Introduction
Termite mounds (TMs) are among nature's most impressive structures. The
aboveground (epigeal) extensions of generally belowground (hypogeal) termite
nests are orders of magnitude larger than the termites themselves, and their
variety in size, shape, structure and complexity is unique among eusocial
insects (Korb, 2011; Noirot and Darlington, 2000). Mounds consist of solid
but porous walls made from soil and termite faeces that provide protection
against the environment, and a complex network of internal chambers that
harbour the termite colony and serve as conduits for gas transport or as
food storage (Korb, 2011; Schmidt et al., 2014). Mound architectures are
highly specific for each termite species; they represent unique solutions to
the problem of efficiently combining contrasting functions vital for the
colony's survival, such as exchange of respiratory gases vs. homeostasis
(King et al., 2015; Korb and Linsenmair, 1999; Turner, 2001; Zachariah et
al., 2017). Yet, due to their opaque and complex nature, the morphology and
structure of TMs are inherently difficult to quantify, and there is a lack of
methods to adequately determine even basic physical parameters such as
epigeal volume VE and surface area AE (Fig. 1).
The external dimensions of a TM and precise estimates of VE and
AE are critical for termite ecology, physiology and
biogeochemistry. Data on TM size are the basis for the assessment of regional
termite abundance via TM population estimates (e.g. Darlington, 1990;
Darlington and Dransfield, 1987). Also, termite populations of individual TMs
can be estimated by counting all termites in a sub-sample with known volume,
then upscaling with VE (Jones et al., 2005). For termite
physiology, there is a need to determine the epigeal surface area
AE through which respiratory gases are exchanged with the
atmosphere (Fig. 1). It has been hypothesised that respiratory gas exchange
of a termite colony directly regulates TM architecture (Korb and Linsenmair,
1999), and models have been proposed to estimate TM population via TM size
(Josens and Soki, 2010). Likewise, accurate estimates of TM volume and area
are crucial for termite biogeochemistry: both parameters contribute directly
to the calculation of gas-flux estimates from chamber-based methods (e.g.
Jamali et al., 2011; Seiler et al., 1984), as do measurement errors therein.
This is relevant on a global scale, as termites are a significant source of
the greenhouse gas methane (CH4) to the atmosphere, but estimates
of the source strength remain highly uncertain (Kirschke et al., 2013;
Saunois et al., 2016). Yet, in studies reporting gas fluxes from TMs,
descriptions of TM physical parameters are often a mere side note, and
sometimes omitted altogether.
The conventional approach to determine VE has been to measure
height, diameter or circumference of the TMs, then approximate the overall
shape by simple geometries such as cone, cylinder or spheroid (Jamali et al.,
2011; Jones et al., 2005; Josens and Soki, 2010). This may work reasonably
well for small and relatively simple TMs, but may also result in large
discrepancies for complex morphologies, e.g. mounds with several chimneys,
large bases or buttresses. An accurate but often impractical approach is the
complete dismantling and sectioning of a TM and subsequent volume measurement
by water displacement, which is destructive and laborious (Holt et al.,
1980). A more elegant approach for VE was described by Seiler et
al. (1984), who determined headspace volume by injecting known amounts of
CH4 into the chamber and measuring its dilution. However, this
approach avoided estimating basal area (AB; Fig. 1) by reporting
fluxes “per mound”, which led to large variability caused by different TM
sizes; an issue also arising when scaling fluxes based on chamber basal area
(Khalil et al., 1990), or a standardised projected area (Brümmer et al.,
2009).
Photogrammetry (PG) via digital surface reconstruction is a relatively new
low-cost approach to documenting and measuring complex three-dimensional
structures in nature. For example, PG has been embraced by the archaeological
community for the documentation of cultural heritage sites (De Reu et al.,
2013), used to measure the bulk density of soil clods (Stewart et al., 2012),
to measure shapes and dimensions of aquatic organisms (Lavy et al., 2015), and to
determine the diameter and biomass of buttressed and irregularly shaped
tropical tree trunks (Bauwens et al., 2017). However, this approach has not
been applied on TMs; therefore, there is currently no accurate, reliable,
non-invasive method to determine the critical external physical parameters of
TMs such as VE, AE and AB.
Similarly, due to a lack of easily applicable methods there is little
quantitative information on the internal structure of TMs. However, such
information is needed to quantify and compare biogeochemical processes within
the mound material, e.g. microbial respiration or CH4 oxidation in
TMs (Holt, 1998; Sugimoto et al., 1998). Investigations into internal
structures were typically based on cross-sectioning TMs with hand tools in
the field (e.g. Kandasami et al., 2016; Turner, 2001), or filling the
internal chambers with gypsum (“endocasting”; King et al., 2015; Turner and
Soar, 2008), which are largely descriptive and quite laborious methods. To
our knowledge, a quantitative interpretation of cross sections has not been
attempted.
