The document discusses a metapopulation model for coral reef fish populations. It defines key concepts like patches that can be occupied or empty, local extinction rates, and dispersal between patches. The model considers patches that are reserves without fishing and patches that are fished. It assumes extinction is higher in fished patches. The model uses variables like the proportion of occupied reserve and fished patches. It shows reserves can prevent regional extinction by replenishing fished patches, thus enabling sustainable fishing. The simple model provides insights into how marine reserves can benefit fisheries through metapopulation dynamics.

1. The Metapopulation Ecology
of Coral Reef Fishes
Presented by- Hina Chaudhary
Population Ecology
Source: Coral Reef Alliance

2. Introduction
Coral reefs are shallow water, tropical marine ecosystems which are
characterized by a remarkably high biomass production and a rich faunal and
floral diversity perhaps unequaled by any other habitat.
Corals require certain conditions to occur and can flourish only in relatively
shallow waters, exposed to direct sunlight, with optimum temperature of 23-
25°c and free from suspended sediments.
The structure of a reef is formed by the calcareous skeleton that houses
corals, a type of soft-bodied, radially symmetrical, marine invertebrates of the
phylum coelenterate. Individuals of a colony are called polyps or hydroids.
Coral Reefs of India: Review of Their Extent, Condition, Research and Management Status by Vineeta Hoon

3. Millions of coral skeletons cemented together over a period ranging from a few
thousand to millions of years give rise to such reefs.
Reefs can vary enormously in structure and complexity and are roughly divided
into three major types.
1. Fringing reefs', reefs
that grow close to the
shore and extend out into
the sea like a submerged
platform.
Eg- Greater Caribbean
Reef
2. Barrier reef: reefs
separated from the land by
wide expanses of water
and follow the coastline.
Eg- Great barrier Reef
3. Atolls: a roughly circular
ring of reefs surrounding a
lagoon, a low lying island,
common in the Indian and
South pacific oceans.
Eg- The Pacific ocean
Coral Reefs of India: Review of Their Extent, Condition, Research and Management Status by Vineeta Hoon

4. Strategies to protect Coral Reef
MPAs or Marine Protection Areas are one of the most prominent forms of reef
management. They promote responsible fishing practices and habitat protection.
In Australia, the Great Barrier Reef is protected by the Great Barrier Reef Marine
Park Authority, including a Biodiversity Action Plan.
In India, Gulf of Mannar –Marine biosphere reserve ,Tamil Nadu,1980.
Why they are at risk?
Coral reefs have been suffering a major threat from climate change, ocean
acidification, blast fishing, cyanide fishing, coral mining, pollution, over
fishing and the digging of canals. This has been increasing for the past 10 – 20
years.
It is estimated that 10% of the world’s coral reefs have already died at that
60% are at risk of human threats. 80% of the coral reefs in South East Asia
are endangered.
(Wilkinson, Clive (2008))

5. A Metapopulation model to see how marine
reserves might help to conserve such
populations and benefit fisheries.
Using the Metapopulation model, they show how reserves can be used to control the
equilibrium of the Metapopulation in such a way that the exploitable stock and
sustainable yield are maximized.

6. •Patch is considered to exist in 2 states, Occupied and Empty
Proportion (p) of all patches that are occupied (0 ≤p≤ 1).
Local population within each patch has a constant rate of extinction (e), so the
proportion of occupied patches decreases at rate (ep)
This decrease is countered by dispersal of propagules from occupied patches to
empty ones.
Basic assumptions of a Metapopulation
The model defines two kinds of patches."
(i) Those open to fishing and
(ii) Those maintained as reserves free from exploitation

7. The rate at which individuals from a occupied patch reach to another patch is
given by the constant m, and the total rate at which these successful migrations
occur is mp.
Since the proportion of occupied patches only increases if the recipient patch
was previously unoccupied, the proportion of occupied patches increases at the
rate mp(1-p).
The flux in p is given by the equation
Eqn-1

8. Metapopulation
Assumption Models
Spatially Implicit Model
(Levin Model)
Infinite, discrete patches
with variations.
Patches are equally
connected via migration
Spatially Explicit Model
Many patches without variation
in patch size and quality.
Migration is distance dependent
Spatially Realistic Model
Finite number of relatively
small patches.
Decline with distance.
Patches are occupied and empty.

