Project outcomes

Species Diversity in a Fractal World

Funded by the Australian Research Council Discovery Programme

(Grant no. DP160102262)

This project was a collaboration between:

Barbara Downes (University of Melbourne, Australia)

Jill Lancaster (University of Melbourne, Australia)

Rebecca Lester (Deakin University, Australia)

Stephen Rice (Loughborough University, UK)

Louise Slater (University of Oxford, UK)

Georgia Dwyer (Deakin University, Australia)

Objectives of this project

The project had three over-arching objectives:

*Test hypotheses that resources and species abundances are fractal (i.e. self-similar) over large scales of space and time

*Test whether the dispersal ability of species is associated with landscape patchiness as predicted by the Spatial Scaling Model (SSM)

*Test whether the SSM is superior to other models (unified neutral model, stochastic niche model) in predicting the diversity of species across patchy landscapes

As set out on the previous page, we fulfilled these tests using aquatic insects that lay their eggs on emergent rocks. Click on links below to read how we did that.


What species of aquatic insects lay eggs on emergent rocks?

How do aquatic insects respond to oviposition landscapes?

How do emergent rock numbers vary through time?

Are movements of aquatic insects related to flight capability?

Are emergent rocks fractal?

Was the Spatial Scaling Model (SSM) supported?

What species of aquatic insects lay eggs on emergent rocks?

A variety of species in the Hydrobiosidae (Trichoptera) as well as some other aquatic insects lay their eggs as individual masses on objects that are emergent from the water’s surface. In mountain streams, these emergent objects are predominantly rocks.

Egg masses of Apsilochorema spp. The egg mass at top right is hatching.
Egg masses of Taschorema and Ethochorema spp.
Egg masses of Ulmerochorema spp.

Egg masses have recognisable morphological differences that allows species-level identification in many cases. These differences encompass the overall size of the egg mass, the amount of jelly and the number and arrangement of eggs inside the mass.

Egg masses are also laid in slightly different places – on the sides of rocks or on the bottom of rocks. Some species lay their eggs well away from other egg masses such that there is typically only one egg mass per rock, whereas other species, such as Ulmerochorema, strongly aggregate egg masses on individual rocks.

The biology of hydrobiosid caddisflies

Larva of a hydrobiosid from the Taschorema complex

Hydrobiosids are free-living (i.e. non-cased) caddisflies. Their larvae are predatory and eat a variety of other stream insects, including mayflies, stoneflies, dipterans and other caddisflies, including hydrobiosids. There are some strong differences between some species in diet, which may relate to the structure of the prehensile foreleg that is used for capturing prey. Larvae pass through five instars before pupating and then emerging as winged adults.

Where you can read about this research:

This research has been published in the following journal articles:

Lancaster, J. and Glaister A. (2019) Egg masses of some stream-dwelling caddisflies (Trichoptera: Hydrobiosidae) from Victoria, Australia. Austral Entomology 58, 561–568

Lancaster, J. (2021) Coexistence of predatory caddisfly species may be facilitated by variations in the morphology of feeding apparatus and diet. Freshwater Biology 66, 745–752.

Contact me for a pdf if you do not have access to Austral Entomology or Freshwater Biology.

Or, you can read the accepted ms for the Austral Entomology paper here (freely available) and the Freshwater Biology paper here (embargoed until 24 Dec 2021)

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How do aquatic insects respond to oviposition landscapes?

We know from previous research that most species of aquatic insects that lay their eggs on emergent rocks respond strongly to factors such as the velocity and depth of water around rocks and rock size and height above the water’s surface. However, most of that information has come from only a few sites, and it is unclear if female insects seeking to lay eggs respond to the total number or arrangement of suitable emergent rocks. Numbers and arrangements of rocks can vary greatly between riffles in the same stream as well as between streams – do these characteristics affect the numbers of egg masses laid at particular locations?

We surveyed every emergent rock in multiple riffles across three rivers. The position of each rock was mapped, and its size and height above the water’s surface recorded, as well as the depth and velocity of water around it. All egg masses on these rocks were counted and identified.

Surveying an emergent rock in the Steavenson River
Measuring water velocity upstream of an emergent rock

Measuring the A, B and C axes of an emergent rock
Counting and identifying egg masses on an emergent rock

In all, we collected data from 4380 separate emergent rocks distributed among 19 riffles in three rivers.