Recently, researchers have applied medical imaging techniques such as X-ray
computer tomography (CT scanning) to characterise TMs' internal structures
(Perna et al., 2008; Perna and Theraulaz, 2017). This revealed not only the
full internal structure and chambers' connectivity, but allowed the
construction of models for a mechanistic understanding of termites'
mound-building behaviour (Eom et al., 2015). While this methodology is
powerful and non-invasive, CT scanning requires expensive equipment that may
not be readily available for non-medical applications. Furthermore, the size
of TMs to be investigated is limited by the capacity of the scanner.
However, a complete 3-D reconstruction may not be required to gain physically
relevant information on internal structure. Like soil, a TM can be described
as porous media, and thus simple concepts such as porosity and pore-size
distribution can be applied (Luxmoore, 1981). We may define the
macro-porosity θM,V of a TM as VM/VF
in Fig. 1, the volume fraction of all chambers and tunnels large enough to
host termites (and thus visible to the human eye); the micro-porosity
θμ as Vμ/VF in Fig. 1, the volume fraction of
microscopic pores within the wall material; and the total porosity
θt as the sum of θM and θμ,
the volume fraction of all pore space within the TM. Such a framework may not
only provide essential information for quantifying transport of gases, water
and energy through the TM, but also reveal physically relevant structural
variations between TMs of different species. However, besides CT scanning
there is currently no simple method to quantify internal volume fractions and
thus porosities in TMs.
Here we describe two readily applicable field methods to quantify physical
and morphological parameters of TMs: (i) a PG method based on
structure-from-motion (SfM) reconstruction from digital photographs, to
determine epigeal volume, surface area and morphological parameters, and
(ii) an image-analysis method based on painted cross sections to determine
internal volumes, porosities and structural parameters. We compare the
methods with previous approaches to quantify termite mound characteristics,
including CT scanning, on three north Australian termite species with
different mound architectures. In an example application, we illustrate
potential errors in CH4 flux measurements when relying on approximate
geometric shapes. Our results demonstrate the feasibility, accuracy and
limitations of the novel methods for characterising TMs of different termite
species.
Materials and methods
Field sites and termite species
All field measurements and TM sampling were performed in a coastal savanna
woodland on the campus of Charles Darwin University in Darwin, Northern
Territory, Australia (12.370∘ S, 130.867∘ E). The site was
dominated by Eucalyptus tetrodonta and Eucalyptus
miniata species over an understory of annual and perennial tropical
grasses, and it experiences a frequency
of fire of approximately 1 in 5 years. The soil type was a Brown Kandosol
typical for the greater Darwin area, with textures of loamy sand to sandy
loam (McKenzie et al., 2004). Termite mounds in a sub-area of approximately
3.5 ha were counted and mapped after a fire in August 2015; the areal
density of TMs was approximately 50–60 TMs ha-1. We selected 29 TMs
of various sizes from the three most frequent mound-building termite species
in this area: Microcerotermes nervosus (Hill) (Mn),
Macrognathotermes sunteri (Hill) (Ms) and
Tumulitermes pastinator (Hill) (Tp). The TMs are named with
their species' abbreviation and numbered from smallest to largest
VE (Table S1 in the Supplement).
All field measurements and sampling were conducted in April and May 2016. The
photogrammetric method was employed on undisturbed TMs to determine
VE, AE and AB of all 29 investigated TMs,
including large ones with a VE > 30 L. For comparison with
conventional estimates, basal circumference and height of the TMs was
determined manually. On 20 TMs of small (VE < 15 L) to
medium (VE < 30 L) volume, we performed measurements of gas
flux between the TM and the atmosphere. A total of 17 of these TMs were then
selected for excavation, CT scanning and cross-sectioning. Termite mounds
were carefully excavated with hand tools by digging from the previously
marked basal perimeter downwards. Most mounds had a relatively clear outer
boundary to the soil, i.e. the wall material was distinct from soil in
texture and density. However, some TMs of M. sunteri, a
soil-interface feeder, featured extended basal areas with relatively soft
hypogeal parts. Greater care was required for this species, and some
peripheral parts had to be discarded as they were too soft for
transportation. Thus, the epigeal ratio of M. sunteri mounds may be
slightly overestimated. After excavation, TMs were weighted in the field,
then transported to the lab for further processing.
