Oikos 118: 67 76, 2009 doi: 10.1111/j.1600-0706.2008.16722.x, # 2008 The Authors. Journal compilation # 2008 Oikos Subject Editor: Tadashi Fukami. Accepted 15 July 2008
Evaluating the relative importance of patch quality and connectivity in a damselfly metapopulation from a one-season survey
Takehiko Yamanaka, Koichi Tanaka, Kenji Hamasaki, Yukinobu Nakatani, Nobusuke Iwasaki, David S. Sprague and Ottar N. Bjørnstad
T. Yamanaka ([email protected]), K. Tanaka and K. Hamasaki, Biodiversity Division, National Inst. for Agro-Environmental Sciences, 3-1-3 Kannondai, Tsukuba, JP 305-8604 Ibaraki, Japan. Y. Nakatani, Natural Resources Inventory Center, National Inst. for Agro- Environmental Sciences, 3-1-3 Kannondai, Tsukuba, JP 305-8604 Ibaraki, Japan. N. Iwasaki and D. S. Sprague, Ecosystem Informatics Division, National Institute for Agro-Environmental Sciences, 3-1-3 Kannondai, Tsukuba, JP 305-8604 Ibaraki, Japan. O. N. Bjørnstad, Depts of Entomology and Biology, 501 Ag Sciences and Industries Building, The Pennsylvania State Univ., University Park, PA 16802, USA.
The area-and-isolation paradigm, which has been the primary focus of metapopulation research, may not hold in some animal metapopulations if within-patch preference is more important than patch area or connectivity. Recently, regression analyses have been used to evaluate the effect of patch connectivity and various patch qualities including area. However, their relative importance is not easy to determine, because patch qualities and connectivity are often spatially autocorrelated. In this paper, we try to evaluate the relative importance of within-patch quality, patch connectivity and spatial autocorrelation using variation partitioning methods from community ecology. We constructed three regression models: within-patch quality, PCNM (principal coordinates of neighbor matrices) and patch connectivity based on a one-season survey of a damselfly Copera annulata metapopulation. The contribution of within-patch quality was larger than that of connectivity. There was no prominent effect of patch area. We conclude that the area-and-isolation paradigm is not applicable to this C. annulata metapopulation. The spatial autocorrelation extracted by PCNM had the largest contribution; it contained almost all of the variation of connectivity and overlapped with variation explained by within- patch quality. Connectivity corresponded most closely to medium-scale spatial structure captured by PCNM (ca 640 m). The mean effective dispersal scale was estimated to be 53 m. Within-patch quality, debris accumulation and vegetation cover in the pond corresponded with the medium and small (ca 201 m) spatial scales from PCNM, though we could not clearly explain the cause of this correspondence. We believe that our method will contribute to quick and effective evaluation of spatial and non-spatial aspects of metapopulation.
The metapopulation theory is a standard and basic tool for (Moilanen and Hanski 1998). These models have clarified understanding population dynamics in fragmented habitats. how metapopulation persistence depends on the balance In the early metapopulation models, habitat patches were between colonization and extinction rates determined by assumed to be identical in quality and position (Levins patch area and isolation. Their approach may be seen as an 1970). Though these models greatly contributed to our area-and-isolation paradigm. This paradigm has proven qualitative understanding of metapopulation dynamics, especially apt for butterflies: for example, Glanville fritillary they were highly conceptual and hardly rigorous for Melitaea cinxia in Finland (Hanski et al. 1996) and dingy empirical testing. This situation has improved over the skipper Erynnis tages in North Wales (Gutie´rrez 2005). last 15 years through the formulation of more realistic There are, however, numerous reports of patterns that models that allow for quantitative prediction, facilitating are not concordant with the area-and-isolation paradigm important applications in the study and management of (summarized by Harrison and Bruna 1999). Thomas et al. rare and endangered species (summarized by Hanski and (2001) reported that within-patch quality was more Ovaskainen 2003). Hanski-type models, many of which important than patch size or isolation for three butterfly inherited the basic structure of his first incidence function metapopulations in the UK (Dennis and Eales 1997, model (IFM, Hanski 1994), were novel in that they used Hanski and Singer 2001). Krauss et al. (2005) reported patch occupancy as the state variable and patch area and that patch size was indeed more important than local isolation as predictors, achieving spatially realistic yet simple covariates but of the same importance as isolation. There models. Researchers and conservation practitioners can are contrary studies reporting that incorporation of local apply these models to their systems relatively easily because patch variables does not improve the predictive power of patch area and position are easy parameters to collect area-and-isolation models (Moilanen and Hanski 1998).