What did we find?

Riffles varied by an order of magnitude in area (from 44 – 480 m2) and in the density of emergent rocks (0.40 – 4.3 / m2). Not all rocks are suitable for egg-laying, and the proportion of suitable emergent rocks with egg masses varied between 0 and 41%.

Map of a riffle in Snobs Creek showing emergent rocks with egg masses (coloured circles, with different colours signifying different species) and those without egg masses (open circles).

The patterns of egg-laying differed between species. Some species like emergent rocks in fast flows, whereas other prefer slow flows, but the amazing thing is these patterns were remarkably consistent – and predictable – across all our riffles despite considerable between-riffle variation in size and numbers of rocks. This suggests that female behaviour is not context-dependent. Instead, females choose rocks for egg-laying in ways that result in the same patterns of distribution regardless of background variation.

This unique research was presented by Jill Lancaster in an invited keynote presentation at the joint meeting of the New Zealand Freshwater Sciences Society and the Australian Freshwater Sciences Society at Waurn Ponds, Victoria (2019), for which she won the Apple Prize (joint with Julian Olden).

Where you can read about this research:

This research has been published in the following journal article:

Lancaster J, Downes B.J., Lester R.E. and Rice S.P. (2020) Avoidance and aggregation create consistent egg distribution patterns of congeneric caddisflies across spatially variable oviposition landscapes. Oecologia, 192, 375–389

If you don’t have access to Oecologia, e-mail me for a pdf, or you can read the accepted manuscript here

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Are movements of aquatic insects related to flight capability?

Above, we showed that adult insects lay eggs in spatial patterns that are consistent between riffles. Nevertheless, the number of egg masses in riffles can vary markedly. The data we reported above (How do aquatic insects respond to oviposition landscapes?) showed that, for some species, the total number of egg masses in a riffle is related strongly to the density of suitable emergent rocks (Lancaster & Downes 2018). This outcome implies that females may be limited by access to suitable egg-laying habitat. Can females easily fly between riffles to locate places to lay their eggs?

To answer this question, we deployed light traps along the banks of two of our study rivers. Light traps capture flying insects because they are attracted to UV light. The light is placed inside a bucket to avoid attracting insects from long distances – because our interest is in insects flying nearby.

Light trap used to capture adult insects, powered by a solar panel and perched next to a stream

The traps were placed either next to riffles, where there were plenty of emergent rocks, or next to pools. Pools are channel units featuring slower, deeper water that separate riffles, and they typically have very few emergent rocks. If we capture hydrobiosid females only next to riffles, it implies they are unable or unwilling to fly up- and down-channel in search of suitable rocks on which to lay their eggs. We also counted the numbers of aquatic insects that do not lay their eggs on emergent rocks. We do not expect these species to be limited to riffles, and so these species are a form of control.

We used some well-established measurements of wing sizes that are connected to the flight capability of insects. Insects with relatively long and narrow wings have a greater capacity for powered flight than insects with short, broad wings, which are better at manouverability but poorer for powered flight.

One set of fore and hind wings from a caddisfly (Tamasia palpata). Wing length and width are key measures of flight capability

What did we find?

The results showed that all hydrobiosid species were found next to riffles. Very few were found between riffles, including at least one species (Ethochorema) that is potentially a strong flyer. In contrast, species that do not lay their eggs on emergent rocks were found at multiple places along the stream. These data imply that hydrobiosids move to the nearest riffle and are then unlikely to fly between riffles.

This is one of the first studies to address whether aquatic insects move up- and down-channel in search of oviposition habitat. From previous work (Bovill W.D., Downes B.J. & Lancaster J. [2019] Variations in fecundity over catchment scales: implications for caddisfly populations spanning a thermal gradient. Freshwater Biology 64, 723-734), we know that adult hydrobiosids disperse relatively long distances prior to mating and egg-laying. These new data show that once females become gravid and reach the margin of a stream, they move only relatively short distances in search of egg-laying habitat.

The research shows that dispersal can comprise different elements – long-distance movements carried out for proper dispersal (e.g. between populations) and short-distance movements where individuals search for resources.