Photogrammetry of termite mounds
The PG method to determine epigeal volume and surface area of TMs consists of
three steps: (i) image acquisition, (ii) digital reconstruction of the TM via
SfM algorithms, and (iii) scaling and measurement of the reconstructed TM
model (Fig. S1 in the Supplement). For the image acquisition step, any
vegetation and debris within 1–2 m of the selected TM were removed to
obtain unobstructed views from all angles. The TM–soil intersection was
carefully cleaned with a brush. The basal perimeter of the TM was determined
by tapping or scraping the soil surface and mound, then marked with a
bright-coloured marker spray (Fig. S1b). Reference objects of known
dimensions, consisting of either the base of a flux chamber or two graduated
rods, were placed on the ground next to the TM. For each TM, 40–50 images
were acquired in RAW format using a digital mirrorless camera (Olympus E-M1,
Olympus Corporation, Tokyo, Japan) with a 18–200 multi-zoom lens (Panasonic
Corporation, Osaka, Japan). To ensure complete coverage and sufficient
precision we followed the recommendations of Wenzel et al. (2013) for optimal
image acquisition for photogrammetric image processing (see Supplement). Care
was taken to ensure the reference objects were visible in all images. Image
acquisition was generally completed in 10–20 min.
All computations in steps (ii) and (iii) were performed on standard laptop
computers using low-cost and free software packages. For the digital
reconstruction and generation of a 3-D mesh we used PhotoScan Standard 64-bit
v1.2.4 (Agisoft LLC, St. Petersburg, Russia). Scaling and computation of
volume and surface areas of the 3-D mesh was performed in MeshLab 64-bit
v1.3.3 (Cignoni et al., 2008). After scaling with the reference objects,
unnecessary parts of the mesh were deleted, with only the epigeal TM open at
its base remaining (“open” mesh; Fig. S1c). A hole-filling algorithm was
then applied to generate a “closed” mesh (see supporting information), and
geometric measures were computed before and after closure. The surface area
of the open mesh represents the epigeal TM surface area AE, the
difference in surface area between open and closed mesh represents the TM's
basal area AB, and the volume of the closed mesh represents the
epigeal volume of the TM, VE.
For validation purposes, the PG method was applied to seven large rocks,
roughly comparable in shape and size to smaller TMs (< 20 L). The
reference volumes Vref of the rocks were determined by water
displacement using a water density of 0.998 kg L-1. The rocks were
placed firmly in an upright position on flat ground, then the PG method was
performed as described above. The number of photographs taken of each rock
was between 37 and 42. Surface areas AE and AB of the
rocks were not determined; studies presenting similar photogrammetric methods
found that if the volume is estimated accurately by the method, the surface
area is similarly accurate (Lavy et al., 2015). The PG method was applied
4 times to one rock to estimate coefficients of variation.
Flux measurements
Gas exchange of CH4 was measured according to the protocol described
in Jamali et al. (2011). Briefly, closed dynamic chambers built from
polyvinyl chloride bins were placed over the selected TM and fixed on
previously installed collars reaching 3–5 cm deep into the soil. The
chambers were open to soil with a total volume (VCh) of 28, 90 or
150 L, depending on the size of the TM. During 5–10 min of chamber
deployment, CH4 concentration change was measured with an optical gas
analyser (Fast Greenhouse Gas Analyzer, Los Gatos Research, Mountain View,
CA) connected to the chamber in a closed loop.
Cross-sectioning estimate of mound porosities
To estimate the internal volume fractions of a TM we developed a simple
method based on cross-sectioning of excavated TMs and subsequent image
analysis. The method requires two assumptions: (i) the TM is roughly
symmetric around a rotational (z) axis, and (ii) the macro-pores are
distributed evenly in x and y directions (Fig. 1). Under these
assumptions, the areal ratio of macro-pores vs. full mound θM,A
(AM/AF; Fig. 1) in a single cross section through the
TM centre should approach the TM macro-porosity θM,V.
The cross-sectioning was performed in the laboratory on 17 TMs previously
excavated for CT scanning for direct comparison of the two methods. The
selected TMs were firmly embedded in a box with sand, then carefully cut with
a manual wood saw from the top centre downwards (Fig. S2a). Care was taken
not to break the outer walls of the TM, especially in the hypogeal part of
the TM where pieces of gravel were prevalent and embedded in the walls.
Damaged parts were excluded from analysis. The cross section was then painted
with a bright colour using a paint roller to highlight the TM wall surface,
thereby creating a distinct, uniform surface independent of the properties of
the mound material (Fig. S3a). The painted cross section was photographed
with the same camera system used for the PG method. The non-painted half of
the TM was broken down to sample termites, then weighted and dried at
105 ∘C for 48 h to determine the water content.
