With people traditionally growing in their own gardens or allotments this has not generally been an issue in the past, but with more people growing in unusual and often public places it is becoming important to think about who owns what.
Ownership - in terms of who legally owns the land, who has 'ownership' of the plot, and who owns the produce - will vary from project to project.
Obviously if you're growing at home or in an allotment the plants and harvest will be yours. But if you're sharing a growing space (perhaps on someone else's land), or have a volunteer workforce, have you considered how the produce might be shared between different people (some of whom may contribute more to the project than others)?
And if you're growing in front of your house, as promoted by Back to Front, for example, how will you feel if passers-by 'scrump' some of your best veg?
If you grow in a public space where you can't erect a fence (such as in a park), you may have to accept that others will help themselves to the fruits of your labours.
On the other hand you may want to encourage public harvesting (as in Incredible Edible Todmorden, where all produce is grow in public and all is available for anyone to pick and use) - but if so, might you need to save some produce for seed?
And how will you stop people picking things before they are ready, or (as in the case of Parks' Edible Beds), if your veg also serves an ornamental function and needs to last through the season?
Research shows that most respect other people's veggie property (though vandalism and theft do occasionally occur), but bear in mind that there are quite a few Incredible Edible-style schemes around where people are actively encouraged to help themselves (not to mention an increasing awareness of the free food such as apples available in Leeds), and if there's one of these help-yourself schemes near you, people might make a simple mistake and assume your crop is up for grabs.
How I Prevent Stealing From My Community Garden https://www.youtube.com/watch?v=PNqbkdoXPCE
Bear in mind that often there is, briefly, an abundance or even glut of one crop or another, when you may be happy to give some away.
Having a 'hedge veg' display area for surplus produce (perhaps with an honesty box) may encourage people to understand which veg is available and which is not.
Signs can also help to prevent confusion. For example the 2013 Feed Leeds Edible Beds in public parks had signs asking people not to pick the produce - because they were an experiment in aesthetics, to see how people would react to cabbages instead of bedding plants, and also to find out how well the displays would last. (The beds were a success and are being repeated in 2014).
If you do want people to help themselves, say so.
And if you want them to have some veg but not others, you could perhaps define a more private area (with planting or fences) where people would feel less comfortable about picking - or just use a simple traffic-light system:
Red - please don't pick
Amber - not ready yet
Green - help yourself!
We have signs like these available to people who grow in public spaces.
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