Refugia -- Protection from Grazing

For a general introduction to consumers, see Consumers. For how surface properties create the physical basis for refugia, see Surfaces.

Why Refugia Are the Difference Between Stability and Collapse

Without refugia, a sufficiently hungry grazer would eat every last algal cell, drive its food to extinction, and then starve to death. The ecosystem would collapse in a boom-bust cycle with no recovery. Refugia — the physical hiding places where prey survives no matter how intense the grazing — are what prevent this. They guarantee a seed population that can regrow once grazing pressure eases, turning a one-way crash into a sustainable oscillation.

This makes refugia one of the most powerful levers in the model. Adding a rough, porous surface to a scenario can shift the outcome from extinction to coexistence, because the crevices and interstices that grazers cannot reach protect enough prey to keep the food web intact. The type, roughness, and amount of surface area in a scenario directly controls how much of each prey population is protected — and that, in turn, controls whether the ecosystem survives. This matches observations from real aquatic habitats: structural complexity promotes species coexistence.

The Core Concept

In a real ecosystem, a grazer cannot eat every last scrap of food. Some algae cells are tucked into tiny crevices in a rock. Some bacteria are buried deep inside a protective biofilm. Some ciliates are hiding in the narrow spaces between gravel particles that a copepod is simply too large to enter. These protected zones are called refugia, and they are critical for ecosystem stability.

In the model, refugia are represented through access fractions. Every grazer-food-surface combination has an access value between 0 and 1. If Copepods have an access of 0.25 to periphyton on gravel, that means Copepods can reach only 25% of the periphyton biomass growing on gravel. The other 75% is in refugia -- hidden in deep interstices between the gravel particles where a 1-2mm copepod simply cannot fit.

The complement of access IS the refugia fraction. Access of 0.25 means 75% refugia.

Maturity-Dependent Access

The access values in the tables below represent mature-biofilm conditions — surfaces with a well-developed EPS scaffold (high biofilm maturity M). On a freshly submerged surface with no biofilm (M = 0), prey are more exposed because there is no EPS structure to hide behind. The model interpolates between a "bare surface" access (higher, roughness-dependent) and the mature values listed here based on each surface's current M. Smooth surfaces like glass show the largest increase when bare, while rough surfaces like ceramic already provide geometric refugia regardless of biofilm state. As the biofilm matures over weeks to months, access gradually decreases toward the static values shown. See Biofilm Maturity for details.

Surface-Specific Access

Each grazer has different access to food on different surfaces. The access value depends on the physical characteristics of the surface and the feeding mode of the grazer.

Copepod Access to Periphyton

Copepods are raptorial feeders that scrape and grab prey from surfaces. Their access depends on how exposed the surface is:

Surface	Access	Refugia	Why
Glass	0.95	5%	Smooth, flat, nowhere to hide
Ceramic (smooth)	0.85	15%	Minor surface texture provides some shelter
Ceramic (porous)	0.65	35%	Cells anchor in pores that copepods cannot enter
Sand	0.40	60%	Small interstitial spaces exclude copepods
Gravel	0.25	75%	Deep interstices completely inaccessible
Biofilm	0.10	90%	Intentional refuge -- thick protective matrix

Copepod Access to Bacteria

Bacteria are very small (0.2-2 micrometers) and most live attached to surfaces in biofilms, making them hard for a 1-2mm copepod to reach:

Surface	Access	Refugia	Why
Glass	0.12	88%	Thin biofilm, some bacteria exposed
Ceramic (smooth)	0.10	90%	Similar to glass
Ceramic (porous)	0.05	95%	Bacteria deep in pores
Sand	0.05	95%	Bacteria in grain interstices
Gravel	0.02	98%	Deep protection
Biofilm	0.01	99%	Nearly complete protection

Copepod Access to Ciliates (Microzooplankton)

Ciliates are 10-300 micrometers and many live on or near surfaces rather than free-swimming. Copepods hunt them raptorially:

Surface	Access	Refugia	Why
Glass	0.50	50%	Some sessile ciliates attached, some free-swimming nearby
Ceramic (smooth)	0.40	60%	Minor surface complexity adds refuge
Default (no surface)	0.30	70%	Many ciliates associated with microhabitats
Ceramic (porous)	0.20	80%	Ciliates can hide in pores
Sand	0.15	85%	Small interstitial spaces shelter ciliates
Gravel	0.08	92%	Copepods cannot enter spaces that ciliates can
Biofilm	0.05	95%	Intentional refuge, thick protective matrix

Daphnia Access to Planktonic Algae

Daphnia are filter feeders working in the water column. Their access to planktonic algae is very high (95% default) because suspended algae are exactly what their filter mesh is designed to capture.