Image analysis was performed using the Fiji software package (Schindelin et
al., 2012). The original colour image was converted to binary with a colour
threshold of ±25 hue values around the hue maximum of the paint in the
HSB colour space (Fig. S3b). To close the macro-pores and generate a cross
section of the “full” mound, the initial binary image was segmented and
subsequently filled (Fig. S3c). The difference of the initial and filled
binary image represented the area of the macro-pores in the cross section,
AM; this was divided by the area of the segmented (full) TM,
AF, to calculate the areal cross-sectional macro-porosity θM,A of the TM.
Calculation of TM internal parameters from physical measures of
mass, volume and area fractions (see Fig. 1). The TM
mass mF refers to dry mass; water content was determined from the
oven-dry weight and subtracted from field weight. Mass of termites and
potential food stores were considered negligible; thus mF is
essentially identical to the mass of wall material, mW. Particle
density ρb of the TM was assumed to be 2.65 kg L-1,
typical for soil particles.
Parameter
Unit
Equations
Bulk density
kg L-1
ρb=mFVF
(2)
Wall density
kg L-1
ρW=mWVW≅mFVW
(3)
Particle density
kg L-1
ρp=mFVP≈2.65
(4)
Macro-porosity (volumetric ratio)
L L-1
θM,V=VMVF=1-ρbρW
(5)
Macro-porosity (areal ratio)
L L-1
θM,A=AMAF≈VMVF
(6)
Micro-porosity
L L-1
θμ=VμVF=1-θM-ρbρp
(7)
Wall porosity
L L-1
θW=VμVW=1-ρWρp
(8)
Total porosity
L L-1
θt=VM+VμVF=θM+θμ=1-ρbρp
(9)
Computer tomography of excavated termite mounds
To perform a complete assessment of the internal physical characteristics of
TMs we scanned 17 selected TMs with X-ray computer tomography using a medical CT instrument (Philips Ingenuity; Koninklijke
Philips N.V., North Ryde NSW, Australia; for technical details see supporting
information). Images issued from the scanner (Fig. S4a) were imported into
Fiji for conversion to binary (Fig. S4b) and subsequent filling of the
macro-pores (Fig. S4c), similar to the cross-sectioning method. The full
volume and volume fractions of the walls and macro-pores were computed with
MATLAB and its Image Processing and Computer Vision Toolbox (Release 2015b,
The Mathworks Inc., Natick MA, United States) by populating a 3-D matrix from
the initial and filled binary images, counting the number of voxels and
scaling with the respective voxel dimensions from the CT scan. To directly
compare the cross-sectioning method with CT we also computed areal ratios of
AM/AF and thus estimated θM,A from CT
slices in the xz and yz directions of the populated matrix. Only the
10 % of slices with the largest area were used to represent cross
sections close to the centre and tip of the TMs.
Calculations and statistical analyses
Internal TM parameters and their calculation from mass, volume and area
fractions are given in Table 1. In addition, we determined surface-to-volume
ratios AE/VE and the fractal dimension D to quantify
morphological differences between termite species. Surface-to-volume ratios
were calculated directly from PG estimates. Calculation of the 3-D fractal
dimension from Wavefront .obj files of TM PG models (DPG) was
based on the Minkowski–Bouligand method at the 3-D level (Backes et al.,
2010), using the freely available Bouligand–Minkowski 3D-Toolbox
(https://www.facom.ufu.br/~backes/mink3d.html, last access:
12 June 2018). Further details on the method and toolbox can be found in
Reichert et al. (2017).
The CH4 flux FCH4 (µmol m-2 h-1)
from TMs was calculated from the change in CH4 concentration
CCH4 over time t in the chamber headspace, after correcting
CCH4 for ambient temperature and pressure:
FCH4=(dCCH4/dt)⋅((VCh-VE)/AB).
Method differences were assessed via ordinary least-square regression with
zero intercept (assuming homoscedasticity and negligible errors in the
reference data). Confidence intervals were calculated from t statistics.
Significant differences (α = 0.05) between termite species'
structural parameters were tested with One-Way ANOVA, and correlations
between epigeal measures with ordinary least-square regression. Statistical
calculations and analyses were performed using R Statistical Software (R
Development Core Team, 2017).
