Linking species richness curves from non-contiguous sampling to contiguous-nested SAR: An empirical study

The species–area relationship (SAR) is one of the few generalizations in ecology. However, many different relationships are denoted as SARs. Here, we empirically evaluated the differences between SARs derived from nested-contiguous and non-contiguous sampling designs, using plants, birds and butterflies datasets from Great Britain, Greece, Massachusetts, New York and San Diego. The shape of SAR depends on the sampling scheme, but there is little empirical documentation on the magnitude of the deviation between different types of SARs and the factors affecting it. We implemented a strictly nested sampling design to construct nested-contiguous SAR (SA_CR), and systematic nested but non-contiguous, and random designs to construct non-contiguous species richness curves (SA_SRs for systematic and SACs for random designs) per dataset. The SA_CR lay below any SA_SR and most of the SACs. The deviation between them was related to the exponent f of the power law relationship between sampled area and extent. The lower the exponent f, the higher was the deviation between the curves. We linked SA_CR to SA_SR and SAC through the concept of “effective” area (A_e), i.e. the nested-contiguous area containing equal number of species with the accumulated sampled area (A_S) of a non-contiguous sampling. The relationship between effective and sampled area was modeled as log(A_e) = klog(A_S). A Generalized Linear Model was used to estimate the values of k from sampling design and dataset properties. The parameter k increased with the average distance between samples and with beta diversity, while k decreased with f. For both systematic and random sampling, the model performed well in predicting effective area in both the training set and in the test set which was totally independent from the training one. Through effective area, we can link different types of species richness curves based on sampling design properties, sampling effort, spatial scale and beta diversity patterns.     

Eco-morphological patterns of the sagitta of Antarctic fish

Morphology and morphometry of the sagittae otolith were studied in pelagic and mesopelagic fish. The shape, margins and rostrum of four groups of otoliths from several species were analyzed: group 1 (pelagic fish associated with the under ice cover N = 42), group 2 (pelagic fish associated with water offshore N = 9), group 3 (mesopelagic fish associated with extensive vertical migration N = 57) and group 4 (mesopelagic fish associated with short vertical migration N = 54). E (maximum width of the sagitta /maximum length of the sagitta %), R (rostrum length (RL)/maximum length of the sagitta %) and S (sulcus area (SS)/otolith area (OS) %) indexes were calculated for each species. Sagittae of pelagic groups (1 and 2) showed the smallest sagitta dimensions in relation to the total length of the fish, in this group the sagitta shape is variable. Sagittae of mesopelagic fish (groups 3 and 4) showed variable shape and edges. The shape in group 4 was polygonal and these species have more width than length. Statistical analysis showed significant differences in the E, R and S indexes. These results were compared with other 19 species, belonging to six families, taken from a publisher-edited literature. E, R and S-values could be used to characterize the sagittae of the Antarctic fish and could be considered as a useful tool for fish ecology studies.     

Which function describes the species–area relationship best? A review and empirical evaluation

Aim The aims of this study are to resolve terminological confusion around different types of species–area relationships (SARs) and their delimitation from species sampling relationships (SSRs), to provide a comprehensive overview of models and analytical methods for SARs, to evaluate these theoretically and empirically, and to suggest a more consistent approach for the treatment of species–area data. Location Curonian Spit in north‐west Russia and archipelagos world‐wide. Methods First, I review various typologies for SARs and SSRs as well as mathematical models, fitting procedures and goodness‐of‐fit measures applied to SARs. This results in a list of 23 function types, which are applicable both for untransformed (S) and for log‐transformed (log S) species richness. Then, example data sets for nested plots in continuous vegetation (n = 14) and islands (n = 6) are fitted to a selection of 12 function types (linear, power, logarithmic, saturation, sigmoid) both for S and for log S. The suitability of these models is assessed with Akaike’s information criterion for S and log S, and with a newly proposed metric that addresses extrapolation capability. Results SARs, which provide species numbers for different areas and have no upper asymptote, must be distinguished from SSRs, which approach the species richness of one single area asymptotically. Among SARs, nested plots in continuous ecosystems, non‐nested plots in continuous ecosystems, and isolates can be distinguished. For the SARs of the empirical data sets, the normal and quadratic power functions as well as two of the sigmoid functions (Lomolino, cumulative beta‐P) generally performed well. The normal power function (fitted for S) was particularly suitable for predicting richness values over ten‐fold increases in area. Linear, logarithmic, convex saturation and logistic functions generally were inappropriate. However, the two sigmoid models produced unstable results with arbitrary parameter estimates, and the quadratic power function resulted in decreasing richness values for large areas. Main conclusions Based on theoretical considerations and empirical results, I suggest that the power law should be used to describe and compare any type of SAR while at the same time testing whether the exponent z changes with spatial scale. In addition, one should be aware that power‐law parameters are significantly influenced by methodology.     

