I will only answer to the biotic connectivity, in the sense that disconnected fragments have lower service levels compared to connected ones. I am not aware of a formal test of positive correlation between biotic connectivity and ecosystem service levels:

One possibility is the break-down of seed dispersal networks. There are several examples how seed dispersal agents for small fragments of remnant habitat lead to the extinction of plants, see e.g. an excellent example for large mammals in Brazil and tree extinctions in Galetti et al. (2013: Science 340: 1086-1090). I am aware that this work did not test connectivity per se, but several other works (Poschlod et al. 2012 chapter 6 in van der Maarel 2012 Vegetation Ecology) also show that large mammals as seed transport agents serve to connect semi-natural vegetation patches and play a role in species-level or genetic diversity.

Another point could be salt-marsh and mangrove communities where in several cases (sorry I don't have these citations on my mind) it has been shown the lack of connectivity (via dams, fish nurseries etc) disables the tide water flow and in this way alter the habitat conditions and also disable the dispersal of propagules from one patch to another.

A third point would be disturbances: in mediterranean woodlands small woodland mammals (rabbits) and wild boar play an important role in the disturbance regimes of these forest, increasing the diversity of some plant groups (and decreasing of others), this is obviously hampered in completely disconnected fragments, but I have yet no work in mind that could sustain this.

All the best,

Arne

Connectivity is a two-edged sword: connectivity may contribute to dispersal of protected/desirable species as well as undesirable invasive aliens. Secondly, the time scale is decisive. On a geological time scale, disconnection may lead to speciation. Thirdly, connectivity may refer to resident species or seasonally migrating animals. Consequently, connectivity is neither a priory positive nor negative for biodiversity, but rather needs a comprehensive site assessment across species. Currently, many ecological corridors and networks are designed and implemented in Europe without much evidence for their cost-benefit across species and over-time. A promising research topic maybe.

In California. let's say that 100 native plant species make up a grassland ecosystem, and you start removing the native species one by one, what I call "spatial extinction".

And then at the same time, start adding exotic plant species one by one until you have 1,000 total, and maybe a few exotic animals with equal biomass to humans of cows and sheep. And these new grazing animals are protected from the native carnivores because you have killed them all, and for these new animals the native grassland is a very yummy thing to eat.

Then at the same time, you remove the native peoples by putting a bounty on them in 1853, the people who were managing the native landscape for the last 15,000 years. So there was an important connection between the native peoples and the landscape that has now been broken.

You can clearly see the biotic connectivity when the species are going in either directions. For example you can see when connections are broken as you remove a species one by one, like unplugging batteries from a circuit. Each species of plant and animal contributes its own energy and support to the system.

However, going in the opposite direction, it is much moire dramatic to see those connections return when you reintroduce a native species that has been spatially extinct, and see how fast the connections return--it looks like adding cells to a wound and watching the wound heal. That is what I have seen at my project in Palo Alto, California that you can see at http://www.ecoseeds.com/arastradero.html.