Results
Epigeal volume and surface area of termite mounds
Verification of the PG method to determine VTM, ATM
and AB was performed on seven large rocks with known VRef (determined by water displacement; Fig. 2). For all
rocks and TMs, no failures were experienced during alignment and matching;
the procedure always resulted in high-quality meshes without structural
deficiencies. The estimated volumes VPG were significantly
correlated with VRef (P < 0.001) across all rock sizes. On
average, the PG method slightly underestimated rock volumes by
1.3 ± 0.65 %. The largest relative error encountered was
-3.5 % for the smallest measured rock. Repeated application of the PG
method for one rock resulted in a coefficient of variation of 0.6 % for
VPG, 0.8 % for APG and 7.8 % for
AB.
Validation of the photogrammetry method (PG) by estimating the
volumes of seven irregularly shaped rocks with similar volumes to small
termite mounds. The dashed line indicates the linear regression between VPG and VRef, with slope, standard error (SE) and root
mean square error (RMSE); the black solid line denotes perfect correlation.
The epigeal volume VE of the 29 investigated TMs spanned across
2 orders of magnitude (Fig. 3 and Table S1). Mounds of M. nervosus
were the smallest (4.6–18 L), followed by M. sunteri (5.2–190 L)
and T. pastinator (6.6–270 L). Epigeal surface area AE
of the TMs was closely related to volume and ranged between 0.17 and
2.3 m2, basal area AB between 0.028 and 1.1 m2 (Table S1).
Correlations with VE were significant for both parameters, with
insignificant differences between species. Basal areas calculated from the
manually measured circumference at the TM–soil intersection (via ideal circle
with radius rB; Table S1) were on average underestimated by 7 to
30 % when compared to the PG method, and up to a factor of 5 for some TMs
(e.g. Ms2) of the soil-interface feeder M. sunteri that featured
large and irregularly shaped AB. Similarly, large differences
were observed when comparing VE from PG with volumes of
approximated geometric shapes (Fig. 3). The cylinder approximation
consistently overestimated VE by a factor of 2 to 4 (Fig. 3)
whereas VE approximated by cones and hemi-spheroids was on
average underestimated by only 4–7 % relative to PG estimates (although
some individual TMs were under- or overestimated by factors of 2 to 3).
Relative errors were high irrespective of the size of the TMs.
Comparison of TM epigeal volumes VE measured by
photogrammetry (PG) and approximated by three geometric shapes, a cylinder
(in red), a cone (in blue) and a hemi-spheroid (in green; Fig. 1). The volumes of the geometric shapes are based on the same
basal radius rB, estimated by measuring the basal circumference
of the TM. By comparing the regression slopes and considering PG as the
reference method, volumes were overestimated by 190 ± 15 % using
the cylinder, and underestimated by 3.6 ± 5 and 7.0 ± 4.5 %
using the cone and hemi-spheroid, respectively.
Binary image of a single CT slice in xz direction for each
investigated species: (a) Microcerotermes
nervosus, (b) Macrognathotermes sunteri,
(c) Tumulitermes pastinator. The thin black line
approximately indicates the soil surface.
To compare potential inter-species variation in TM morphology, we computed
area-to-volume ratios AE/VE and DPG from PG
models (Table 2). Area-to-volume ratios were highest for M. nervosus, slightly smaller for M. sunteri and significantly
smaller for T. pastinator. This relationship held true even when
considering only small and medium-sized TMs with VE < 30 L.
In contrast, no significant differences were found when comparing
DPG between species (Table 2); computed values were around 1.9
for all species.
Mean physical and morphological parameters of TMs from three termite
species. Errors represent 95 % confidence intervals; significance levels
of the one-way ANOVA to test differences between species are indicated with
*.
Microcerotermes nervosus
Macrognathotermes sunteri
Tumulitermes pastinator
PG method
n=10
n=10
n=9
Epigeal surface-to-volume ratio AE/VE (cm2 cm-3)**
0.29 ± 0.030
0.24 ± 0.059
0.18 ± 0.053
Fractal dimension DPG
1.88 ± 0.046
1.91 ± 0.045
1.93 ± 0.058
CT scans
n=6
n=5
n=6
Macro-porosity θM,V***
0.24 ± 0.043
0.19 ± 0.046
0.36 ± 0.037
Micro-porosity θμ***
0.35 ± 0.058
0.39 ± 0.074
0.23 ± 0.019
Total porosity θt
0.59 ± 0.051
0.58 ± 0.044
0.58 ± 0.022
Bulk density ρB (kg L-1)
1.10 ± 0.14
1.10 ± 0.12
1.10 ± 0.060
Wall density ρW** (kg L-1)
1.43 ± 0.18
1.36 ± 0.18
1.71 ± 0.040
Wall porosity θW**
0.46 ± 0.067
0.49 ± 0.067
0.35 ± 0.015
Epigeal ratio VE/VF
0.74 ± 0.092
0.73 ± 0.096
0.70 ± 0.094
Cross-sectioning
n=6
n=5
n=6
Macro-porosity θM,A***
0.25 ± 0.039
0.20 ± 0.050
0.49 ± 0.071
Significance levels: *** P < 0.001;