Where you can read about this research:

This research has been published in the following journal articles:

Lancaster, J. & B.J. Downes (2018) Aquatic vs terrestrial insects: real or presumed differences in population dynamics? Insects 9, (4) 157 (freely available)

Lancaster J., Downes B.J. and Dwyer G. (2020) Terrestrial–aquatic transitions: local abundances and movements of mature female caddisflies are related to oviposition habits but not flight capability. Freshwater Biology 65, 908–919

Contact me for a pdf if you do not have access to Freshwater Biology or you can read the accepted ms here

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How do emergent rocks numbers vary through time?

Depth logger attached to ruler, which allowed manual checks on water depths

It’s not rocket science to recognise that emergent rocks will disappear as discharge goes up but it may not be so apparent that emergent rocks can also disappear as discharge goes down.

That’s because most emergent rocks are along the banks and can become stranded out of the water when discharge falls. Rocks on dry land are useless to these aquatic insects.

So what is the relation between discharge variability and the availability of emergent rocks?

This is a very tricky question! Although there are off-the-shelf hydraulic models, they largely only work in rivers that have simple morphology (e.g. have nice repeatable sequences of riffles and pools).

Depth logger installed inside stilling well at top of a site

So, we installed data loggers that could measure the depth of water at the top and bottom of riffles in three rivers.

Installing cameras on-site

We also installed cameras to take pictures of each riffle so that we could see how many rocks were emergent at any particular time.

We got water depths and accompanying pictures of each riffle every 30 minutes for 2 years.

We also did manual surveys of emergent rocks in riffles at a range of discharges to ensure we could link data on water depth to availability of emergent rocks. Discharge data for the catchment were downloaded from the Victorian government Water Measurement Information System

We also obtained data on the phenology of egg-laying by counting and identifing the numbers of egg masses on emergent rocks every month for a year.

All these data enabled us to link discharge in each river to emergent rock availability in different seasons, different rivers, and in different years and hence to the patterns of egg-laying in different seasons.

What did we find?

Our data show that even moderate increases in discharge will drown all the available emergent rocks…

Little River 24 April 2017 at 1 pm

…as we see from the picture below after a rainfall event overnight.

Little River 25 April 2017 at 10 am

The water level drops relatively slowly and rocks along the banks emerge first….

Little River 26 April 2017 at 11.22 am

…with rocks in the centre of the stream emerging only later.

Little River 27 April 2017 at 3.10 pm

In the picture below, we can see how low flows mean more rocks in the centre of the river are emergent but many along the banks are now stranded out of the water. It shows that the relation between discharge and availability of emergent rocks is complicated.

Surveying emergent rocks in the Little River 8 March 2017

In the winter and spring, rainfall means base-flows are higher and there may be only a few emergent rocks available for many weeks.

Little River 14 September 2017 in early Spring. There are relatively few emergent rocks available for female insects to use for egg-laying. The river may stay this high for months.

In these situations, we found that aquatic insects are forced to crowd their egg masses onto the few emergent rocks that are available – which may have consequences for the survival of their offspring.

This is a totally cool story that has been picked up by the Geomorphology Division (GM) of the European Geosciences Union (EGU) and Phenology News (a site for people interested in phenology).

This research was presented in an invited keynote presentation by Jill Lancaster in 2019 at the Symposium for European Freshwater Sciences in Zagreb, Croatia, which attracted over 500 scientists from around the world.

The research was also presented in a public seminar by Jill Lancaster in March 2021, which was advertised widely and had >50 participants, with many watching on Zoom from around the world.

Where you can read about this research:

This research has been published in the following journal article

Lancaster J., Rice S.R., Slater L., Lester R.E. and Downes B.J. (2021) Hydrological controls on oviposition habitat are associated with egg-laying phenology of some caddisflies. Freshwater Biology 66, 1311-1327

Contact me for a pdf if you do not have access to Freshwater Biology, or you can read the accepted ms here (unfortunately embargoed until 31 Dec 2022).

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Are emergent rocks fractal?

With the above data in hand and a bit more we collected, we can address the pivotal questions for this project: Are emergent rocks fractal, and, if so, is the Spatial Scaling Model Correct?

If emergent rocks are fractal, it means their distribution in space – and perhaps time – reflect patterns that are scale-independent, i.e. the patterns are evident regardless of the scale of observation. Patterns that have this characteristics are called self-similar (see previous page), and they can be measured with a single number, the fractal dimension.

