The importance of patch shape at threshold occupancy: functional patch size within total habitat amount

The habitat amount hypothesis (HAH) stresses the importance of total patch amount over the size of individual patches in determining species richness within a local landscape. However, the absence of some species from patches too small to contain a territory would be inconsistent with the HAH. Using the association of territory size with body size and the circle as optimal territory shape, we tested several HAH predictions of threshold patch occupancy and richness of 19 guilds of primarily insectivorous breeding birds. We characterized 16 guild-associated patch types at high spatial resolution and assigned one type to each guild. We measured functional patch size as the largest circle that fit within each patch type occurring in a local landscape. Functional patch size was the sole or primary predictor in regression models of species richness for 15 of the 19 guilds. Total patch amount was the sole or primary variable in only 2 models. Quantifying patch size at high resolution also demonstrated that breeding birds should be absent from patches that are too small to contain a territory and larger species should occur only in larger patches. Functional patch size is a readily interpretable metric that helps explain the habitat basis for differences in species composition and richness between areas. It provides a tool to assess the combined effects of patch size, shape and perforation on threshold habitat availability, and with total patch amount can inform design and/or evaluation of conservation, restoration or enhancement options for focal taxa or biodiversity in general. Supplementary Information The online version contains supplementary material available at 10.1007/s00442-023-05453-3.

a An example of a guild defined using this classification system would be the Deciduous (D) Low Canopy (L) Gleaning (G) Insectivores (I) that are associated with an edge patch type (2).This is abbreviated as DLGI2.(See Hamel et al. 1982) b Species categorized as carnivores, plantivores, graminivores, or scavengers were not included in the final analysis due to insufficient sample sizes or the occurrence of extensive portions of territories of these generally wide-ranging species far beyond plot boundaries OR 6. Assignment of 59 breeding bird species at the Connecticut Hill WMA to guilds using the classification system outlined in OR 5 a .From Keller et al. (2003).

1) DLGI1
2) DMGI1 3) DHGI1 4) DTGI1 OR 9 MDC's for different solid patch types within broader cover types of forest and clearcut.Note the heterogeneity and resulting high number of edges (e.g., trees adjacent to open grass) within the oldfield at upper right.This is inconsistent with the concept of MDC as pertaining to homogeneous patch types, thus leading to the desirability of a comparable variable (DEAC) to quantify the density of edge types associated with particular species or guilds.Also note the many types of edges that occur within the more general classification of the oldfield and 24 ha clearcut outlined in yellow (see Fig. 4 for examples of edge types at higher spatial resolution)

OR 10
The pattern of edge addition (solid lines) to the progressively larger samples examined by the edge scanning algorithm ESCAN.A prespecified number of annuli are examined for the presence of type T edges starting within each cell on the GIS map.See OR 11 for an example of the output from this program.To see how this approach can be applied as a practical measure of habitat size and quality for edge-associated species, examine the "Poor" vs "Good" cover type interspersion of northern bobwhite quail (Colinus virginianus) habitat quality depicted in fig. 9 of Leopold (1933).A 1 annulus sample = 6 total edges, B 2 annuli sample = 30 total edges, C 3 annuli sample = 72 total edges.From Keller and Smith 2014 OR 11.An example of the output from the edge density scanning algorithm ESCAN (OR 10) as applied to shrubsapling / opening edge within a hypothetical oldfield (Fig. 5).The program locates the area on the map with the highest density of edges of any specified patch type (T) for each sample size (i.e., number of annuli, column 1), then compares edge density across all sample sizes and selects that sample size with the highest absolute edge density (EI), in this case EI=9.7.The area of cells within the number of annuli exhibiting the highest value of EI is converted to DEAC (last column), the diameter of the equivalent area circle.See Figure 5 and the text for further description of the technique.From Keller and Smith (2014).

Annulus a
Starting  Theoretically, small species are more likely to be the first species to occur in smaller patches because they require less patch area in which to breed (Schoener 1983).This leads to small species generally being more abundant than larger species.A possible null hypothesis based on observed frequency of occurrence would include, and therefore obscure, this potential effect of body size (Colwell and Winkler 1984).Therefore, our null hypothesis was that all species had an equal likelihood of occurrence.Except for the mid-canopy foliage-gleaners (Guild 2), which were of interest because of the wide range of distinct body sizes they presented, no attempt was made statistically to analyze higher orders of species combinations within guilds (Keller 1986).