67 These contradictions may arise because environmental Material and methods requirements and dispersal ability vary from species to species and these biological differences affect patch occu- The study species pancy in metapopulations. In specialist herbivores including some butterfly species, the size of the host plant can be a Copera annulata (Zygoptera: Platycnemididae) occurs in surrogate for patch capacity and the area-and-isolation central China, Korea and Japan. It is univoltine in most paradigm may hold to some degree (Dennis et al. 2003). parts of Japan and is typically observed in June through However, in carnivores and generalist herbivores whose August. As a damselfly species, early life stages from egg to habitat patches are difficult to quantify, patch capacity the final instar larva occur in water. After emergence, the should be evaluated not only by area but also by other adult insect can fly among water bodies for mating and factors within the patch. In addition, strong dispersers may oviposition. We chose C. annulata as a model species for easily cover the whole region, in which case patch isolation our study because of the ease of delineating its habitat may not affect metapopulation structure (Harrison 1991). patches: namely, farm ponds. In addition, it has been Recently, applied ecologists are starting to evaluate the reported that C. annulata prefers small and shady pond conditions (Sugimura et al. 1999) and, therefore, the pond effect of patch isolation (or conversely, patch connectivity) area cannot simply be assumed to represent patch capacity. and patch qualities in addition to area by various regression analyses (Thomas et al. 2001, Fleishman et al. 2002). The importance of patch connectivity or within-patch quality can be evaluated by various goodness-of-fit measures, such Field observation 2 as coefficient of determination (R ). These approaches offer The study area is located in the northeastern Kanto plain, greater insights into the processes structuring metapopula- Ibaraki prefecture, Japan (10 10 km, 3688’N, 14088’E; tions than do the process-oriented models based on area and Fig. 1). The typical land use in the area is a mixture of isolation. There has been, however, a problem in these forests, fruit orchards, crop fields, rice paddy fields, golf simple uni- or multivariate regression analyses; that is, courses and residential areas. We perused the national basic within-patch qualities are often spatially autocorrelated maps (1: 2500) and aerial photographs of the area from across the landscape. Connectivity is also autocorrelated 1994 to 1999 (about 1: 10 000 scale, stored and managed by definition since it is calculated by a distance decay by the Japan map center; Bhttp://www.jmc.or.jp/)to function among habitats. Consequently, it is not easy to locate potential habitats for C. annulata such as ponds and determine the relative importance of within-patch qualities water holes in marshy areas. Rivers and ditches were and habitat isolation. excluded from our survey because they are largely unsuitable One way to mediate this problem is to use ‘variation (Sugimura et al. 1999). All potential habitats were explored partitioning’, also known as ‘commonality analysis’,in to determine whether they had water year-round. Artificial the regression analysis (Kerlinger and Pedhazur 1973). ponds such as water reservoirs and swimming pools were Variation partitioning has been widely used in community also excluded as unsuitable. Seventy-four ponds were ecology (Borcard et al. 1992, Legendre and Legendre 1998, selected as potentially suitable habitats for C. annulata. Legendre et al. 2005), but less so in population ecology Each pond was surveyed at least once by four well- (Heikkinen et al. 2005). Using this technique, we can trained observers on sunny days between 16 June and 22 evaluate the contribution of patch connectivity, that July, 2004 from the period of early to peak adult of within-patch quality and the overlap of these contribu- emergence. The margins of the pond were explored tions. exhaustively by four observers on foot to catch adult In this paper, we seek to evaluate the importance of individuals. In the first round of the survey of 74 ponds, within-patch quality, spatial autocorrelation and connectiv- we found C. annulata adults only at ponds which had ity in a damselfly metapopulation from a one-season survey aquatic and riparian vegetation. Therefore, additional using variation partitioning. Connectivity was calculated capturing trials were conducted only for those ponds; we based on the assumption of a Hanski-type metapopulation. did not visit the other ponds again. As a result, 25 ponds were visited only once, 35 ponds twice and the rest three Various patterns of spatial structure were extracted by a times. Though this visitation schedule could introduce a semi-parametric method: principal coordinates of neighbor bias in which suitable ponds would have a larger detection matrices (PCNM) (Legendre et al. 2005, see also Statistical probability, it maximized our ability to detect small analysis) separate from metapopulation measures of con- populations. To evaluate our imperfect survey, we used a nectivity. Though we expect connectivity and the PCNM maximum likelihood estimation of the detection probability component to be similar and to