The first step to evaluating the Spatial Scaling Model is to test whether an essential resource – here, emergent rocks – is fractal.

The above data provided substantial information about the distribution of emergent rocks (and egg masses) over riffles – i.e. in two dimensions. However, we started with a simpler data set, which looks at the distributions of emergent rocks in one dimension – that is, we counted up the number of emergent rocks (regardless of their position across the bed) within contiguous 5 m lengths of channel for up to 1 km in our three study rivers.

Counting the number of emergent rocks in 5 m channel lengths in the Steavenson River

We also did extensive surveys of the morphology of channels so that we could link the distribution of emergent rocks (fractal or not) to the underlying physical processes that shape channels.

Surveying the Steavenson channel to capture its morphology

We were also able to use data on emergent rocks and egg masses collected in a previous study on streams in Scotland (see: Lancaster J., Downes B.J. & Arnold A. (2010) Environmental constraints on oviposition limit egg supply of a stream insect at multiple scales. Oecologia 163, 373–384), thus expanding our data set to six streams and allowing us to compare rivers in different regions.

What did we find?

Dye Water in Scotland showing riffle-pool sequences

Emergent rocks ARE fractal! Their distributions show repeatable patterns within rivers regardless of whether the data are examined at the original 5 m scale or are bulked together into units of increasing length.

Additionally, different rivers have different fractal dimensions. Values varied between 0.91 and 1.05. So, what do different values mean? Lower values are caused by greater spatial organisation of emergent rocks along channel lengths, whereas higher values represent somewhat more chaotic distributions. Thus river channels with well-organised morphology containing (for example) regular riffle-pool sequences have greater spatial organisation of emergent rocks and hence a lower fractal dimension.

Either way, the fact that emergent rocks are fractal means that we have shown that an essential resource – substrata for laying eggs that permit successful reproduction – is predictably related to physical processes in rivers that shape their morphology.

Without emergent rocks, there can be no reproduction for a wide variety of aquatic insects. That means understanding variation in availability of these rocks in time and space delivers a new way of assessing the ecological condition of rivers and streams. In particular, we expect that human interference in the discharge regimes of rivers may be creating catastrophic reproductive failure for a whole suite of aquatic insects that lay eggs on emergent objects. This question is being investigated by PhD student Handoko Wahjudi in a project funded by the Department of Primary Industries in NSW. Han gave a talk on this project at the Joint meeting of the New Zealand Freshwater Sciences Society and the Australian Freshwater Sciences Society annual meeting 2019 (Waurn Ponds, Victoria)

Where you can read about this research:

This research has been published in the following journal article:

Dwyer, G.K., Cummings C.R., Rice S.P., Lancaster J., Downes B.J., Slater L. and Lester R.E. (2021) Using fractals to describe ecologically-relevant patterns in distributions of large rocks in streams. Water Resources Research, 57(7) e2021WR029796

You can learn more about this paper here

Contact me for a pdf if you do not have access to Water Resources Research, or you can read the accepted ms here

It has been presented at several conferences:

Australian Society for Limnology 2017 (Sydney, NSW, Australia)

Ecological Society of Australia annual meeting 2020 (on-line)

Was the the Spatial Scaling Model (SSM) supported?

The finding that emergent rocks, which are an essential resource for ovipositing insects, are fractal meets the first requirement for the SSM. However, a second requirement for this model is that species must differ in their ability to move along channels to locate suitable patches of resources. Above (Are movements of aquatic insects related to flight capability?) we found that species do not differ greatly in this characteristic. Although adults may fly considerable distances prior to reproduction, the evidence suggests that once females approach channels to lay eggs they probably move to the closest riffle. There were no strong differences between species even though some are more suited to powered flight. Thus the SSM was not supported for this system.

Where you can read about this research:

This research will be published in forthcoming mss. It was also presented at the following conferences:

Ecological Society of America annual meeting 2019 (Louisville, Kentucky, USA), which was well-received.

Joint meeting of the New Zealand Freshwater Sciences Society and the Australian Freshwater Sciences Society annual meeting 2019 (Waurn Ponds, Victoria)

Ecological Society of Australia annual meeting 2020 (on-line)

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