factors affecting the population dynamics nevertheless frequently forces neighbouring populations out of phase.     

Life history strategies affect climate based spatial synchrony in population dynamics of West African freshwater fishes

Spatial synchrony in species abundance is a general phenomenon that has been found in populations representing virtually all major taxa. Dispersal among populations and synchronous stochastic effects (the so called "Moran effect") are the mechanisms most likely to explain such synchrony patterns. Very few studies have related the degree of spatial synchrony to the biological characteristics of species. Here we present a case where specific predictions can be made to relate river fish species characteristics and synchrony determined exclusively by a Moran effect through the expected sensitivity of species to the regional component of environmental stochasticity. By analyzing 23-year time series of abundance estimates in two isolated localities we show that species associated with synchronized reproduction during the wet season, high fecundity, small egg size and high gonado-somatic index (the so called "periodic" strategy) have a higher degree of spatial synchrony in population dynamics than species associated with the opposite traits (the so called "equilibrium" strategy). This is supported by significant relationships (P values <0.01) between species traits and the levels of synchrony after removing taxonomical relatedness. Spatial synchrony computed from summed annual total catches by groups of species, separated into strategy types also showed a significantly higher degree of synchrony for the periodic (r=0.83) than the equilibrium (r=0.46) group. Regional hydrological variability is likely to be partly responsible for the observed synchrony pattern and a regional discharge index showed better relationships with the periodic group, supporting the expected differential effect of regional environmental correlation on population dynamics.     

Climate-driven synchrony in seed production of masting deciduous and conifer tree species

Aims Understanding fluctuations in plant reproductive investment can constitute a key challenge in ecology, conservation and management. Masting events of trees (i.e. the intermittent and synchronous production of abundant seeding material) is an extreme example of such fluctuations. Our objective was to establish the degree of spatial and temporal synchrony in common four masting tree species in boreal Finland and account for potential causal drivers of these patterns.Methods We investigated the spatial intraspecific and temporal interspecific fluctuations in annual seed production of four tree species in Finland, silver birch Betula pendula Roth, downy birch Betula pubescens Ehrh., Norway spruce Picea abies (L.) H.Karst. and rowanberry Sorbus aucuparia L. We also tested to see whether variations in seed production were linked to annual weather conditions. Seeding abundance data were derived from tens of stands per species across large spatial scales within Finland during 1979 to 2014 (for rowanberries only 1986 to 2014).Important findings All species showed spatial synchrony in seed production at scales up to 1000 km. Annual estimates of seed production were strongly correlated between species. Spring and summer temperatures explained most variation in crop sizes of tree species with 0-to 2-year time lags, whereas rainfall had relatively little influence. Warm weather during flowering (May temperature) in the flowering year (Year t) and 2 years before (t ?2) were correlated with seed production. However, high May temperatures during the previous year (t^-1) adversely affected seed production. Summer temperatures in Year t^-1 was positively correlated with seed production, likely because this parameter enhances the development of flower primordials, but the effect was negative with a time lag of 2 years. The negative feedback in temperature coefficients is also likely due to patterns of resource allocation, as abundant flowering and seed production in these species is thought to reduce the subsequent initiation of potential new flower buds. Since the most important weather variables also showed spatial correlation up to 1000 km, weather parameters likely explain much of the spatial and temporal synchrony in seed production of these four studied tree species.     

Interspecific synchrony among foliage-feeding forest Lepidoptera species and the potential role of generalist predators as synchronizing agents

While synchrony among geographically disjunct populations of the same species has received considerable recent attention, much less is known about synchrony between sympatric populations of two or more species. We analyzed time series of the abundance of ten species of spring foliage feeding Lepidoptera sampled over a 25-year period at 20 sites in the Slovak Republic. Six species were free-feeders and four were leaf-rollers as larvae. Twenty-nine percent of interspecific pairs were significantly synchronous and correlations were highest among species exhibiting similar feeding strategies. Similar patterns of interspecific synchrony have been previously demonstrated in several other taxa, and the synchronizing effects of weather and/or specialist predators have been proposed as mechanisms. As an alternative explanation, we explored a model in which two species within the same feeding guild were synchronized by the functional response of generalist predators. In this model, species remained unsynchronized in the complete absence of predation or when predatory pressures were applied to only one species. Pairs of prey species projecting relatively similar search images to predators were more highly synchronized than species with relatively different search images. Prey handling time only influenced synchrony when it was very high relative to the total time prey was exposed to predators. Our model's prediction of greater synchrony among species that project similar search images to predators was in agreement with our field study that showed greater synchrony among species sharing similar larval feeding strategies and morphologies.     