fully overlap if dispersal and implemented by the software Presence ver. 2.0 (MacKenzie metapopulation dynamics are the only sources of spatial et al. 2002). We assumed the probability of the estimation autocorrelation, the autocorrelation can also arise from the would not change during our survey or among ponds. effects of other biotic processes, such as trophic interactions The individuals captured were counted and marked by (Bjørnstad and Bascompte 2001), or spatially structured removing the right middle tibia with forceps. Those environmental factors (Thomas 1991, Borcard et al. 1992). without the right middle tibiae were not counted to avoid Following variation partitioning among the within-patch double recording. The sample tibiae were kept in a deep environment vs spatial vs connectivity models, we discuss freezer for future genetic analysis. In damselflies, loss of this the relative importance of within-patch quality and con- tibia does not significantly shorten life span (Fincke and nectivity. Hadrys 2001). The mean number of individuals captured
68 4 006 000
4 004 000
4 002 000 Northing (meters : Tokyo UTM, Zone 54)
4 000 000
424 000 426 000 428 000 430 000 432 000 Easting (meters : Tokyo UTM, Zone 54)
Figure 1. A summary map of the study area. The ponds surveyed are colored in black. The black and grey lines indicate rivers and the contour lines of elevation, respectively. The map was projected onto the UTM (Universal Transverse Mercator) coordinates, Tokyo UTM, Zone 54. per observation in a pond was natural log-transformed after namely dead branches and leaves, was measured at three adding 0.5 (Yamamura 1999). Linear trends in spatial points in the littoral area of each pond bottom and coordinates were further eliminated from the log-trans- averaged. Accumulated debris has been reported as a formed abundance, because PCNM cannot detect broader suitable habitat for larvae (Sugimura et al. 1999). (5) The spatial trends than those of the study area (Borcard and area of the ponds (‘area’) was also considered. Area is of Legendre 2002). The detrended abundance (hereafter primary importance in many metapopulation studies but denoted as the ‘population size’ in this paper) was calculated may negatively affect C. annulata because they appear to as the residuals of the regression on XY spatial coordinates. prefer small shady ponds. (6) The percentage of the pond perimeter with revetment (‘revetment’) was also extracted using GIS (ArcView ver. 9.1) constructed specifically for Within-patch quality our study based on the national basic maps (1:2500). Revetment was recorded because we suspected that artificial For within-patch quality, i.e. the pond environmental alteration of the pond bank would reduce C. annulata condition, six variables were selected in our study (variables are numbered, hereafter). We recorded the following three habitat. biotic factors in the ponds in August 2005: (1) predatory fish score (‘fish’), (2) abundance of benthos fauna (‘benthos’), and (3) cover area of aquatic and riparian Statistical analysis vegetation in each pond (‘vegetation’). For predatory fish, the combined abundance of largemouth bass Micropterus Our data contain numerous cases with zero abundance (74 salmoides and bluegill sunfish Lepomis macrochirus was 16 58 ponds). The recent advance in regression theory surveyed by a D-frame net and/or a casting net at the may provide a more sophisticated tool to analyze our raw littoral area and was recorded in three categories (abundant, heteroscedastic data such as logistic regression or negative existing, none). For benthos, chironomid larvae and naidid binomial regression than our classical regression of trans- worms (Oligochaeta) were collected using a plastic frame formed data. However, partial correlations, which are the (25 25 cm, 20 cm height) and a hand net (mesh size bases of variation partitioning, are in turn based on about 300 mm, aperture 10 8.5 cm) from four sample variance-stable data (Gaussian) are not applicable to other sites of each pond. Wet weights (g) were measured and regressions (Nagelkerke 1991, Shieh 2001). All analyses summed for the four samples from each pond. For were performed using the function ‘glm’ in the statistical vegetation, the total coverage area (m2) of aquatic and environment R (R Development Core Team 2006). riparian vegetation in each pond, including emergent plants (Typha latifolia, Acorus calamus, Phragmites australis, etc.) and floating plants (Nelumbo nucifera, Nymphoides peltata, Regression analysis of within-patch quality etc.), was measured in the field. Adults utilize vegetation for perching and oviposition (Sugimura et al. 1999). We checked for normality of all within-patch factors We also measured three physical conditions of the plotted against normal quantiles, and transformed them to ponds. (4) The thickness of the debris layer (‘debris’), stabilize variation if necessary: percentage data (revetment)