Daphnia Access to Periphyton

Daphnia cannot scrape surfaces. They can only capture periphyton cells that naturally detach and float into the water column. Smooth surfaces release cells more readily than rough ones:

Surface	Access	Refugia	Why
Glass	0.70	30%	Smooth, high detachment rate
Ceramic (smooth)	0.55	45%	Some cells anchored in texture
Ceramic (porous)	0.35	65%	Cells anchored in pores rarely detach
Sand	0.30	70%	Cells deep in grain interstices never reach water column
Gravel	0.15	85%	Deep interstices, very low detachment
Biofilm	0.05	95%	Thick EPS matrix, minimal detachment

Daphnia Access to Bacteria

Daphnia filter suspended bacteria from the water column. Like periphyton, they can only reach bacteria that are free-floating or loosely attached:

Surface	Access	Refugia	Why
Glass	0.65	35%	Thin biofilm, higher fraction suspended
Ceramic (smooth)	0.50	50%	Moderate biofilm protection
Ceramic (porous)	0.30	70%	Bacteria deep in pores, rarely suspended
Sand	0.25	75%	Bacteria in grain interstices, rarely suspended
Gravel	0.10	90%	Deep protection
Biofilm	0.05	95%	Nearly complete protection

Density-Dependent Refugia

Static access fractions are only part of the story. In reality, when prey populations are small, the remaining individuals tend to occupy the very best hiding spots. As the population grows, those prime spots fill up and newcomers are forced into more exposed positions. The model captures this with density-dependent refugia.

The way it works: the static access value is multiplied by a scaling factor that depends on prey density. At zero prey density, the factor drops to a minimum (nearly all survivors are hiding). As prey density increases, the factor rises toward 1.0 (most prey are exposed). The transition follows a saturation curve controlled by two parameters:

refugia_K_mol_L (half-saturation density) -- The prey density at which the scaling factor is halfway between its minimum and maximum. Below this density, refugia protection increases steeply. Above it, most additional prey are exposed.
refugia_min_frac (minimum factor at zero density) -- How much the access shrinks at extremely low prey density. A value of 0.02 means that at near-zero density, effective access drops to 2% of the static access value.

Example: Copepod Hunting Periphyton

Copepods have static access of 0.80 to periphyton (default surface), with density-dependent refugia parameters: K = 5e-4 mol/L, minimum fraction = 0.02.

At high periphyton density (well above K): effective access is close to 0.80 (nearly all prey exposed)
At periphyton density equal to K: the scaling factor is about 0.51, so effective access is about 0.41
At very low periphyton density: effective access drops to 0.80 times 0.02 = 0.016 (almost all survivors are hiding)

This creates powerful stabilization. As Copepods graze periphyton down, the remaining periphyton become harder and harder to find. The grazing rate drops faster than the prey population, preventing complete wipeout.

Which Interactions Have Density-Dependent Refugia

Not all interactions use density-dependent refugia. It is enabled for prey types where the "last survivors hide in the best spots" logic makes biological sense:

Copepods on periphyton: K = 5e-4 mol/L, min = 0.02
Copepods on microzooplankton (ciliates): K = 2.5e-5 mol/L, min = 0.02
Daphnia on planktonic algae: K = 5e-5 mol/L, min = 0.105
Daphnia on periphyton: K = 5e-4 mol/L, min = 0.02

Interactions without density-dependent refugia (like detritus) use their static access values at all prey densities. Note that for bulk prey pools like bacteria and microzooplankton, the static per-surface access values are combined into a surface-area-weighted average, so the effective access depends on the scenario's surface composition even without density-dependent scaling.

How Refugia and Surface Type Interact

The surface-specific access value and the density-dependent refugia factor work together multiplicatively. Consider Copepods eating periphyton on gravel:

Static access on gravel: 0.25 (75% in physical refugia from gravel interstices)
Density-dependent factor (at moderate periphyton density): maybe 0.60
Effective access: 0.25 times 0.60 = 0.15

So only 15% of periphyton on gravel are actually reachable by copepods at moderate densities. On smooth glass at the same density:

Static access on glass: 0.95
Density-dependent factor: still 0.60 (same prey density)
Effective access: 0.95 times 0.60 = 0.57

This means glass provides almost four times the food access of gravel, which is why surface choice has such a large impact on grazer-prey dynamics in the model.

Practical Implications

Adding rough surfaces (gravel, porous ceramics) to a simulated jar creates refugia that protect algae and prevent grazer-driven crashes.
Biofilm surfaces are designed as intentional refuges with very low access values across all grazers and food types.
Density-dependent refugia prevent total extinction of prey species even on smooth surfaces -- as prey gets rare, the survivors effectively "disappear" from the grazer's perspective.
Different grazers see different refugia. Daphnia (filter feeder) has no access to surface-attached food directly, only to cells that detach. Copepods (scraper/hunter) have high access to exposed surfaces but cannot enter narrow spaces. This means the same gravel surface provides different refugia for different grazer-periphyton pairs.