** 0.001 < P < 0.01; * 0.01 < P < 0.05.
Internal termite-mound porosity and structure
Complete characterisation of porosities and internal structure was achieved
for 17 TMs using CT scanning (Fig. 4 and Table 2). Full volume
VF of the scanned TMs ranged from 6.7 to 34 L, of which
70–75 % was epigeal. Size and distribution of chambers was clearly
different between the three species (Fig. 4). Mounds of T. pastinator featured thinner walls with a network of longer and larger
chambers compared to the other species, and a thick outer wall with little or
no chambers close to the surface. This pattern was reflected in the
porosities of the TMs (Table 2). Mean θM,V calculated as
volumetric ratio was 0.24 ± 0.04 and 19 ± 0.05 for M. nervosus and M. sunteri, respectively, significantly lower than
T. pastinator with 0.36 ± 0.04. An inverse pattern was
observed for θμ and θW (corresponding to TM
wall density ρW), with walls of T. pastinator mounds
being the least porous (Table 2). The mean total porosity θt
(corresponding to TM bulk density ρB) was nearly identical for
the three species (Table 2).
The cross-sectioning method, a simple field-based approach to estimate
macro-porosity θM,A from areal ratios of single
cross sections, was compared against θM,A and
θM,V from CT scanning (Fig. 5 and Table 2). For M. nervosus and M. sunteri mounds, θM,A from
cross-sectioning were 0.25 and 0.20 respectively, nearly identical to
θM,V from CT scans and with a mean error of +3 %.
Similarly, for M. nervosus and M. sunteri mounds the
θM,A from the largest 10 % of CT slices encompassed
values of θM,A estimated from cross-sectioning (Fig. 5). The
error in θM,A from CT slices compared to
θM,V from full CT scans, i.e. the bias of calculating
θM from areal ratios of slices instead of volumetric ratios,
was around ±3 % for M. nervosus and M. sunteri. In
contrast, for T. pastinator mounds θM,A from
cross-sectioning was 0.49 ± 0.07, substantially higher than
θM,V (0.36 ± 0.04); the mean error was +38 %
(Fig. 5 and Table 2). When comparing θM,A from CT slices
with θM,V from full CT scans there was a mean bias of
+17 % for T. pastinator mounds. Despite these differences
between species when estimating porosity, the fractal dimension from
cross sections, DXsec, was similar between species and compared
to DCT (Table 2).
Comparison of areal estimates of TM macro-porosity
θM,A against volumetric estimates of TM macro-porosity
θM,V for each CT-scanned TM. Volumetric estimates were
calculated from full CT scans; areal estimates were obtained via manual
cross-sectioning of TMs (open symbols), and from individual CT slices in
xz and yz directions (closed symbols). The latter represent the mean
θM,A ± 95 % confidence intervals of the 10 %
of slices with the largest area, thus covering the tip (and likely the
centre) of the TM.
Termite-mound methane flux
Fluxes of CH4 across the TM–atmosphere interface were calculated
according to Eq. (1) using volume and basal area measured with PG
(FPG), or approximated by geometric shapes (Fgeom)
that shared the same height h and basal radius rB. All but one
of the TMs were a source of CH4 to the atmosphere, with net fluxes
FPG ranging from
42 to 960 µmol CH4 m-2 h-1. Assuming
FPG was the reference, mean errors of Fgeom were on
average 14–48 %, depending on the geometric shape (Fig. 6). Compared
against FPG, the cylinder approximation (FCy)
performed better than the cone (FCo) and hemi-spheroid
(FHs), despite grossly overestimating VE. Mounds of
M. sunteri showed the largest differences between FPG
and Fgeom, up to a factor of 5 for mound Ms2. When excluding
mounds with high leverage from the regression model (Ms1 and Ms2, Fig. 6),
mean errors of FCo and FHs improved to 11 and 12 %,
with 49 and 52 µmol CH4 m-2 h-1 RMSE,
respectively; FCyl remained at 14 % and
200 µmol CH4 m-2 h-1 RMSE.