9. Model for an exploited metapopulation with
reserves
First, local patches are defined, a priori, to be of two types: either maintained as
reserves or open to exploitation.
Second, the state of a patch is determined by whether or not it contains
individuals recruited to the fishery.
Third, the assumption that local extinction of recruited individuals is a
consequence of exploitation.

10. First, local patches are defined, a priori, to be of two types:
either maintained as reserves or open to exploitation.
We consider a region in which a proportion q1 of the patches is to be held
unexploited as marine reserves and a proportion q2 (where q2 = 1 - q1) is to be
exploited.
The proportion q1 is taken to be the principal parameter controlled in the
management of the fishery. The Metapopulation lives in both kinds of patch, and it
is assumed that the rate of successful migration m from a given patch requires only
that the patch is occupied, not on its status as a reserve or exploited area.
On the other hand, the rate of local extinction, e1 and e2 for reserves and
exploited patches respectively, is likely to be greater in the presence of fishing, so
they assume e1 << e2.
This difference in the behavior of local populations in reserves and exploited
patches means that the model has two dimensions.

11. Second, the state of a patch is determined by whether or
not it contains individuals recruited to the fishery
The two state variables p1 and p2 describe respectively the proportion of
reserve patches and of exploited patches in which recruited individuals are
present (where 0 ≤ p1 ≤ q1 and 0 ≤ p2 ≤ q2).
Since m is independent of whether the donor patch is exploited or maintained as
a reserve, the total rate of successful migration is the product m(p1+p2).
Migration increases the proportion of reserve patches containing recruited fishes
at a rate that depends on the proportion of reserve patches unoccupied
m(p1+p2)(q1-p1); in the same way migration increases the proportion of
exploited patches with recruited fishes at the rate m(pl+p2)(q2-p2).
Positive effects of migration are countered by local extinctions in reserves and
exploited patches; the rate at which the proportion of occupied patches decreases
through exploitation is e1p1 and e2p2 respectively.

12. Eqn-2

13. Third, the assumption that local extinction of recruited
individuals is a consequence of exploitation
Exploitation is assumed to give rise to a substantial local extinction rate, so
that e2 > 0.
In contrast, reserves, because they are not fished, are assumed to experience a
negligible rate e1 = 0. The dynamics are then given by
c = e2/m.
Eqn-3

14. Extinction rate in reserves in eqn (3), that all reserve patches typically become
colonized by fishes. The reserves then replenish the exploited patches in which
the fishes are absent.
Fig. 1. Phase portrait of the p1, p2 space, with ql = 0.4, m =0.7 and e2 = 0.5.
The lines indicate the orbits of
numerical solutions of eqn (3)
from different initial conditions.
• equilibrium point to which
the orbits tend. All solutions are
confined to the region
0 ≤ p1 ≤ 0.4, 0 ≤ p2 ≤ 0.6.

15. Once at equilibrium, it is straightforward to determine
(i) the proportion of local patches that should be held as reserves to maximize
the exploitable stock at equilibrium, and
(ii) the benefit of these reserves to the fishery in terms of the equilibrium yield.

16. Conclusion
Reserves should have the effect of preventing regional extinction of heavily
exploited Metapopulation by providing a source for the replenishment of
fished-out local patches so that sustainable exploitation is possible in the
future.
A system much simplified from the real world. It has the advantages of
simplicity, allowing us to see some important basic relationships.
Methods of Metapopulation dynamics become important tool/method in the
field of Conservation Biology

17. References
Man, Alias, Richard Law, and Nicholas VC Polunin. "Role of marine reserves in
recruitment to reef fisheries: a metapopulation model." Biological
Conservation 71.2 (1995): 197-204.
Wilkinson, Clive (2008) Status of Coral Reefs of the World: Executive Summary
Global Coral Reef Monitoring Network
Coral Reefs of India: Review of Their Extent, Condition, Research and
Management Status by Vineeta Hoon

18. Thank you.