# Seed Viability Equation: Viability Utility

(Ellis & Roberts, 1980)

The viability equations were developed from the 1960s onwards and underpin all seed conservation practices. They predict the proportion of seeds in a population that are viable after any period of storage in a wide range of environments and are of use to both seed bank managers and researchers investigating seed longevity.

You can learn more about the seed viability equations here or start using them right away....

- Predict storage time
- Predict final viability
- Estimate moisture content to give viability at known temperature
- Estimate temperature to give viability at known moisture content

### Useful Tools and Conversions

- Calculate seed equilibrium moisture content from known environmental conditions and oil content
- Calculate equilibrium relative humidity from known temperature, seed fresh weight and known oil content
- Convert between probits, NEDS and percentages
- Convert dry weight to fresh weight
- Predict days to lose 1 probit
- Predict required storage temperature
- Estimate the species viability constant K
_{E}from the "universal" temperature constants C_{H}and C_{Q}in the case of single temperature Cw estimates - Estimate log σ at different temperatures using the "universal" temperature constants C
_{H}and C_{Q}and a known test temperature

### About the seed viability equations

The viability equations are mathematical models that have been developed to predict seed storage life in different environments. The lifespan of a seed-lot, or the time until all the seeds have lost viability, depends upon:

- The storage behaviour of the species in question. The vast majority of species produce seeds with orthodox behaviour that respond in a quantifiable and predictable way to both moisture content and temperature. The viability equations apply only to orthodox or desiccation tolerant seeds.
- Environmental conditions. In general terms, and within determined limits, the drier and cooler the storage conditions, the longer-lived the seeds.
- The initial seed quality or the proportion of the seeds which are viable at the start of storage.
- The species in question. Although all orthodox seeds respond to relative humidity and storage temperature in a broadly similar way, some species are inherently longer-lived than others.

The viability equations are useful in designing and managing seed banks. They allow you to:

- Estimate the final viability of a species stored under known environmental conditions for a specified period of time
- Estimate the likely storage life of a species stored under known environmental conditions
- Estimate how long it will take to lose a certain amount of viability under known environmental conditions
- Estimate the storage temperature required to achieve a particular level of viability after a period of storage at a specified moisture content
- Estimate the equilibrium moisture content the seed lot needs to be dried to in order to achieve a specified viability after a period of storage under known temperature conditions

To use the viability equations you must know the initial viability of the seeds and any 2 of the following 3 pieces of information:

- Storage temperature
- Storage period
- Equilibrium moisture content of the seeds

The viability equations also require species-specific constants. These are determined by a series of experiments in which seed are aged under several combinations of temperature and moisture content. Using this methodology (Hay *et al*, 2003), models have been published for around 66 species from 26 families. The majority of these are crop species. You may also input species constants that you have set yourself.

For seed bank design purposes, if species constants are not available for the species to be conserved, we suggest you use *Hordeum vulgare* L. (Barley) as an example of a medium/ average lived species, *Ranunculus sceleratus* L. (Celery-leaved Buttercup) as a short-lived species and *Brassica napus* L. (rape) as a long-lived species.

Remember that the results you get are estimates, and may have large confidence intervals, for example, Arabidopsis seeds stored at 5 % moisture content and -20 °C are predicted to remain viable for 1908 years (with a 95 % confidence interval of 1387 To 2430 years) (Hay *et al*, 2003).

### Explaining the terms used in the viability equation and viability modelling

**v** = final viability (expressed as %, NEDs or probits) after p days storage.

**P** = storage time (days)

**m** = % moisture content (fresh weight basis)

**t** = temperature (°C)

**K _{i}** = initial viability of the seed lot at p = 0 days (seedlot constant)

**C**and

_{H}**C**= species-specific temperature constants

_{Q}**K**and

_{E}**C**= species-specific moisture content constants.

_{W}**NEDs, probits and percentages**

In a seed population (or seed lot), a few seeds die earlier than others, a few die later, but most die around the mid-point in storage time. Plotting this sort of data produces the familiar bell-shaped normal distribution. To facilitate statistical analysis, percentage seed viability values are linearly transformed to normal equivalent deviates (NEDs). Before the widespread use of calculators and computers, it was difficult to make calculations with negative numbers and so NEDs were converted to 'probits' by adding 5. Probits are still commonly used in viability modelling. A single probit unit is equivalent to 1 standard deviation of the normal distribution of seed deaths over time.

To convert between percentages, NEDS and probits, click here.

**Days to lose one probit (also referred to as sigma - σ)**

This refers to the time taken for viability to fall by 1 probit. The viability models predict that σ is constant between different seed-lots of the same species stored under identical conditions.

The MSB has developed a protocol for comparative seed longevity testing in which sigma values are used to rank species, allowing comparisons to one another, and to 'marker' species of known longevity. The protocol involves artificially ageing seeds at 60%RH and 45°C; a lower or higher temperature may be used for seed lots expected to be short-lived or long-lived respectively. The measured sigma value at the test temperature can be converted to an estimate of sigma at 45°C, facilitating comparisons between species.

What a 1 probit loss in viability means in percentage terms is governed by the normal distribution. At the extremes (≥95%, ≤5%), 1 probit represents a small amount. For example, a fall in viability from 99.87% to 97.72% or from 2.28% to 0.13%. In contrast, at viabilities nearer the mean (50%), one probit, for example, represents the difference between 69.15% and 30.85%

**Species constants**

To determine the species constants, seeds are aged under several combinations of temperature and moisture content. This is time consuming and consumptive of many resources especially seeds. K_{E} may be affected by seed maturity.

C_{H} and C_{Q} are species-specific temperature constants. The effect of temperature on seed longevity is similar for all species, at least between −30°C and +90°C, and if individual constants are unknown the "universal" C_{H}, and C_{Q} constants of 0.0329 and 0.000478 may be used.

For more background on the seed viability equations and their use, please download this pdf.

#### Examples of using the viability equations

To work through the equation using some examples provided, please download this pdf and follow the instruction

**Further information:**

Pritchard, H.W. and Dickie, J.B. (2003). Predicting Seed Longevity: the use and abuse of seed viability equations, pp. 653-721. In: R.D Smith,. J.D Dickie,. S.H. Linington, H.W Pritchard &. R.J Probert (eds) *Seed conservation: turning science into practise.* Royal Botanic Gardens, Kew, UK.

Ellis, R.H. and Roberts, E.H., (1980), Improved equations for the prediction of seed longevity, *Annals of Botany* **45**, 13-30

Hay, F.R., Mead A., Manger, K. and Wilson F.J., (2003), One-step analysis of seed storage data and the longevity of *Arabidopsis thaliana* seeds, *Journal of Experimental Botany* **54** (384), 993-1011

Cromarty, A.S. Ellis, R.M. & Robert, E.H. 1982: The Design of Seed Storage Facilities for Genetic Conservation, IBPGR, Rome

**Citing the Viability Calculation**

Flynn, S. & Turner, R.M. 2004. Seed Viability Equation: Viability Utility (release 1.0, September 2004) http://data.kew.org/sid/viability/index.html

**Feedback**

This calculation tool is an adaptation of the equation originally derived by Ellis & Roberts 1980, and while every effort is made to ensure that errors are kept to a minimum, we have not yet added in any validation rules for data value input and emphasise that this is an estimation tool and all results should be considered accordingly.

We welcome all constructive criticism and other feedback.

Please send comments and feedback to sid@kew.org