Alexander, I am not sure what you getting at, but fish are like trees, except they move and you cannot see them. This makes them very hard to count.

I think this is where the support of MPAs as a solution to overexploitataion breaks down. Choice of locations is dominated by how much a particular site appeals to human perceptions of the sites "importance" rather than any real knowledge of whether the site is likely to increase recruitment or productivity. In addition, because the biomass that accumulates in the MPA is not subtracted from the yield stream, all the fish outside of the MPA are marginalizes because 100% of the yield is extracted from those outside. It seems to me that quite a bit of hubris is involved with the notion that we know enough about a fisheries ecosystem to know where exactly to site an MPA. I think we would be better offer off in the long run to be more conservative in the overall exploitation rates on 100% of the stocks involved.

Dear colleagues

Let me clarify the question on an example from physics. There are aerodynamics (which describes the motion of physical bodies in the air) and hydrodynamics (which describes the motion of physical bodies in a liquid). Unlike physics in biology is no distinction between the population dynamics of terrestrial and aquatic organisms. Although elementary arguments from physics suggest that the specifics should be. In general terms the population dynamics can be written as

dN/dt=F(N, some parameters )N (1)

Question is this: are there specific (for aquatic environment) function F(N, some parameters) and a set of parameters?

1. Yes, but first we need to define a parameter that separates the air from the water. From physics we know of such a parameter , it is the Reynolds number Re. Thus of the equation (1) can be rewritten as

dN(t)/dt=F(N(t) , Re, some biological parameters )N(t) (2)

where Re = speed* body_Length / viscosity

Next you need to link the biological parameters with Re (within function F).

Definition of a (local) population within the meta-population, usually focuses on the spatial boundaries between (local) populations. Whereas, the definition of conspecific (single-species) community focuses on the organizational boundaries.

Conspecific community is always a kind of a local population, but the converse is not always true, the local population may consist of several communities. For example the local wolf population may consist of several wolf packs.

I think the issue depends upon the size of the fish (animals) that you are dealing with . Of course the viscosity of sea water is an enormous issue in low Reynolds number environments, which is why copepods have developed specialized apparatus to generate feeding currents to bring food to their mouth parts. Moreover, larval fish benefit from microscale turbulence in the sea because of motions imparted on both predators and prey increase encounter rates. Diffusion has been studied extensively as it effects plankton patchiness, including patches of fish eggs and larvae as well as patches of their prey. For larger fishes, we know that ocean physics play a large role in large scale patterns of distribution, predator prey interactions, larval retention areas, development of linear oceanographic features (langmuir cells, frontal boundaries, etc) which are important sites of trophic transfer. Water column stability is also important because some larvae require high prey densities that accumulate at density discontinuities to initiate feeding. That said, larger fishes see the world from a high Reynolds number perspective and have adapted to living in a viscous environment. So I say again, physics play a role at all levels, and the connectivity between disparate populations in the sea have been well studied, even if stocks are not managed with this in mind owning to jurisdictional concerns. In recent years, this problem is receiving more attention as we struggle to implement ecosystems based fisheries management.

Alexander, why do you need to define a parameter that separates the air from the water? really you need it?

Air: space usually uninhabitable for fish (except lungfish). Is it not sufficient?

Is it not better you concentrate your efforts in defining the water conditions (flow direction, physicochemical gradients...)

Excuse me if I am talking nonsense (and excuse my "hard" english) but I don't understand well your aim.

Thank you for your patience with me.

I think an important variable to consider is the 3D space of marine systems which affects the 'openness' of populations to each other. Most species have evolved to be very successful in 3d space by having specific adaptations and varied ontogenetic life stages that enable to utilize specific conditions of water such as currents to their advantage to increase dispersion. So what I'm trying to argue is that there are different conditions for marine population dynamics and therefore direct comparisons shouldn't be made. An interesting point about dispersion in marine fish populations is the ability to self-recruit and for larvae to return to source locations, again a specific adaptation that some fish have evolved that make population dynamics operate in a different way to terrestrial systems

Population dynamics models describe how individuals are added to populations or taken away, whether due to births and deaths or immigration and emigration. I fail to see how whether an organism is aquatic or terrestrial effects the fact that the population can change only due to these fundamental mechanisms. What would a fisheries stock assessment model gain from having an "aquatic viscosity" parameter? It sounds silly to me. Which of the mechanisms of population change would you be able to model more effectively with such a parameter?

In general, the population dynamics (at least as taught in universities) describes how population growth depends on population size. There is no universal (for all species) growth function, it largely depends on the availability of resources and energy costs on the resource search.

Fundamental mechanism here is the search and then converting resources into the survival, growth and reproduction. Feature of many underwater organisms is that the cost of searching for food strongly depends on the size of the group (shoal), because swimming together much more energy efficient than moving alone. This is the effect of the viscosity of water; it is particularly strong for large and fast moving fish.

Ignoring shoal structure in fisheries stock assessment models leads to

(1) Biased estimates of stock (overestimation in “good years” and underestimation in “bad” ones), because the catchability (which used as basis for stock assessment) significantly depends on the shoals size and structure.

(2) Strongly limited predictability of future stock sizes, inability to prevent the possibility of collapse.

As a result, errors in the determination of fishing quotas lead to multi-billion losses. I'm still not rich enough to consider the loss of several billion per year as silly.

Perhaps there is reasonable to ask another question - Why are so naïve (without density dependence) and outdated (at list 270 years old) models that are now used for stock assessment, still sometimes work?

The answer can be found in my article on Shoal based fish population dynamics.

https://sites.google.com/site/concomdynamics/working-papers