北京山区河岸带植物群落种-面积关系

种-面积关系是群落生态学的基本问题之一,是了解植物群落结构的重要途径。为摸清北京山区河流河岸带植物群落调查最小样方面积,在北京市怀柔区怀九河河岸带沿线,采用基于河岸带立地条件逐步扩大样地面积的方法布设50个80m长样地,调查计算并拟合不同类型河岸带所需的最小样地面积。研究结果表明:北京市怀柔区怀九河河岸带植物种数255种,隶属于70科185属。通过聚类分析将怀九河河岸带分为自然河岸带、近自然河岸带、人工岸坡乔灌草河岸带、人工岸坡观赏性乔灌草河岸带、人工岸坡疏乔灌草干砌石河岸带和人工岸坡浆砌石河岸带6种类型。根据赤池信息量准则AIC可知自然河岸带、近自然河岸带、人工岸坡乔灌草河岸带和人工岸坡疏乔灌草干砌石河岸带优先选取S=c-ae~(-bA),人工岸坡观赏性乔灌草河岸带优先选取S=aA/(1+bA),人工岸坡浆砌石河岸带优先选取S=c/(1+ae~(-bA))。满足相同比例植物种调查,不同类型河岸带所需最小样地面积存在明显差异,当满足河岸带植物调查80%植物种时,人工岸坡浆砌石河岸带(84m~2)和自然河岸带(217m~2)所需样地面积较小,其次是人工岸坡疏乔灌草干砌石河岸带(362m~2),近自然河岸带(450m~2)和人工岸坡乔灌草河岸带(460m~2)所需样地面积相似,而人工岸坡观赏性乔灌草河岸带所需样地面积最大为571m~2。所得出的河岸带植物调查最小样地面积对于河岸带生物多样性保护和指导河岸带生态修复具有重要意义。     

Multiple source pools for Galápagos plant species richness: a critical analysis of the line of sight connectivity index

An index (C_i*E) combining the number of line‐of‐sight islands (C_i) within a radius i and target island elevation (E) has been proposed as an improved predictive model of plant species richness (S_t) in the Galápagos Archipelago. We examined this index critically and found that several major flaws preclude it from being a useful predictive tool for the archipelago. Although the number of collecting trips to an island was reported over 20 years ago to have substantial predictive value for reported plant species richness in the Galápagos Islands, this relationship was ignored in multiple regression analyses of the index. When we included the number of collecting trips in different multiple regression analyses of the index, C_i*E had less predictive power than collecting trips or ceased to be significant at all. Additionally, the strong significant relationship between elevation and area in the Galápagos Archipelago results in area having a major confounding influence on the C_i*E index. When elevation is removed from the C_i*E index, the predictive power of C_i is far less than area alone. Finally, the data used to construct and correlate the C_i*E index with (S_t) were based only on a subset of the islands and species lists that were incomplete or out of date. Species richness on islands can be related to the interaction of different factors, so development and testing of indices like C_i*E is not inappropriate. However, it is important to examine the interrelationships among the components of these indices thoroughly, and not ignore the effect of factors already known to have high predictive power. We propose several ways in which more meaningful indices of source pool(s) capacity can be constructed.     