Rainfall and host reproduction regulate population dynamics of a specialist seed predator

1. Mast seeding is a widespread resource pulse caused by synchronized and intermittent production of a large seed crop by plant populations. The effects of masting on wildlife have been well documented in granivorous vertebrates, but less is known about its impact on population dynamics of insects. 2. This study investigated, over 6 years, variation in abundance of a specialist weevil (Curculio elephas) preying on holm oak (Quercus ilex) acorns. 3. An immediate bottom-up effect of seed production on weevil larval abundance was detected, which was driven by an increase in realised fecundity and aggregation at seed-rich trees. Moreover, trees producing on average more and larger acorns sustained larger weevil populations. However, no correlation was found between current and previous year adult abundance, suggesting that C. elephas did not capitalise on the reproductive bottom-up effect. 4. It was rainfall, not masting, that most strongly shaped the temporal variation in insect abundance. Rainfall facilitates emergence after diapause at underground earth cells and was also responsible for among-tree synchronisation in adult weevil population dynamics. 5. In spite of their trophic specialisation, not only food availability, but also weather affects weevil numbers. The present results indicate that moving beyond bottom-up effects is required to better understand complex systems that involve masting plants and insects that consume their seeds.     

Spatial heterogeneity in climate change effects decouples the long‐term dynamics of wild reindeer populations in the high Arctic

The ‘Moran effect’ predicts that dynamics of populations of a species are synchronized over similar distances as their environmental drivers. Strong population synchrony reduces species viability, but spatial heterogeneity in density dependence, the environment, or its ecological responses may decouple dynamics in space, preventing extinctions. How such heterogeneity buffers impacts of global change on large‐scale population dynamics is not well studied. Here, we show that spatially autocorrelated fluctuations in annual winter weather synchronize wild reindeer dynamics across high‐Arctic Svalbard, while, paradoxically, spatial variation in winter climate trends contribute to diverging local population trajectories. Warmer summers have improved the carrying capacity and apparently led to increased total reindeer abundance. However, fluctuations in population size seem mainly driven by negative effects of stochastic winter rain‐on‐snow (ROS) events causing icing, with strongest effects at high densities. Count data for 10 reindeer populations 8–324 km apart suggested that density‐dependent ROS effects contributed to synchrony in population dynamics, mainly through spatially autocorrelated mortality. By comparing one coastal and one ‘continental’ reindeer population over four decades, we show that locally contrasting abundance trends can arise from spatial differences in climate change and responses to weather. The coastal population experienced a larger increase in ROS, and a stronger density‐dependent ROS effect on population growth rates, than the continental population. In contrast, the latter experienced stronger summer warming and showed the strongest positive response to summer temperatures. Accordingly, contrasting net effects of a recent climate regime shift—with increased ROS and harsher winters, yet higher summer temperatures and improved carrying capacity—led to negative and positive abundance trends in the coastal and continental population respectively. Thus, synchronized population fluctuations by climatic drivers can be buffered by spatial heterogeneity in the same drivers, as well as in the ecological responses, averaging out climate change effects at larger spatial scales.     

Testing Moran's theorem in an agroecosystem

The abundance and reproductive effort of populations frequently fluctuate across space and time, a phenomenon known as spatial synchrony. Knowledge of the causes of this behavior underlies the ability to manage species, protect the health of humans and the environment, and increase agricultural sustainability. We used an agroecosystem to test Moran's theorem – spatial synchrony results from environmental entrainment. The controlled conditions of the agroecosystem allowed us to create a highly correlated environment while negating the effects of the alternative hypotheses: dispersal and trophic interactions. Under such conditions, synchrony of fruit production by 4288 trees was high over six years in a 32.5 ha pistachio orchard and occurred at similar temporal frequency as weather patterns demonstrating the Moran effect. The spatial synchrony of fruit production was less than the presumed synchrony of the environment supporting research from microcosms and observational studies showing the Moran effect is degraded by local mechanisms. Indeed even under the homogeneous environment of this system, synchrony declined significantly with distance among trees. We present evidence suggesting that the correlation of the local environment affects intrinsic dynamics to cause these patterns. Our findings demonstrate that the Moran effect is, at minimum, partially responsible for the synchronous fruit production in this system. Agroecosystems are often overlooked in basic ecological research; this experiment provides an example of their comparative advantages for the study of some ecological questions.     

有色环境噪音对空间异质种群动态同步性的影响

随着种群动态和空间结构研究兴趣的增加,激发了大量的有关空间同步性的理论和实验的研究工作。空间种群的同步波动现象在自然界广泛存在,它的影响和原因引起了很多生态学家的兴趣。Moran定理是一个非常重要的解释。但以往的研究大多假设环境变化为空间相关的白噪音。越来越多的研究表明很多环境变化的时间序列具有正的时间自相关性,也就是说用红噪音来描述更加合理。因此,推广经典的Moran效应来处理空间相关红噪音的情形很有必要。利用线性的二阶自回归过程的种群模型,推导了两种群空间同步性与种群动态异质性和环境变化的时间相关性(即环境噪音的颜色)之间的关系。深入分析了种群异质性和噪音颜色对空间同步性的影响。结果表明种群动态异质性不利于空间同步性,但详细的关系比较复杂。而红色噪音的同步能力体现在两方面:一方面,本身的相关性对同步性有贡献;另一方面,环境变化时间相关性可以通过改变种群密度依赖来影响同步性,但对同步性的影响并无一致性的结论,依赖于种群的平均动态等因素。这些结果对理解同步性的机理、利用同步机理来制定物种保护策略和害虫防治都有重要的意义。