Discussion
Photogrammetry of termite mounds
Applying the PG approach to TMs of three common termite species allowed us to
accurately determine VE, AE and AB with a
single method that took on average 15 min of field work per mound. This is
close to the time required for determining height and circumference of larger
and more complex Macrotermes TMs (Darlington and Dransfield, 1987).
While being simple and rapid to apply in the field, the PG approach is
clearly superior in accuracy to any traditional approach for estimating
VE based on simple geometric shapes (Fig. 3). Such an accurate
VE can then be the basis of reasonable termite population
estimates, if subsamples of TMs are representative for the whole in termite
numbers and composition, and their volume is determined equally accurately (Jones et al., 2005). However, the largest uncertainties
are likely not derived from errors in estimating VE, but rather
in the immobilisation and counting of within-mound termite population
(Darlington, 1984; Jones et al., 2005).
The PG method also allows rapid and accurate determination of
surface-to-volume ratios of TMs with different and complex morphologies. This
enables the collection of large data sets on TM morphology to test hypotheses
relating to the role of mound structure in determining gas exchange and
thermal homeostasis. To date such analyses have been compromised by small
sample sizes (Korb and Linsenmair, 1999). Our data demonstrate this by
revealing significant differences between species, with M. nervosus
and M. sunteri having a larger surface-to-volume ratio than
T. pastinator, despite having a significantly lower wall porosity
(Table 2). Interestingly, we could not detect inter-species differences in
the fractal dimension DPG of the TM surface models (Table 2),
even though this parameter was more sensitive than surface-to-volume ratios
in describing morphological differences between corals (Reichert et al.,
2017). Yet, surface-to-volume ratios have a direct physiological meaning and
may integrate effects of both external and internal structural parameters of
TMs, while the fractal dimension is a measure for the complexity of a shape
and thus only reflects external factors. However, it may also be that the PG
method does not resolve the small-scale surface morphologies as well as the
industrial-grade high-resolution 3-D scanner used by Reichert et al. (2017).
Comparison of CH4 flux calculated according to Eq. (1) with
TM epigeal volumes VTM and basal areas AB from
photogrammetry (FPG), and with TM volumes approximated by three
geometric shapes: a cylinder (FCy), a cone (FCo) and
a hemi-spheroid (FHs). Considering PG as the reference method,
fluxes were overestimated by 14 ± 14 % for the cylinder,
42 ± 16 % for the cone and 48 ± 16 % for the
hemi-spheroid.
The reconstruction process of the PG method and its accuracy and precision
depend on several technical factors, including camera equipment and software,
as has been discussed elsewhere (Koutsoudis et al., 2013, 2014; De Reu et
al., 2013; Wenzel et al., 2013). In our case, natural factors and
environmental conditions may be more important for a successful and accurate
digital reconstruction. Even though we encountered no failures during
reconstruction, Bauwens et al. (2017) reported a failure rate of 21 % for
the PG reconstruction process of buttressed trees, which was attributed to
vegetation obscuring the trees to be photographed. Application of the PG
method to TMs in open woodlands was not affected by vegetation which can be
readily removed from the mound surroundings without significant impact. In
dense tropical forests the PG method may be limited by the need to remove of
trees or shrubs adjacent to the target mound. Marking the TM–soil
intersection and cutting the 3-D model is another potential source of error
evident from the larger CV of AB compared to VE and
AE. To some extent, and specifically for soil- and litter-feeding
termites, this is unavoidable, as the soil-mound boundaries are inherently
fuzzy. We tried to minimise variability by careful probing and marking of the
soil–TM boundary, and by letting the same person do all manual editing on the
3-D mesh (Fig. S1c). In future attempts, the latter process may be automated
using feature detection available in Photoscan Professional, but this
software comes with a higher price tag.
Internal termite-mound porosities
The use of CT scanning as a reference method allowed us to accurately
calculate the TMs' full, wall and chamber volume, and thus macro-and
micro-porosity, as well as the epigeal ratio. Most mounds had 65–75 % of
their volume above ground, with little variation between species (Table 2).
This is consistent with qualitative descriptions of M. nervosus and
T. pastinator mounds (Abensperg-Traun and Perry, 1998; Bristow and
Holt, 1987), and close to the general assumption of 75 % epigeal mass
stated by Josens and Soki (2010). These authors also mentioned
species-specific TM bulk densities (“specific mass”) of 0.95 kg L-1
for carton-based nests, and 1.2 kg L-1 for soil-based mounds, thus
encompassing our values of 1.1 kg L-1. Holt et al. (1980) reported
bulk- and wall-density data for some northern Australian termite species and
estimated a similar value (0.40) for the macro-porosity of T. pastinator (without reporting wall density).