69 were arcsine-square-root transformed, and others (benthos, material). (2) calculate the connectivity matrix W based on debris and area) were natural log-transformed after D: adding 0.5. d 2 Variable-selection procedures such as the stepwise regres- W [w ] 1 ij (3) sion have been criticized for introducing bias in parameter ij 4 th estimations, inconsistencies among model selection algo- where th is the maximum distance of the minimum rithms, and inappropriate reliance on a single best model spanning tree (Legendre and Legendre 1998). (3) calculate (Whittingham et al. 2006). Therefore, our study takes, at the eigenvectors {ui:i 1, 2,...., 82 (the number of ponds least partly, the information-theoretic approach (Burnham nine supplementary points 1)} of the centered connectiv- and Anderson 2002). We constructed linear regression ity matrix, models of every possible combination of the six within- patch factors (26 1 63 models) assuming no interaction 11T 11T V (I )W(I )(4) effect. Because our sample size was small (74 ponds), AICc n n instead of AIC was calculated (Hurvich and Tsai 1989): where I is the identity matrix and 1 is a vector whose 2 m (m 1) V AICc AIC elements are all ones. The eigenvectors of are PCNM n m 1 themselves and represent various spatial scales. Those corresponding to large eigenvalues represent the global 2 m n n log(sˆ 2) (1) scale of the spatial trend; those with medium eigenvalues, n m 1 the regional scale; and those with small eigenvalues, the local or fine spatial trends. The eigenvectors associated with where n is the number of samples (74 ponds), m is the negative eigenvalues represent negative spatial autocorrela- number of parameters to be estimated including the tion. In this study, only eigenvectors having positive intercept and variance of the regression model, and sˆ 2 is eigenvalues {PCNMi:i 1 (the largest), 2, . . . , 32 (the the estimated error variance. The model with the smallest smallest)} were used to model spatial autocorrelation, since AICc (AICcmin) value may be best supported by data but we were primarily interested in detection of positive spatial other models with small AICc values may also have support. autocorrelation. PCNM values were calculated using the R Therefore we calculated Akaike weights (wi) for all the library ‘spacemakeR’ developed by Dray et al. (2006). (4) models instead to choose a single model (Burnham and Select relevant spatial autocorrelation structures by linear Anderson 2002): regression analyses of PCNMs. Here again, we took the 1 information-theoretic approach. Thirty-two PCNMs were exp Di equally divided into four subsets of spatial categories, 2 w (2) that is, large (PCNM1, PCNM2, . . . , PCNM8), medium i X63 1 (PCNM9,PCNM10, . . . , PCNM16), medium-small exp D 2 r (PCNM17,PCNM18, . . . , PCNM24) and small i 1 (PCNM , PCNM , . . . , PCNM ). It was impossible ^ 25 26 32 where i AICci AICcmin. The relevance of a factor was to execute regression analyses for all combinations of the 32 evaluated by summing all wi’s of the models including that PCNMs, and we were interested in spatial categories, which factor (the summed Akaike weight) (Burnham and Ander- are biologically interpretable, rather than individual son 2002). We did not use model averaging for multi-model PCNMs. Every combination of the four spatial categories inference, which is recommended by Burnham and Ander- was regressed to population size. The Akaike weights were son (2002), because variation partitioning could not be calculated for all the regression models and summed across implemented among the compounded models produced by each category. The inclusion or exclusion of each spatial model averaging. category was determined by this summed Akaike weight. The spatial scale of each category was further measured by a non-parametric correlogram function (NCF) devel- Spatial autocorrelations extracted by PCNM oped by Bjørnstad and Falck (2001). Visual determination is difficult when the data are taken from irregularly Principal coordinates of neighbor matrices (PCNM) is a allocated sites. The population size predicted by the method to extract spatial structures at various scales regression model of each spatial category was used to (Legendre and Anderson 1999, Borcard et al. 2004). The evaluate the spatial scale of the category. The spline method creates a set of spatial predictors (PCNM), which correlogram of the predicted population size was then are orthogonal to each other, from a geographic distance calculated. The x-intercept of the correlograms was used as matrix. The most prominent spatial autocorrelation can be our estimate of the scale. Confidence intervals of estimated extracted by regressing population size on the PCNMs. spatial scales were calculated by 1000-time bootstrapping of There are some derivatives from the original method and we the data. NCF was executed using the R library ‘ncf’ based our analysis on Dray et al. (2006) as follows: (1) developed by Bjørnstad and Falck (2001). calculate a geographic distance matrix for all pairs of ponds (D [dij]). Pond positions were represented by their centroids. Nine points were added to reduce the largest Estimation and evaluation of connectivity distance between adjacent ponds. Providing these supple- mentary points enhances the detection of small spatial We defined the connectivity strength of pond i according to structures (Peres-Neto et al. 2006 in the supplementary the model of Hanski and Singer (2001):