Regional and local impact on species diversity – from pattern to processes

The impact of regional factors (such as speciation or dispersal) on the species richness in local communities (S_L) has received increasing attention. A prominent method to infer the impact of regional factors is the comparison of species richness in local assemblages (S_L) with the total number of species in the region (S_R). Linear relations between S_R and S_L have been interpreted as an indication of strong regional influence and weak influence of interactions within local communities. We propose that two aspects bias the outcome of such comparisons: (1) the spatial scale of local and regional sampling, and (2) the body size of the organisms. The impact of the local area reflects the scales of ecological interactions, whereas the ratio between local and regional area reflects the inherent moment of autocorrelation. A proposed impact of body size on the relation is based on the high dispersal and high abundance of small organisms. We predict strongest linearity between S_R and S_L for large organisms, for large local areas (less important ecological interactions) and for sampling designs where the local habitat area covers a high proportion of the regional area (more important autocorrelation). We conducted a meta-analysis on 63 relations obtained from the literature. As predicted, the linearity of the relationship between S_L and S_R increased with the proportion of local to regional sampling area. In contrast, neither the body size of the organisms nor the local area itself was significantly related to the relation between S_L and S_R. This indicated that ecological interactions played a minor role in the shape of local to regional richness plots, which instead was mainly influenced by the sampling design. We found that the studies published so far were highly biased towards larger organisms and towards high similarity between the local and regional area. The proposed prevalence of linear relationships may thus be an artefact and plots of S_L to S_R are not a suitable tool with which to infer the strength of local interactions.     

The species-area relation I. A model for discrete sampling

A simple mathematical model describing the species-area relation was developed. This paper dealt with the case that discrete random samples are combined. Modelling was made on the assumption that the occurrence probability of a species in a quadrat has a continuous density distribution. The model, given by the equation (6), holds only for a particular size of quadrat (i.e. the characteristic area). More general form applicable to the quadrats the size of which is near to the characteristic area was represented by the equation (9). Validity of the model was examined for the data of plant and insect communities, and it was concluded that the observation can be predicted by the model unless the size of sampling unit considerably differs from the characteristic area. The uniformity of specific density (i. e. the number of species per quadrat) and the size of characteristic area were discussed as being important in an understanding of community structure.     

Elements pour une théorie statistique du tableau phytosociologique homogène

Summary A new model, based on information theory, for determining the equation of Raunkiaer frequency curves in a homogeneous phytosociological table is proposed. The forms of these curves are explained in relation to the geographical area covered by the relevés of the phytosociological table involved. The statistical distribution of species in a syntaxon (and the variability of a syntaxon as measured, by (E/E _m)-1, where E is the total number of species in the table, and E _m is the average number of species per relevé) are closely correlated with the size of the distribution area of relevés. Many examples are given and several consequences for the phytosociological method are indicated.

     

Estimating biomass of submersed vegetation using a simple rake sampling technique

We evaluated the use of a simple rake sampling technique for predicting the biomass of submersed aquatic vegetation. Vegetation sampled from impounded areas of the Mississippi River using a rake sampling technique, was compared with vegetation harvested from 0.33-m² quadrats. The resulting data were used to model the relationship between rake indices and vegetation biomass (total and for individual species). We constructed linear regression models using log-transformed biomass data for sites sampled in 1999 and 2000. Data collected in 2001 were used to validate the resulting models. The coefficient of determination (R ²) for predicting total biomass was 0.82 and ranged from 0.59 (Potamogeton pectinatus) to 0.89 (Ceratophyllum demersum) for individual species. Application of the model to estimate total submersed aquatic vegetation is illustrated using data collected independent of this study. The accuracy and precision of the models tested indicate that the rake method data may be used to predict total vegetation biomass and biomass of selected species; however, the method should be tested in other regions, in other plant communities, and on other species. Handling editor: S. M. Thomaz     

Four years host–parasitoid food web: testing sampling effort on trophic levels

Incomplete sampling is a major problem affecting data quality with respect to food webs. We described a host–parasitoid food web based on data from four years of sampling, evaluated the dataset robustness of the food web, and tested the hypothesis that different trophic levels require different sampling efforts. We sampled Senegalia tenuifolia fruits at eight sampling sites in three areas, during four years (2011–2014) in the Brazilian cerrado (savanna). We recorded 26 insect species in three trophic levels associated with S. tenuifolia. For species accumulation curves, all insect trophic levels, areas and years reached the asymptote, except for one area. The cumulative species richness in each trophic level suggested that the third level (primary parasitoid) should be sampled for a longer time than the second and fourth levels, supporting our hypothesis. In conclusion, the sampling effort employed was sufficient to assess most of the insect species richness, and provided a high-quality and well-represented host-parasitoid food web, even though trophic levels require different efforts.     