OR
Linear regression model of Guild 1 species richness with functional patch size (m).See OR 14a Linear regression model of Guild 4 species richness with functional patch size (m) 2 .MDC4 was the primary variable in the most parsimonious multivariate regression model for Guild 4, the terrestrial gleaning insectivores (Table 3) OR 14b Linear regression model of Guild 4 (terrestrial gleaning insectivores) species richness with Total Patch Amount (m-2).Based on AIC values and the Cp statistic, the multivariate model including TOTAMT4 was not plausibly equivalent to the most parsimonious model for species richness of Guild 4 (Table 3) Guild 4 Species Richness vs.Total Patch Amount OR 15a Linear regression model of Guild 9 species richness with functional patch size (m).DEAC9 was the sole variable in one of the two most plausible multivariate regression models (Table 3) for Guild 9, the deciduous lowcanopy-edge gleaning insectivores (DLGI2, OR 5 and OR 6) OR 15b Linear regression model of Guild 9 species richness with Total Patch Amount.TOTAMT9 was a secondary variable in one of the two most plausible multivariate regression models (Table 3) for Guild 9, the deciduous low-canopy-edge gleaning insectivores (DLGI2, OR 5, OR 6) Guild 9 Species Richness vs.Total Patch Amount OR 16a Linear regression model of Guild 13 (black-throated blue warbler Setophaga caerulescens) occupancy with functional patch size (m) (MLGI2, OR 5 and OR 6).Like TOTAMT below, although highly significant, DEAC13 was not the strongest predictor of patch occupancy for this guild.

OR 16b
Linear regression model of Guild 13 occupancy with TOTAMT13.Although TOTAMT13 was a highly significant predictor of occupancy for Guild 13 (black-throated blue warbler Setophaga caerulescens (MLGI2, OR 5 and OR 6), within-patch heterogeneity (NUMHAB13) was a better predictor (R 2 = 0.721) in the multivariate regression model (OR 16c, Table 3) OR 17.Effect Tests (F Ratio) for predictor variables when multiple variables were included in plausible (AIC) linear regression models of avian within-guild species richness at the Connecticut Hill WMA in central New York (Table 3).Predictor variables entered in trials for each guild are those identified in a Number in parentheses is the number of species that could occur in the guild.For Guild 1 (DLGI1), the rubythroated hummingbird and black-and-white warbler were not included in this analysis because they were classified as foliage-gleaners for only 4 of 28 and 5 of 15 observations, respectively.The potential for climatic or other environmental uncertainty to disrupt the influence of factors such as habitat structure, which may serve to organize communities, has been well documented by Paine (1966Paine ( , 1984)), Wiens (1977), and others.In this study, fluctuations in the richness of resident species, the apparently random composition of single-species occurrences of resident woodpeckers (Guild 18, Table 5) and bark-gleaners (Guild 17), and absences of the black-capped chickadee as the initial representative of its guild (DMGI1, Guild 2, Table 5) may be at least partially attributable to the negative effects of severe overwintering conditions on survivorship of the smallest members of these guilds (Keller 1986, Root 1988;Meehan et al. 2004).As a result, suitable patches for such residents may remain unsaturated because, even when individual habitat requirements are met, overwintering conditions can reduce population levels of some or all guild members (cf.O'Conner and Fuller 1983).
Patch conditions related to a species' natural history traits (e.g., lack of appropriate nest sites [Scott 1979;Dickson et al. 1983]) also may influence the sequence of species appearance in a guild.Snag densities were significantly lower on 6 of 7 plots where the chickadee was not the first species of its guild to appear.Natural history traits of the resident bark gleaners (DBGI, Guild 17) also may help explain the occurrence of the larger white-breasted nuthatch rather than the brown creeper as the more frequent representative in single-species occurrences of this guild (Table 5).The creeper is more restricted to mature forests than the nuthatch and has more restrictive nest site requirements (beneath loose bark as opposed to secondary cavities) (Hejl et al. 2002;Pravosudov and Grubb 1993).

