Harvesting

1
Harvesting
2
(No Transcript)
3
SUSTAINABILITY
Imagine an earthworm 7 segments long
This earthworm produces two segments per day
- Dr Anesh Govendars Earth-worm model
4
What is the maximum sustainable number of
segments that can be harvested each day?
If you harvest three segments per day
5
If you harvest one segment per day
6
If you harvest two segments per day
7
(No Transcript)
8
Building harvesting into a model
Model applies for a species showing discrete
breeding use R not r Assume intra-specific
competition occurs
Nt1 (Nt R) / 1 Nt.(R-1)/K
Step 1 Project population into future for x time
units without competition Calculate R and
recruitment (additions) for each time step Plot
population size against time (line-graph) Plot
recruitment against population size (X-Y
graph) Determine what the maximum recruitment is
and when it occurs
9
Project 100 years
If N0 12, R 1.63, K 368 974
10
Step 2 We will start by using a constant yield
model (i.e. a fixed number of individuals are
harvested from the population each year) Label a
cell Fixed Annual Yield and, in the adjacent
cell, put an arbitrary starting value say
1 Create a harvest (h) column next to the
additions column. This is the number of
individuals that you are going to harvest in each
interval. Make each cell address equal to the
value of your Fixed Annual Yield, with the
exception of t0, which make equal to 0 Calculate
Total harvest over the 100-year projection by
summing the harvest column (should equal 100, at
this stage) You must now subtract the harvest
each year from the numbers in the population
.BUT.do you subtract the harvest from the
population BEFORE or AFTER it has
reproduced? What is the difference?
Constant Yield Model
Nt1 ((Nt ht1).R) / 1 (Nt
ht1).(R-1)/K
Nt1 ((Nt R) / 1 Nt.(R-1)/K) ht1
11
(No Transcript)
12
STEP 3 Adjust your value of Fixed Annual Yield
and adjust the time of first harvesting in order
to maximise the total harvest over the 100 year
projection BUT remember it is important that
the final R (R99) value is greater than or equal
to 1.0000 (i.e. the population is sustainable)
PLAY
Advantages Fixed Yield Models are liked by
industry because they can plan plant and
workforce in advance Communities like Fixed Yield
Models because they know how much money will be
coming in in advance
Disadvantages Data-hungry small errors in Yield
can result in population crashes
13
Management implications of MSY models

• Set a Total Allowable Catch (TAC) each year
• Apportion TAC amongst rights holders
• Open the resource to exploitation
• Keep a cumulative log of harvest and close access
  to rights holder when TAC reached