Modelling both dominance and species distribution provides a more complete picture of changes to mangrove ecosystems under climate change

Dominant species influence the composition and abundance of other species present in ecosystems. However, forecasts of distributional change under future climates have predominantly focused on changes in species distribution and ignored possible changes in spatial and temporal patterns of dominance. We develop forecasts of spatial changes for the distribution of species dominance, defined in terms of basal area, and for species occurrence, in response to sea level rise for three tree taxa within an extensive mangrove ecosystem in northern Australia. Three new metrics are provided, indicating the area expected to be suitable under future conditions (E_occupied), the instability of suitable area (E_instability) and the overlap between the current and future spatial distribution (E_overlap). The current dominance and occurrence were modelled in relation to a set of environmental variables using boosted regression tree (BRT) models, under two scenarios of seedling establishment: unrestricted and highly restricted. While forecasts of spatial change were qualitatively similar for species occurrence and dominance, the models of species dominance exhibited higher metrics of model fit and predictive performance, and the spatial pattern of future dominance was less similar to the current pattern than was the case for the distributions of species occurrence. This highlights the possibility of greater changes in the spatial patterning of mangrove tree species dominance under future sea level rise. Under the restricted seedling establishment scenario, the area occupied by or dominated by a species declined between 42.1% and 93.8%, while for unrestricted seedling establishment, the area suitable for dominance or occurrence of each species varied from a decline of 68.4% to an expansion of 99.5%. As changes in the spatial patterning of dominance are likely to cause a cascade of effects throughout the ecosystem, forecasting spatial changes in dominance provides new and complementary information in addition to that provided by forecasts of species occurrence.     

Effects of stand age and tree species on canopy transpiration and average stomatal conductance of boreal forests

We quantified the effect of stand age and tree species composition on canopy transpiration (E_C) by analysing transpiration per unit leaf area (E_L) and canopy stomatal conductance (G_S) for boreal trees comprising a five stand wildfire chronosequence. A total of 196 sap flux sensors were used on 90 trees consisting of Betula papyrifera Marsh (paper birch; present in the youngest stand), Populus tremuloides Michx (quaking aspen), Pinus banksiana Lamb. (jack pine), and Picea mariana (Mill.) (black spruce). While fine roots were positively correlated with stand E_C; leaf area index, basal area, and sapwood area were not. Stands less than 70 years old were dominated by Populus tremuloides and Pinus banksiana and stands greater than 70 years old were composed almost entirely of Picea mariana. As Populus tremuloides and Pinus banksiana increased in size and age, they displayed an increasing sapwood to leaf area ratio (A_S : A_L), a constant minimum leaf water potential (Ψ_L), and a constant proportionality between G_S at low vapour pressure deficit (Dj G_Sref) and the sensitivity of G_S to D (–δ). In contrast, A_S : A_L, minimum Ψ_L, and the proportionally between –δ and G_Sref decreased with height and age in Picea mariana. A G_S model that included the effects of D, A_S : A_L, tree height, and for Picea mariana an increasing soil to leaf water potential gradient with stand age, was able to capture the effects of contrasting hydraulic properties of Picea mariana, Populus tremuloides and Pinus banksiana during stand development after wildfire.     

Evaluation of statistical precision and design of efficient sampling for the population estimation based on frequency of occurrence

The binomial sampling to estimate population density of an organism based simply upon the frequency of its occurrence among sampled quadrats is a labour-saving technique which is potentially useful for small animals like insects and has actually been applied occasionally to studies of their populations. The present study provides a theoretical basis for this convenient technique, which makes it statistically reliable and tolerable for consistent use in intensive as well as preliminary population censuses. Firs, the magnitude of sampling error in relation to sample size is formulated mathematically for the estimate to be obtained by this indirect method of census, using either of the two popular models relating frequency of occurrence (p) to mean density (m), i.e. the negative binomial model, p=1−(1+m/k)^−k, and the empirical model, p=1−exp(−am^b). Then, the equations to calculate sample size and census cost that are necessary to attain a given desired level of precision in the estimation are derived for both models. A notable feature of the relationship of necessary sample size (or census cost) to mean density in the frequency method, in constrast to that in the ordinary census, is that it shows a concave curve which tends to rise sharply not only towards lower but also towards higher levels of density. These theoretical results make it also possible to design sequential estimation procedures based on this convenient census technique, which may enable us with the least necessary cost to get a series of population estimates with the desired precision level. Examples are presented to explain how to apply these programs to acutal censuses in the field.     