Stronger Correlations of SR with Total Patch Amount
Only 5 of the 19 guilds had stronger relationships of species richness with total patch amount than with functional patch size (OR 21).Of these 5, the black-and-white warbler and black-throated blue warbler appear to be forestinterior-edge (canopy gap) adapted (Goetz et al. 2010;Keller and Smith 2014).Thus, they may only require a small amount (i.e., minimal DEACs) of their preferred edge type to establish territories and may tend to avoid larger openings.More detailed research on within-territory habitat structure, particularly for the black-and-white warbler, might better illuminate its habitat association with the edge between mature trees and regenerating forest or dense understory (Yahner 1986).Ultimately all of the first-cut species-/ guild-habitat associations can be refined further.Lastly, the ruby-throated hummingbird also maintains a very small defended territory (Robinson, et al. 1996).However, the hummingbird is much less conspicuous than syntopic passerines detected in the study and as a result, its observed distribution may include sampling bias.
The difficulty of identifying patch types that are internally uniform across landscapes The veery (Guild 5) provides an example of the difficulty, even when employing HR imagery, of identifying patch types that are internally uniform enough that associated individual species habitats are evenly represented across the full range of within-patch heterogeneity.First, although the veery is larger than the ovenbird, the smallest species in the guild, its territory size is reportedly smaller than that of the ovenbird (Van Horn and Donovan 1994;Bevier et al. 2004;Derochers et al. 2010, table 1).Thus, by a territory size definition of expected occurrence, the veery would be expected to occur more often as sole representative of the understory-gleaning guild.However, the veery's frequent appearance as the only member of the guild seems more related to its habitat structure than its smaller territory size.
Although the veery occurs in mature forests (Bertin 1977;DeGraaf and Rudis 1986), its association with dense understory coupled with a minimum requisite canopy height of only 2.5 m (Keller et al. 2003) broadens the range of forest age classes (cover types) in which it occurs.Dense understory was most prevalent on early successional clearcuts (CCA, CCB, N = 52 of 97 survey years) during post-cut years 4-10 where the veery became the most abundant breeding bird by post-cut year 8 (Keller et al. 2003:552, table 5, fig. 6).None of the other members of this guild occurred on these early stage clearcuts leading to the overwhelming occurrence of the veery in single species incidences of the guild (30 of 32 single species occurrences, Table 5), despite it not being the smallest species in the guild.
Conversely, the ovenbird, predicted by size to be the first species of the guild to appear at threshold patch sizes, inhabits the very open shrub layer or understory typical of pole stage or older closed canopy forests (DeGraaf and Rudis 1986;Keller et al. 2003).As a result, the ovenbird occurred on no sites in the study younger than post-cut year 24 (Keller et al. 2003:552).Sites older than this (CCC-2, F-SGA, F-NHHB-D, Table A1) typically supported multiple members of the deciduous understory gleaners (Keller et al. 2003, table 5, fig. 7).Thus although "forest understory" represents a restrictive subset of "forest"-related patch types, its structure varies over a wide range of forest age classes.Within the patch type, the veery's habitat type extends across most of this successional breadth, while other members of the guild are restricted to smaller portions of the same successional gradient.

