"When predators are smaller, they are not as efficient in their energy use so the food, such as stream insects, available in the habitat will support fewer and smaller fish."
The study specifically showed that smaller rivers supported fewer fish per unit of prey resource compared to larger rivers, and offered a theory explaining why that happened.
"The theory is based on how the dimensions of a habitat constrain the body size of individual predators, the fish in our case, and how that affects the efficiency of prey use."
Study co-author Associate Professor Michael Plank said the mathematical theory served to highlight the underlying causes of population declines.
"This means we can be better informed when making decisions that affect habitats for key species in New Zealand."
Of our freshwater fish species particularly, three quarters were either threatened with or at risk of extinction.
How much water was taken out of rivers is a hot topic and the subject of much public debate and lengthy court battles.
The researchers expected this work will have an important influence on decisions about resource use, particularly regarding the flow in rivers.
"We make many decisions about how to manage natural resources which affect the size of habitats, for example when we take water from rivers," co-author Dr Helen Warburton said.
"Our work shows that those changes in habitat size affect how food webs work, and that they could have a detrimental effect on the capacity of those habitats to support fish in rivers.
"Moreover, these effects haven't generally been considered in how we make decisions about natural resource management."
More than half of the water consented by councils in New Zealand was for irrigation, but it wasn't clear how much was actually being used, with varying data and records around the country.
A recent Ministry for the Environment stocktake found Canterbury accounted for 64 per cent of the total consented volume of water for irrigation, while a further nine per cent of the total consented volume was in Marlborough, followed by seven per cent in Otago.
According to that report, the cumulative effect of consented water takes on downstream river flows showed that irrigation had the highest potential to cause "widespread reductions" in downstream river flows, compared with other water uses.
From November 2016, it became mandatory for most water users to provide continuous records of water takes each year.
The Government also this year announced new guidelines requiring all infrastructure in rivers and streams to be lower than 4m should be built to allow some fish species to make it to their ocean breeding grounds.