70 X d 1.0 and that of the ponds visited twice (including those S N exp ij (5) i j a visited three times, but for which only the first two data i"j were incorporated) was 0.904. This high probability, which where Nj represents the actual abundance in pond j (the is partly due to the conspicuousness of C. annulata, verifies row average number of individuals before the transforma- the data for further analyses in spite of our imperfect survey tion). The equation represents the total summation of the schedule. Only two ponds having one or two individuals product of population size in the emigration patch and an were absent in the first survey but present in the second exponential dispersal kernel from pond j to pond i. Each survey. Removing these two ponds did not affect the results product can be seen as the number of propagules reaching (not shown); therefore, we concluded that our approach was pond i from pond j (Moilanen 1999). Though other fat- robust for minor detection failures. tailed dispersal kernels are possible (Moilanen 2004), Eq. 5 was chosen because it is tractable and easy to interpret: a is the mean generational dispersal distance. To estimate a we Regression result of within-patch quality used a modification of the profile likelihood method of Havel et al. (2002); that is, the population size was regressed The regression model including within-patch quality for connectivity defined in Eq. 5 assuming a sequence of indicated that debris, vegetation and benthos had positive values for the parameter a (increased at 1.0 m intervals), effects while revetment, area and fish had negative effects on and the value of a that gave the minimum residual sum of the population size (Table 1, fish results are not shown but squares (RSS) was selected. The minimum RSS corresponds their effect was observed by plotting against the population to the maximum likelihood estimate for Gaussian regression size). Judging from the total Akaike weights in Table 1, models (Venables and Ripley 1998). debris had the most prominent effect (0.975). Vegetation was also of secondary relevance (0.597). Though the other four were not relevant compared to debris and vegetation, Variation partitioning for three components even fish (0.200) would be selected in 20 times out of 100 similar data sets if they had been virtually available. Since So far, three regression models have been described: those for there is no clear-cut criterion like the a-level to remove (1) within-patch quality, (2) spatial autocorrelation by factors in the information-theoretic approach and we PCNM and (3) connectivity. In addition to these three judged that they all had substantial effects, we did not models, we conducted regressions on all predictors simulta- 2 neously and all pairs. The R2 (coefficient of determinations) remove any of them. The adjusted R for the regression was calculated and transformed by Ezekiel’s adjustment to model with six factors was 0.193. make them comparable among models having different numbers of predictors (Peres-Neto et al. 2006), Spatial structure estimated by PCNM n 1 R2 1 (1 R2)(6) adj n p 1 Our procedure decomposed spatial autocorrelation into four spatial scales which were measured as 1696 m, 640 m, where n is the number of samples (74 ponds) and p is the 2 392 m and 201 m by NCF, respectively (Table 2). The number of predictors excluding the y-intercept, and R is the large spatial category was highly relevant, as the summed original coefficient of determination, i.e. the residual sum of Akaike weight was 0.973. While the other three categories, squares standardized by total variance of the data. Variation medium, medium-small and small, were less relevant than partitioning was then conducted to determine the contribu- the large, the medium-small scale was the most trivial (less tion of the pure components, the paired components, and the than 10 times less information-retaining than the other 2 Ø full suite of explanatory variables using Radj ( kland 2003). two). Therefore, we removed the PCNMs of the medium- Although it was impossible to further decompose the small category. The final spatial autocorrelation including overlapping fraction into each factor by variation partition- large, medium and small spatial categories had an adjusted ing, a correlation matrix was calculated among the factors. R2 of 0.407. This helped to interpret the merged effects in the over- lapped fractions, especially in conjunction with the spatial Table 1. Regression analysis for within-patch factors and their autocorrelation. Overlapped fractions represent correlation relevance estimated by their summed Akaike weights. structures among factors (Legendre and Legendre 1998). The fish score was not incorporated in the matrix because it Factor Estimated coefficients$ Summed Akaike weight§ was an ordered score. The medium-small spatial category y-intercept 0.018 was removed for the final PCNM model (Results) and was Debris 0.461 0.975 also discarded for the calculations. Vegetation 0.261 0.597 Benthos 0.106 0.293 Revetment 0.030 0.279 Area 0.037 0.239 Results Fish 0.200
$ Copera annulata was found in 16 out of the 74 ponds The coefficients were calculated for the full model. It was not reported for the fish as this factor had an ordered score. surveyed. The largest number of C. annulata captured was §A summed Akaike weight for each factor was calculated as the 41; the smallest was one (at one pond). The detection summation of Akaike weights in all the models including the factor probability for the data of the ponds visited three times was (see Statistical Analysis for details).