Online Resource 26 -Considering Within-Patch Heterogeneity: Why Spatial Resolution Matters
The occurrence of multiple guild-specific patch types within most local landscapes in this study (e.g., OR-9) and the significant relationship of species richness with intra-patch heterogeneity for 8 of 13 guilds (OR-24) support the observation that patch types defined at any scale tend to occur in clumped distributions or along gradients (Margules and Stein 1989); and so, too, do associated species distributions (May et al. 2019).As noted, this means that interpretations of the influence of patch size, total amount, and spatial arrangement on species richness rely heavily on how precisely species groups are defined, and on the composition and uniformity of associated patch types (Fahrig 2013(Fahrig :1656;;MacDonald et al. 2021:13).Results here and elsewhere support the argument that specieshabitat associations are the most appropriate way to determine delineation of patches (Kupfer et al. 2006;Shriner et al. 2006;Arponen et al. 2012;Haddad et al. 2017).If so, the resolution at which patch types are defined needs to approach the grain at which focal species or species groups perceive and respond to the subset of the landscape they occupy (Keller and Smith 2014).Otherwise, the inability to separate the subset of the landscape used by focal species from more general cover types dilutes the strength of species-habitat correlations (Huston 2002;Betts et al. 2014, fig.1;Gaston et al. 2017).In GIS-based analyses, this capability depends upon initial researcher choices of image spatial resolution, classification system, and minimum size delineation or minimum mapping unit (MMU) (Stohlgren et al. 1997;Wulder et al. 2004;Gallant 2009;McDermid et al. 2009;Keller and Smith 2014).
Most tests of the HAH have defined species groups and habitat patch types broadly (Fahrig 2013, fig. 1b).This level of classification appears most often associated with use of Landsat imagery in GIS-based analyses.Landsat has spatial resolution (GRD) ³ 30 m.Even with a more restrictive classification such as "native forest" (Fahrig 2013, fig.1bii), Landsat and other lower resolution (LR) imagery cannot resolve individual landscape elements such as trees and shrubs, or consistently correctly classify variously aged forest or agricultural types (Stoms 1992;Smith et al. 2003;Luoto et al. 2004;McDermid et al. 2009;Arponen et al. 2012; but see Shirley et al. 2013 use of unclassified Landsat imagery).This has several consequences.
First, it can result in larger minimum mapping units that often exceed the size of the home ranges of focal species, rendering impossible quantification of within-territory composition or structure that might explain a species presence in one patch but not another (Holland et al. 2004;Farrell et al. 2013;Keller and Smith 2014;Bombi et al. 2018;Rechsteiner et al. 2019).Second, the inability of LR imagery to accurately classify more restrictively defined (i.e., more uniform and potentially more ecologically appropriate) patch types means that individual patches of more broadly defined types (i.e., biotopes) are much more likely to contain multiple (guild-specific) patch types classified as a single cover type (Stohlgren et al. 1997;Bar-Massada et al. 2012;Keller and Smith 2014;compare OR 1, OR 2 and OR 9).This confounds interpretation of the individual effects of either patch size or total patch amount (Fletcher et al 2018).Note, although potentially cost prohibitive or simply unavailable until recently, free or low-cost HR imagery (e.g., Maxar Technology imagery embedded in Google Earth) is becoming increasingly available worldwide for use with species or species groups that warrant HR analysis (Keller and Smith 2014, Rechsteiner et al. 2017).
The local scale relationship of species richness with structural heterogeneity (OR8, OR 24) points to 1) a more general relationship of richness with increasing environmental heterogeneity over larger geographic areas (Wiens 1989;Ricklefs and Lovette 1999;Tews et al. 2004;Kallimanis et al. 2008;MacDonald et al. 2018) and 2) the likelihood that at LR a smaller proportion of the total patch area classified as habitat actually represents habitat as perceived by the focal species or group (Goetz et al. 2010;Tattoni et al. 2012;Farrell et al. 2013;Betts et al. 2014, fig.1;Bombi et al. 2018).This is especially true for habitat specialists (Holland et al. 2005;Mathews et al. 2014;Rechsteiner et al. 2019).
Ultimately, LR classification limitations dictate defining species groups broadly to match the limit of patch type identification.Yet, equating broad cover types such as "forest" with "habitat" for all forest dwelling species, is an acknowledged oversimplification (Watling et al. 2020:7).This not only leads to the potential inclusion of nonhabitat within the patch (type T) as noted above, but also raises the question of whether habitat breadth of some species may include other patch types that exist in the surrounding matrix (Andren et al. 1997)? Fahrig (2013:1656) recognized this problem and noted "To test the HAH directly, we need a single value of habitat amount for each sample site; it is not clear what that value would be if the habitat amount available to each species (both present and absent) is different." As examples, roughly half of the Atlantic Forest small mammals identified to species and classified as "savanna woodland" species in Melo et al. (2017) or "forest" species in Vieira et al. (2018), are listed on the IUCN Red List of Threatened Species (iucnredlist.org/species/#habitat-ecology,2016 assessments) as also occurring in other biotopes (e.g., shrubland, savanna, grassland, artificial [i.e., anthropogenic or degraded former forest]), which are acknowledged as potentially occurring in the surrounding matrices in both studies.Thus, for any species for which habitat associations are broader than "woodland" or "forest", interpretations of the influence of patch size or total amount would be less meaningful because, rather than entirely a barrier, the surrounding matrix may serve as a conduit or even as habitat (i.e., a source) (Andren et al. 1997;Dunford and Freemark 2004;Kupfer et al. 2006;Kuefler 2010;Aben et al. 2012).This confounding of patch isolation/connectivity due to matrix quality, although present in most systems (Fahrig 2013;Fletcher et al. 2018), should be more recognizable and addressable as image and landscape component spatial resolution, associated classification accuracy (Aben et al. 2012), and the potential for species group-habitat specificity increase (Hanski 2015).

