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Stable isotopes analysis,especially carbon and nitrogen,are now commonly used to study material circulation and energy flow within ecosystems.Carbon isotope ratios(δ13C) are used to trace food sources of consumers,while nitrogen isotope ratios(δ15N) are mainly used to quantify trophic levels of organisms.Traditionally,δ13C vs.δ15N bi-plots have been used to describe food web structure for a single time period or ecosystem,but this method show less power in comparisons of food webs across time and space.Meanwhile,simple qualitative descriptions of food webs cannot test hypotheses regarding food web complex changes.Here we present statistical methodologies for quantitatively comparing stable isotope food web data.We demonstrate the utility of circular statistics and hypothesis tests for quantifying directional food web differences using a case study,a freshwater fish community from Meiliang Bay,Lake Taihu,over seasons.We used arrow diagrams for angle of change for fishes along a gradient of seasons,in which each arrow represents a single species and the direction in trophic niche space the species moved.The length of the arrow represents the magnitude of change for that particular species.Concentric circles correspond to magnitude of change.The straight line is the mean vector of change among all species;the curved line on the rim indicates the 95% confidence interval around the mean vector of change.Directional change(magnitude and angle) and statistics quantifying change in isotope niche space for fish communities were also calculated.Based on these results,we found that most species from the freshwater fish community showed statistically significant shift in the same direction in food web space toward more pelagic-based production except summer to autumn seasons.In support of these patterns,the Rayleigh′s test indicated significant pattern of consistent change among species in autumn to winter,winter to spring and spring to summer seasons.The Watson-William′s test for comparison of the community in different time indicated that significant difference between the directional change in the fish community between autumn to winter and winter to spring seasons.Seasonal dynamics of food web energy pathways at the community-level in the current study was attributed to seasonal dynamics of stable isotope composition of available resources and foraging shifts of fish species.Meanwhile,because of the high omnivory in fish community in the current system,temporal variations in pelagic primary productivity strongly drive the energy flows in local food web.Therefore,seasonal dynamics of food web energy pathways at the community-level in eutrophic ecosystem may imply the decrease of food web stability in this eutrophic system with the dynamics of resource availability.As an understanding of food web structure and functioning is of growing importance in ecology theory and ecosystem management,our study demonstrate the quantifying food web differences from the standard stable isotope analysis.

The reproductive characteristics of four plant species of the genus Nitraria L.in Ulan Buh Desert,Nitraria tangutorum Bobr.,N.sibirica Pall.,N.roborowskii Kom.,N.sphaerocarpa Maxim.,were studied.The reproductive allocation characteristics of reproductive tillers were studied based on measurements of the reproductive modules during blooming.The results showed significant quantitative differences exist in some reproductive modules of the four species,such as ramet height,reproductive tiller length,reproductive tiller diameter,number of flowers per tiller,dry weight of cymes,and dry weight of branches and leaves.Of the four plant species,N.sphaerocarpa was the smallest based on the above measured characters.N.sibirica allocated 44.51% of its mass to reproduction while the other three species allocated less than 20%.Statistical analyses were performed on the reproductive characteristics of four plant species.A significant linear correlation was found between reproductive tiller length and ramet height(P0.05).The correlation coefficients were 0.8207,0.7408,0.8401,and 0.9144 for N.tangutorum,N.sibirica,N.roborowskii,and N.sphaerocarpa,respectively.The statistical significant test level of the curve fitness was 0.0067,0.0224,0.0046 and 0.0006 for N.tangutorum,N.sibirica,N.roborowskii,and N.sphaerocarpa,respectively.Also,the cymous dry weight was significantly correlated to ramet height.Specifically the absolute biomass allocated to the reproductive organs from the total biomass of the reproductive tillers increased as ramet height increased.The correlation coefficients of the two indices for N.tangutorum,N.sibirica,N.roborowskii,N.sphaerocarpa were 0.9283,0.6631,0.8350,and 0.8324,respectively.The fitted curves of the two indices for N.tangutorum and N.roborowskii followed a linear relationship,whereas that of N.sibirica followed a power law,and that of N.sphaerocarpa was quadratic.Third,the reproductive allocation of the four plant species decreased as the biomass of the reproductive tillers increased which represented the size of the plant.The fitted curves of the two indices for N.sibirica and N.roborowskii were linear,and those for N.tangutorum and N.sphaerocarpa were inverse.Plant size had a significantly negative correlation with the reproductive allocation.The characteristics of the reproductive allocation of four plant species of genus Nitraria reflect their strategies for the resource utilization and the trade-off with the clonal propagation and ecological adaptation to the environment.