71 Table 2. Spatial autocorrelation extracted by PCNM and its The mean nearest-neighbor distance was 357m (944 m relevance for population size. PCNMs were decomposed into four SE) among 52 pairs of ponds and was greater than a 53 m. spatial scales, large, medium (Mid), medium-small (MidS) and small. However, because there were still enough nearest-neighbor distances in closer ranges (seven pairs B100 m, 15 pairs Spatial categories Spatial scale (m)$ Summed Akaike B200 m), we postulated that the pond configuration in our § weight study area was suitable for estimation of a valid a. If more ponds had been clustered in a smaller region, the damselfly Large (PCNM1 PCNM8) 1696.4 0.973 (1076.9 2614.2) could have move in a stepping-stone fashion and could have Mid (PCNM9 PCNM16) 640.2 0.116 dispersed much further. Consequently, connectivity might (423.6 1211.2) be estimated as greater than 53 m or its effect might be MidS (PCNM17 PCNM24) 392.2 0.007 (0 877.4) estimated as less important than 0.157. If ponds were Small (PCNM25 PCNM32) 200.7 0.099 separated by much greater distances, C. annulata might not (0 592.4) have lived in this region.
$The population size predicted by each regression model (large, medium, medium-small and small) was used to evaluate its spatial scale. The spatial scale was estimated as the x-intercept of the non- Variation partitioning and interpretation of the parametric correlogram function (NCF) of the predicted abundance spatial structure of each spatial category. Confidence intervals (ranges in the parentheses) of estimated spatial scales were calculated by 1000 For simplicity, each adjusted R2 was renamed as R2 ( times bootstrapping. See text and Bjørnstad and Falck (2001) for S details. 0.407, S represents spatial autocorrelation extracted by § 2 A summed Akaike weight for every category was calculated as the PCNM), RE ( 0.193, E represents within-patch quality) 2 summation of the Akaike weights in all the models including the set and RC ( 0.157, C represents connectivity), respectively. of PCNMs in it. Notice that regression analyses were not based on The variation of all three combined models was calculated the PCNM individually but on each spatial scale including eight 2 2 as RS@ C 0.435 and those of all pairs were RS@ E 0.430, PCNMs, respectively. 2 2 RS@ C 0.418 and RE@ C 0.290. Following Økland (2003), the pure contributions of the three regression 2 2 models were RS½(E@ C) 0.144, RE½(S@ C) 0.016 and Effect of connectivity 2 RC½(S@ E) 0.005, respectively. The overlapping contribu- 2 2 2 tions were RSS C½E 0.092, RSS E½C 0.117 and RES C½S The profile likelihood estimated a (i.e. the generational 2 0.006 and RPS ES C 0.053. When small fractions (less mean dispersal distance) to be 53 m (Fig. 2a). Though this than 0.01) were neglected, the contributions could be value may seem small for damselflies, another mark- depicted as in Fig. 3. The contribution of spatial auto- recapture study in another area confirmed that this species correlation extracted by PCNM was the largest, and it seldom migrates more than 100 m (Yamanaka unpubl.). contained almost all of the variation of connectivity and Such short-distance dispersal behavior has also been also of within-patch quality. One-third of its contribution reported for other damselfly species (McPeek 1989, Rou- overlapped with the contribution of connectivity. Another quette and Thompson 2007). The adjusted R2 for the one-third of its contribution overlapped with within-patch connectivity model based on a 53 m was 0.157. quality (not overlapping with connectivity). The rest of its
90 (a) (b) 3
85 2
RSS 1
80 0
alpha = 53m -1 Pop size (log scaled and detrended) 75 0 200 400 600 0 1 2 3 4 5 alpha (mean effective distance) Connectivity
Figure 2. (a) The profile likelihood analysis of connectivity in relation to parameter a. (b) The relationships of connectivity with the estimated a ( 53 m) and C. annulata population size. Population sizes were natural log-transformed after adding 0.5. They were also linearly detrended to remove the global trend, and there were some negative points jittering around loge(0.5) 0.693. The straight line in (b) represents the regression line in our study (see text).