a
Number of annuli (i.e., rings of cells) in the sample b Location of the row (I) and column (J) of the sample center on the hexagonal-celled map depicted in Figure 5 c The Actual Area (# of cells) Sampled by the procedure d Modification of Patton's Edge Index: EI = No. of type T edges in the sample AAS -.5e Diameter of the Equivalent Area Circle (m); calculated only for the annulus size >1 with the highest EI used to identify nonrandom patterns of species additions to a guild based on body size.Guild members are ranked 1-i, from smallest to largest.From Keller 1986.observations of guild size K Testing for the nonrandom occurrence of the initial guild member based on body size: 9 (edge length as number of cell sides) 13 (edge length as number of cell sides) Guild 13 Occupancy vs.Total Patch Amount N = 97 OR 16c Linear regression model of Guild 13 occupancy with the within-patch heterogeneity (NUMHAB) of Patch Type 13 present on a site.NUMHAB13 was the best predictor of occupancy for Guild 13 (black-throated blue warbler Setophaga caerulescens (MLGI2, OR 5 and OR 6, Table 3) OR 16d Predicted probability of threshold occupation of the black-throated blue warbler Setophaga caerulescens (Guild 13, MLGI2) vs. total amount of Patch Type 13 (northern hardwoods-hemlock/shrub edge).Probability of occupation is near 0 at small amounts of the edge type and increases to near 1.0 as TOTAMT13 approaches 1700 m (275 edgelengths x 6.2 m per cell side) on a site.Total amount of patch Type 13 edge was significantly greater (x ̅ TOTAMT = 191 edges = 1184 m) on occupied plots than on unoccupied plots (x ̅ TOTAMT = 36 edges = 223 m, t-test, p<0.001,N=79) Guild classification system a for breeding birds at the Connecticut Hill WMA b .FromKeller et al. (2003).
Guilds listed include all species used in the final data analysis.Within guilds, species are listed in general order of decreasing relative abundance.Guilds were numbered to facilitate reference from the text.Numbers generally correspond to patch types identified in Table1and more fully described in OR 8 b Standardized abbreviations follow USGS Bird Banding Laboratory (BBL) Codes (https://www.pwrc.usgs.gov/bbl/MANUAL/speclist.cfm).See OR 4 c Species was placed in more than one guild based on observed foraging behavior and plant community structured d Although the EABL uses a different foraging tactic (i.e., pouncing) than the other members of DTGI1, it was judged to consume essentially the same prey items OR 7. Landscape component classification system for the Connecticut Hill WMA in Tompkins County, NY.Percentages are the proportion of a single GIS map cell (actual area = 100 m-2) represented by the type.Definitions of 16 exploratory patch types (T) using the landscape component classification system in OR 7.Patches 1-7 are solid types (see text).Patches 8-16 are edge types and are identified in the description by the '/' between adjacent patch types composing the edge.Used for all CCA sites in 1979-81 except CCA-4,8,9 and for both CCB sites in all years h Measurements of the patch type (e.g., using ESCAN) were made only on internal edges (i.e., not including the site border)

Table 3 .
Primary variable in the model is in bold.Average size (MDC or DEAC) of patch type T a for unoccupied patches of type T vs. the average size of type T patches with occurrence of the guild in the absence of the largest species, and with occurrence of the largest species in each of the 13 multispecies guilds.Statistical differences between the categories are noted.For guild abbreviations and guild members, see OR 5 and OR 6. Predicted threshold and effect sizes of functional patch size (MDC/DEAC) in linear regression models of species richness within multispecies avian guilds at the Connecticut Hill WMA in central New York.OR 21.Trends in the occurrence of the initial species, based on body weight, for the 13 multispecies guilds.Those guilds for which the occurrence of the smallest species or species combination is significantly nonrandom are noted.For guild abbreviations and guild members, see OR 5 and OR 6.
a Guild classification and composition in OR 5 and OR 6, respectively b ** P<0.01, *** P<0.0001 c All N = 97 OR Categorical linear regression model illustrating threshold occupancy of patches of Type 7 (open grass) by breeding birds of Guild 7 (OTGI1).Distribution of functional patch sizes (MDC [m]) is shown at 2 occupancy levels -unoccupied (0) and occupied but not including the largest species (1).Occupied patches were significantly larger (x ̅ MDC = 94 m) than unoccupied patches (x ̅ MDC = 20 m).See Table 4 and OR 19 bc x ̅ patch size with guild present without largest species vs. x ̅ patch size with largest species + p=0.06, p<0.03 (Italics), p<0.001 (BOLD), NS Not Significant, IS Insufficient samples to test statistically e Clearcuts CCA and CCB 1980-81 only; Rank Sum Test OR 20.
Simple linear correlations (r) of guild species richness of breeding birds with measures of functional patch size and total patch amount of guild specific patch types on 23 clearcuts, oldfields, and forests surveyed between 1977 and 1981 at the Connecticut Hill WMA in central New York.Guild species richness-patch metric correlations attempted match patch type associations identified in Table1.Values in bold indicate highest correlation for the guild.All highest correlations were highly significant (p<0.001)except for Guild 19 (ruby-throated hummingbird), p<0.01.Linear regression models of Total Species Richness (SR), Guild Richness, and Shrubland Bird SR with SITESIZE (Table2).