Seasonal patterns of leaf photosynthetic and secondary xylem vascular traits in current‐year stems of three Sorbus species with contrasting growth habits

Seasonal effects of environmental variables on photosynthetic activity and secondary xylem formation provide data to demonstrate how environmental factors together with leaf ageing during the season control tree growth. In this study, we assessed physiological responses in photosynthetic behaviour to seasonal climate changes, and also identified seasonal differences in vascular traits within differentiating secondary xylem tissue from three diploid species of the taxonomically complex genus Sorbus. From sampling day 150, a clear physiological segregation of S. chamaemespilus from S. torminalis and S. aria was evident. The shrubby species S. chamaemespilus could be distinguished by a higher photosynthetic capacity between days 150 and 206. This was reflected in its associations with net CO₂ assimilation rate (P_N), maximum photochemical efficiency of PSII (F_v/F_m), variable‐to‐initial fluorescence ratio (F_v/F₀), potential electron acceptor capacity (‘area’) in multivariate space, and also its associations with log‐transformed vessel area and log‐transformed relative conductivity between days 239 and 268. The maximum segregation and differentiation among the examined Sorbus species was on sampling day 206. The largest differences between S. torminalis and S. aria were found on day 115, when the latter species clearly showed closer associations with high values of vessel density and transpiration (E). Sampling day clusters were arranged along an arch‐like gradient that reflected the positioning of the entire growing season in multivariate space. This arch‐like pattern was most apparent in the case of S. chamaemespilus, but was also observed in S. torminalis and S. aria.     

Genetic diversity of the endangered Chinese endemic herb Primulina tabacum (Gesneriaceae) revealed by amplified fragment length polymorphism (AFLP)

Primulina tabacum Hance, is a critically endangered perennial endemic to limestone area in South China. Genetic variability within and among four extant populations of this species was assessed using AFLP markers. We expected a low genetic diversity level of this narrowly distributed species, but our results revealed that a high level of genetic diversity remains, both at population level (55.5% of markers polymorphic, H _E = 0.220, I _S = 0.321), and at species level (P = 85.6% of markers polymorphic, H _E = 0.339, I _S = 0.495), probably resulting from its refugial history and/or breeding system. High levels of genetic differentiation among populations was apparent based on Nei’s genetic diversity analysis (G _st=0.350). The restricted gene flow between populations is a potential reason for the high genetic differentiation. The population genetic diversity of P. tabacum revealed here has clear implications for conservation and management. To maintain present levels of genetic diversity, in situ conservation of all populations is necessary.     

Stem CO2 efflux in six co‐occurring tree species: underlying factors and ecological implications

Stem respiration plays a role in species coexistence and forest dynamics. Here we examined the intra‐ and inter‐specific variability of stem CO₂ efflux (E) in dominant and suppressed trees of six deciduous species in a mixed forest stand: Fagus sylvatica L., Quercus petraea [Matt.] Liebl, Quercus pyrenaica Willd., Prunus avium L., Sorbus aucuparia L. and Crataegus monogyna Jacq. We conducted measurements in late autumn. Within species, dominants had higher E per unit stem surface area (E_s) mainly because sapwood depth was higher than in suppressed trees. Across species, however, differences in E_s corresponded with differences in the proportion of living parenchyma in sapwood and concentration of non‐structural carbohydrates (NSC). Across species, E_s was strongly and NSC marginally positively related with an index of drought tolerance, suggesting that slow growth of drought‐tolerant trees is related to higher NSC concentration and E_s. We conclude that, during the leafless period, E is indicative of maintenance respiration and is related with some ecological characteristics of the species, such as drought resistance; that sapwood depth is the main factor explaining variability in E_s within species; and that the proportion of NSC in the sapwood is the main factor behind variability in E_s among species.     