72 accumulates. If revetment is installed in a pond, vegetation will be destroyed and consequently debris will be reduced. S Discussion C E From a one-season survey of the damselfly Copera annulata, we successfully evaluated the relative importance of within- 0.090.06 0.12 0.02 patch quality, connectivity (as quantify using standard metapopulation methods) and various spatial structures (quantified using PCNM) (Fig. 3). The contribution of within-patch quality was larger than that of connectivity. 0.14 Moreover, the area of the ponds was much less important than debris and vegetation. From this result, we conclude 0.57 that the classic area-and-isolation paradigm from metapo- pulation theory will not hold for the C. annulata Figure 3. Schematic diagram of the contributions. S, the spatial metapopulation. Though the contribution of connectivity autocorrelation extracted by PCNM; C, the connectivity effect; E, was the smallest among three regression models, it was still the environmental effects (debris and vegetation). The numbers in substantial (0.157). Therefore, we cannot ignore the the figure represent the relative contributions of the fractions to importance of pond configuration when studying the the total variation ( 1.0). distribution of this species. There is a caveat for interpreting the modest importance contribution was not explained by connectivity or within- of connectivity; that is, we only considered the Euclidean patch quality. The contribution of connectivity was distances among ponds. Recent studies have revealed that substantial but fully embodied within spatial autocorrela- the effective distance, which is calculated from the cost tion as we had expected. Because PCNM expresses various surface of the land-use mosaic between patches, can be a spatial scales of autocorrelation, the one created by the better measure of distance than the Euclidean distance connectivity effect should be totally enveloped within the (summarized by Taylor et al. 2006). A greater part of the PCNM spatial scales if the method works properly. Within- variation of spatial autocorrelation might have been attrib- patch quality also largely overlapped with spatial autocor- uted to connectivity if the connectivity had been calculated relation, which represents that a large portion of the based on effective rather than Euclidian distance. To do so environmental variation is spatially structured. was, however, impossible in our study because its calculation To gain further insights on the overlapping variations in requires behavioral data or mark-and-recapture experiments. Fig. 3, correlations among factors were calculated in Table Though spatial autocorrelation extracted by PCNM was 3. None of the correlations was high; this represents the fact found to have the largest contribution in explaining local that there were no strong complementary relationships abundance, this fact tells us little about the underlying among factors. Connectivity had the largest correlation with metapopulation processes since PCNM is too flexible to the medium spatial category (Table 3). Though there was pick up spatial structures at various scales. Therefore, the no strong relationship between spatial autocorrelation and correlations among factors were calculated to determine within-patch quality, debris was slightly correlated with the which spatial scale each factor had. We found that medium (0.23) and small scales (0.25) and vegetation with connectivity had the most correspondence with the medium the small scale (0.23). Debris and vegetation were some- spatial scale. We postulated that the dispersal behavior of what correlated but both were negatively correlated to 53 m on average connects neighboring patches and that revetment. This result is easy to interpret in a biological these patches make clusters at the scale of the medium spatial sense. The more vegetation exists, the more debris category (640 m). Though we could not detect a clear
Table 3. Correlation matrix among all the factors, connectivity (C), within-patch quality (debris, vegetation, benthos, revetment and area) and spatial scale (large, mid and small).
C$ Debris Vegetation Benthos Revetment Area Large§ Mid§ Small§
C 1.0 0.22 0.11 0.07 0.12 0.02 0.18 0.42 0.19 Debris 1.0 0.48 0.19 0.44 0.05 0.16 0.23 0.25 Vegetation 1.0 0.09 0.45 0.11 0.18 0.14 0.23 Benthos 1.0 0.19 0.19 0.17 0.14 0.03 Revetment 1.0 0.29 0.27 0.0 0.13 Area 1.0 0.09 0.05 0.06 Large 1.0 0.02 0.01 Mid 1.0 0.01 Small 1.0
$Connectivity was calculated for every pond using Eq. 5 with the estimated a ( 53 m). §The spatial autocorrelation effects were the predicted population abundances by the categorized regression models, like those in Table 2. The numbers in bold are the top five largest absolute correlation values. Fish is an ordered score and was excluded from the analysis.