Despite nearly identical bulk density and total porosity, our investigated
species showed clearly different species-specific pore-size distributions
(Table 2): TMs of M. nervosus and M. sunteri appeared to
have the largest fraction of internal gas volume in the walls
(θM < θμ), while for T. pastinator
the bulk of the gas was in the chambers
(θM > θμ). Another widespread north
Australian termite species, Amitermes vitiosus, showed a similar TM
wall density than T. pastinator (1.7 kg L-1), yet a
significantly higher bulk density of 1.41 to 1.48 kg L-1 (Holt et al.,
1980). This translates to a much lower macro-porosity (0.13) compared to the
species investigated here, but a micro-porosity (0.32) similar to M. nervosus and M. sunteri. Such a pore-size distribution suggest that
gas exchange may be driven by passive diffusion in M. nervosus,
M. sunteri and A. vitiosus TMs, which is likely to limit
the colony's respiration and thus total size (Josens and Soki, 2010), but may
provide additional insulation in the high-temperature habitats of the
tropical savanna (Holt et al., 1980). In contrast, pore-size distribution and
surface-to-volume ratios in T. pastinator TMs hints towards a
convective internal mixing mechanism to facilitate diffusion
across the dense outer walls (Bristow and Holt, 1987; King et al., 2015).
The simple cross-sectioning method presented here worked well for M. nervosus and M. sunteri
and allowed rapid, accurate estimation of TM porosities when combined with PG
and bulk density estimates. Yet, both species featured evenly distributed
macro-pores and relatively thick, porous walls. In contrast, T. pastinator featured thick dense outer walls and thin inner walls, and thus
an asymmetric radial distribution of macro-pores. Therefore, the outer walls
are under-represented when extrapolating from a 2-D slice to a 3-D structure
due to the cubic increase in volume with radius. This likely explains the
17 % bias when comparing θM,A from individual CT slices
to θM,V from full CT scans. In addition, the manual sawing
was sometimes damaging the thin, brittle internal walls found in T. pastinator, thus resulting in additional positive errors in
θM,A compared to θM,V.
Consequently, the cross-sectioning method will work best on epigeal TMs with
thick, firm walls and an even distribution of chambers. For TMs with an
uneven distribution of chambers or brittle walls, an alternative approach for
estimating macro- and micro-porosity can be entirely based on PG by
determining TM wall density with the “clodometer” method (a PG adaptation
of the soil-clod method; Stewart et al., 2012), and the PG method described
here for epigeal TM bulk density. Macro- and micro-porosity can then be
calculated according to Eqs. (5) and (7).
Improved biogeochemical flux estimation
Using PG measures of TMs substantially improved the accuracy of CH4
flux measurements compared to conventional approaches by 15–50 % on
average, and up to a factor of 4 for individual TMs (Fig. 6). Interestingly,
the cylinder approximation performed better than cone or hemi-spheroid, even
though VE was grossly overestimated; this illustrates that
(i) errors in VE and AB compensate each other to some
extent, as the two measures are linked, and (ii) errors in
VE are masked if the flux chamber volume VCh is much
larger than VE. In general, errors in fluxes due to errors in
basic geometric measures were significant and can largely be avoided using
the PG method. Compared to destructive water displacement measurements, the
PG method preserves the integrity of the TM and allows repeated flux
measurements to capture seasonal or diurnal trends (Jamali et al., 2011). In
combination with species-specific bulk density and porosity information, it
is even possible to compare biogeochemical rates based on the mass of the TM
without destroying the mound. This is relevant for microbial processes that
occur in the wall material, such as microbial respiration or CH4
oxidation (Ho et al., 2013; Holt, 1998; Sugimoto et al., 1998). Furthermore,
fluxes of termite respiratory gases (CO2 and O2) can be
accurately related to the TM surface area AE to calculate
specific “respiration coefficients” (i.e. the rate of gas exchange per
surface area) for comparison of the respiratory efficiency of different TM
architectures (Josens and Soki, 2010). In an open savanna landscape, it may
also be possible to estimate TM abundance and size with the PG method using
drones as an inexpensive alternative to lidar systems (Davies et al., 2014;
Verhoeven, 2011). Long-term aerial monitoring of TMs may thus inform not only
on a spatial but also on a temporal scale, e.g. on TM growth and decay rates, as
well as temporal shifts in abundance. Furthermore, combining such information
with biogeochemical rates has the potential to greatly improve the accuracy
of landscape-, continental- or even global-scale emission estimates of
termite-produced greenhouse gases (Livesley et al., 2011; Saunois et al.,
2016).