Performance of nonparametric species richness estimators in a high diversity plant community

Abstract. The efficiency of four nonparametric species richness estimators — first‐order Jackknife, second‐order Jackknife, Chao2 and Bootstrap — was tested using simulated quadrat sampling of two field data sets (a sandy ‘Dune’ and adjacent ‘Swale’) in high diversity shrublands (kwongan) in south‐western Australia. The data sets each comprised > 100 perennial plant species and > 10 000 individuals, and the explicit (x‐y co‐ordinate) location of every individual. We applied two simulated sampling strategies to these data sets based on sampling quadrats of unit sizes 1/400th and 1/100th of total plot area. For each site and sampling strategy we obtained 250 independent sample curves, of 250 quadrats each, and compared the estimators’ performances by using three indices of bias and precision: MRE (mean relative error), MSRE (mean squared relative error) and OVER (percentage overestimation). The analysis presented here is unique in providing sample estimates derived from a complete, field‐based population census for a high diversity plant community. In general the true reference value was approached faster for a comparable area sampled for the smaller quadrat size and for the swale field data set, which was characterized by smaller plant size and higher plant density. Nevertheless, at least 15–30% of the total area needed to be sampled before reasonable estimates of S_t (total species richness) were obtained. In most field surveys, typically less than 1% of the total study domain is likely to be sampled, and at this sampling intensity underestimation is a problem. Results showed that the second‐order Jackknife approached the actual value of S_t more quickly than the other estimators. All four estimators were better than S_obs (observed number of species). However, the behaviour of the tested estimators was not as good as expected, and even with large sample size (number of quadrats sampled) all of them failed to provide reliable estimates. First‐ and second‐order Jackknives were positively biased whereas Chao2 and Bootstrap were negatively biased. The observed limitations in the estimators’ performance suggests that there is still scope for new tools to be developed by statisticians to assist in the estimation of species richness from sample data, especially in communities with high species richness.     

Reproductive effort,fecundity and energy allocation in two species of the genus Perinereis (Polychaeta: Nereididae)

Summary

The reproductive effort in terms of fecundity and energy allocation was studied in two species of semelparous polychaetes belonging to the genus Perinereis, living in the same environment, with different reproductive modalities. There is a great individual variability both in terms of reproductive effort and fecundity. Fecundity varied from 4080 to 15000 oocytes in P. rullieri and from 7000 to 26000 in P. cultrifera; no linear relationship was found between oocyte number and total jaw length utilised as size index. The energy content of germinal and somatic tissues was determined by Differential Scanning Calorimeter (DSC). The reproductive effort was calculated as RE = E_G/(E_G + E_S) where E_G is the total energy in germinal tissues and E_S is the total energy in somatic tissues. Reproductive effort is very high with mean values of 0.62 for P. rullieri and 0.79 for P. cultrifera. The different amounts of energy allocated in germinal tissues can be attributed to the different reproductive modalities—P. rullieri reproduces in the atokous phase whereas P. cultrifera has conserved epitoky in its life-cycle. The lack of correlation between reproductive effort and size index strongly suggests that reproductive allocation does not increase with age. In semelparous species the variability in fecundity and reproductive effort observed cannot be interpreted in terms of a trade-off between fecundity and survival as in iteroparous species. In fact, in semelparous an individual allocates all available resources to reproduction and then dies.     

Stem CO2 efflux of ten species in temperate forests in Northeastern China

Stem CO₂ efflux (E _S) is an important component of forest ecosystem carbon budgets and net ecosystem CO₂ exchange, but little is known about E _S in temperate forests in Northeastern China, an area with a large extent of forest. We measured E _S along with stem temperature at 1?cm depth (Ts) over a 9?month period in 2007 on ten dominant tree species of secondary forests of the region. Other measurements included the autotrophic component of soil CO₂ efflux (E _A) and stem diameter at breast height (DBH). Our objectives were to (1) examine the seasonal patterns and species differences in E _S, and (2) determine the correlations between E _S and Ts, DBH and E _A. Mean E _S for the measurement period ranged from 1.09 to 1.74?μmol?CO₂?m^?2?s^?1 among the ten species. The sensitivity of E _S to Ts (Q ₁₀ ) ranged from 1.87 to 2.61. Across the ten species 57–89% of variation in E _S was explained by T _S and DBH. There was also a linear relationship between mean E _S and E _A. E _S was better predicted by Ts in the dormant season than the growing season, indicating that additional factors such as growth respiration and internal transport of CO₂ in the xylem became more important contributors to E _S during the growing season. Stem CO₂ efflux increased, and Q ₁₀ decreased, with increasing DBH in all species. Although temperature exerts strong control on the rate of cellular respiration, we conclude that in tree stems in situ, T _S, DBH and many other factors affect the relationship between CO₂ evolution by respiring cells and the diffusion of CO₂ to the stem surface.