73 relationship between the within-habitat quality and the that is, a long-term colonization effect is estimated from a scales of autocorrelation, debris and vegetation seemed to snapshot of spatial pattern data. However, ter Braak et al. have some correspondence with the medium and the small (1997) conducted a power analysis of the regression model scales. If there is a regional trend for pond management and of metapopulations using simulated data and concluded utilization, and we suspected such was the case in our study, that the coefficient of connectivity can be estimated the environment in the ponds (i.e. debris and vegetation) relatively well from snapshot surveys. Therefore, our might have some spatial trends. dispersal estimate may in practice correctly reflect the The overlapping area between connectivity and within- underlying biology despite these theoretical concerns. patch quality is rather difficult to explain. Connectivity The variation here attributed to connectivity and should technically be segregated from environmental factors dispersal may conceivably be due to underlying spatial because it is based on the mechanistic assumption of a structures other than metapopulation processes. However, Hanski-type metapopulation (IFM). In some steam-fish the particular model of spatial decay (exponential, in this metapopulations, the position in the stream gradient has a case, though for example Gaussian or Bessel functions would great influence on the local population incidence (Gotelli also be appropriate; Bjørnstad and Bolker 2000) is derived and Taylor 1999), and connectivity calculated by Eq. 5 from fundamental models for animal movement (Levin et al. might represent some spatially autocorrelated environmen- 2003). This variation may therefore be parsimoniously tal condition rather than the dispersal-induced spatial attributed to movement processes. Subsequent to the structure. The environmental conditions were, however, statistical calculations it is of course necessary to check that assumed to have a different spatial effect than that of the estimated range of connectivity represents a plausible connectivity in our two-dimensional study area where scale given the mobility of the species in the study (as is the damselflies can fly without structural limitations to their case for our analysis of C. annulata). We believe that pathways though the overlapping fraction between con- partitioning out the ‘connectivity’ portion of the pattern nectivity and within-habitat quality (0.06 in Table 3) may separate from the broader spatial structures is useful because reflect how they share some similar scales of autocorrelation. it provides a meeting ground for the geostatistical and the Our method provides a tool to elucidate processes metapopulation branches of spatial ecology. structuring a metapopulation from a one-season survey. It Since our method can only be applied to a specific will be beneficial especially for species whose biology has landscape and a specific species, it may seem less attractive not been well studied and also especially in cases in which in basic ecology and is phenomenological at a glance. patch area cannot be used as an indicator of patch capacity However, every metapopulation is formed by an integrated because our method uses a multi-regression model to effect of the behavior of the specific species and the evaluate within-patch quality and we can incorporate any characteristics of the focal landscape configuration (Calabr- suspected factors. Though it might also be possible to ese and Fagan 2004, Fagan and Calabrese 2006). We hope incorporate patch qualities into the more process-oriented our method can contribute to quick and effective evaluation approaches (e.g. SPOMs, Moilanen and Hanski 1998, for a specific metapopulation system before more specia- Ozgul et al. 2006), such models require much deeper lized mechanistic simulations are conducted. knowledge of how the factors affect the processes. In addition, even a simple IFM requires many years’ accumu- Acknowledgements We appreciate the suggestions of the tough lation of the population census for robust estimates of the editor for forging both the logic and methodology of our study. parameters (Moilanen 1999) and for valid future predic- We are grateful to Segovia Golf Club in Chiyoda, Chiyoda tions (Thomas et al. 2002). However, it should be noted Country Club, Niihari Golf Club and owners of the surveyed farm that mechanistic metapopulation models may provide us ponds in Niihari, Chiyoda, Sitsuku and Yasato district for their more information about the biological consequences of the kind support in conducting the odonate census. We thank Eelke Jongejans and Lidewij Keser, the botanists in PSU and TY’s best metapopulation and are much more robust for future friends in Long Meadow Lane, who kindly gave us useful predictions than our approach because our method evalu- comments on an early draft. This study was founded by a project ates the ‘relative’ effect of factors. Our approach will not titled ‘Shizen-kyousei (Developing Technology for Coexisting provide absolute biological estimations but can evaluate with Nature within Agro-forest and Aquatic Watershed Land- their relative importance. Particularly if all patches were scapes)’ of the Japanese Ministry of Agriculture, Forestry and equally good quality or conversely equally poor quality, the Fisheries of Japan (TY, KT, NI and DSS) and the US Dept of relative effect of within-patch quality would be reduced. Agriculture National Research Initiative Grants no. 2002-35302- Our approach constructs the most parsimonious regression 12656 and 2006-35302-17419 (ONB). models in a specific location and can be used to evaluate the current conditions of a specific species in a focal area. A new population census and environmental data collection would References be required for the same species in a different situation. Like the IFM models, our method does not require extra Bjørnstad, O. N. and Bolker, B. 2000. Canonical functions for experiments to infer dispersal ability (a) such as mark-and- dispersal-induced synchrony. Proc. R. Soc. Lond. B 267: recapture. Every applied ecologist who has undertaken 1787 1794. Bjørnstad, O. N. and Bascompte, J. 2001. Synchrony and second- mark-and recapture in the field recognizes that it is an order spatial correlation in host parasitoid systems. J. Anim. arduous task and that it sometimes takes several years. Ecol. 70: 924 933. There is, however, one caveat. Our method (as well as the Bjørnstad, O. N. and Falck, W. 2001. Nonparametric spatial IFM models) is based on a strong hidden assumption of the covariance functions: estimation and testing. Environ. Ecol. stationarity of metapopulation processes (Moilanen 1999); Stat. 8: 53 70.
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