14
How do you calculate MSY without playing around?
Remember the earthworm model the MSY was
achieved by harvesting the number of recruiting
segments to the worm (population) two per day.
How do we find the equivalent of the two
segments per day MSY in our population?
15
In our example here the maximum number of
individuals that recruit to the population is 44
524 over the period 21- 22
16
If you remove this number of individuals
(starting at time 22), the population will remain
at a constant size. In other words
these individuals are surplus to the population
and we refer to this type of model as a Surplus
Production Model.
17
Small errors in MSY can have BIG consequences
18
Some Stock Recruit Curves
19
Harvesting from a population (in a sustainable
way) does not harm the population.
WHY?
By preventing a population from reaching the
carrying capacity, you maintain it in a constant
state of growth and ensure that the negative
effects of intra-specific competition are reduced.
20
Constant Effort Model
Let us imagine a population, size N. You go out
today and spend 2 hours harvesting from the
population (with efficiency e) and come back with
aa individuals But you went out yesterday and
spent 4 hours harvesting from the population
(with efficiency e), and came back with bb
individuals Which is larger aa or bb?
WHY?
21
Let us imagine a fish population, size N. You go
out today and spend 2 hours harvesting from the
population using a motor-powered vessel and a
trawl net and come back with aa individuals But
you went out yesterday and spent 2 hours
harvesting from the population using a canoe and
a throw net, and came back with bb
individuals Which is larger aa or bb?
WHY?
http//www.hope-for-children.org/images/transafric
a_moz03.jpg
22
NOW You go out today and spend 2 hours
harvesting from the population using a
motor-powered vessel and a net and come back with
120 546 individuals But you went out yesterday
and spent 2 hours harvesting from the population
using a motor-powered vessel and a net and came
back with 98 113 individuals
WHY?
23
Catch is proportional to effort, efficiency and
population size. If we fix efficiency (assume
hereafter that it is equal to 1), then catch will
reflect population size and effort. If we fix
effort, then catch will reflect population size
in other words the numbers caught will reflect
some fixed proportion of the population.
24
Building a Constant Effort Model
Step 2 Label a cell Efficiency and, in the
adjacent cell, enter a value of 1 (100
efficient) Label a cell Effort and, in the
adjacent cell, put an arbitrary starting value
say 0.1. You are going to play around with this
number in just a minute. Label a cell EE (Effort
x Efficiency) and make it equal to the product of
the aforementioned Efficiency and Effort cells
(it should equal 0.1). Create a harvest (h)
column next to the additions column. This is
the number of individuals that you are going to
harvest in each interval. Make this number in
each cell equal to the product of the EE cell and
the population size with the exception of t0,
which make equal to 0 In order to avoid circular
arguments that will arise when you subtract the
harvest from the population size, you need to
re-enter the formula to calculate population size
at t1 into the harvest calculations. Thus the
harvest at (e.g.) t5 is calculated as
h5 ((N4 R) / 1 N4.(R-1)/K) EE
25
Step 2 Calculate Total harvest over the 100-year
projection by summing the harvest column You
must now subtract the harvest each year from the
numbers in the population .BUT.do you
subtract the harvest from the population BEFORE
or AFTER it has reproduced? What is the
difference?
Nt1 ((Nt ht1).R) / 1 (Nt
ht1).(R-1)/K
Nt1 ((Nt R) / 1 Nt.(R-1)/K) ht1
26
Harvesting after reproduction
The shape of both lines should be similar one
is just 10 of the other (EE 0.1)
Total Harvest 2 258 460
27
AFTER
BEFORE
28
STEP 3 Adjust your value of EFFORT and adjust
the time of first harvesting in order to maximise
the total harvest over the 100 year
projection BUT remember it is important that
the final R (R99) value is greater than or equal
to 1.0000 (i.e. the population is sustainable)
PLAY
Advantages Fixed Effort Models are liked by
management authorities because they are not as
sensitive as Fixed Yield models to mistakes. A
10 change in effort will not necessarily crash
the population, whilst a 10 increase in a Fixed
Yield probably will!
Disadvantages Because the numbers harvested each
year will vary (with population size), industry
and communities have problems planning in advance.
29
Management implications of MSY models

• Set a Total Effort each year
• Apportion Effort amongst rights holders
• Open the resource to exploitation
• Keep a cumulative log of effort and close access
  to rights holder when Total Effort reached

• Effort can be limited by (in the case of fishing)
• Closed seasons
• Closed areas
• Fleet size, vessel type, engine power
• Gear used number of hooks or lines, mesh size of
  nets
• Time at sea
• etc

30
Building environmental variability into your
models
All the models you have developed so far are
deterministic (essentially fixed), but we know
that populations change in size all the time due
to extrinsic factors such as the weather. Weather
conditions have an impact on the amount of
resources available to a population, which in
turn influences the carrying capacity. We need
to build some sort of environmental variability
into our models if they are to more accurately
reflect patterns in the real world, and to
minimise the chance of over-exploiting the
population when we start to harvest. Before we
start this exercise, we need to know how often
bad or good weather conditions occur, and we
need to know how these affect the carrying
capacity. Whilst the first set of information can
be readily obtained from long-term weather sets,
the latter is difficult to pin down. That does
not matter in a modeling scenario because we
are exploring the processes rather than the
actual numbers. In our models, we are going to
use random numbers to indicate the state of the
weather each year, and we are going to ask
MSExcel to look at these numbers and see if they
are greater or less than the numbers we propose
to indicate good or bad weather, and then to
assign a carrying capacity accordingly. This
modified k value will then be used in our
equations to model population size
31
Weather calculations
If bad weather happens, on average, once every
15 years, we can say that the probability of bad
weather is 1 / 15 0.0667
If good weather happens, on average, once every
9 years, we can say that the probability of good
weather is 1 / 9 0.111
32
Incorporating weather into an unexploited
population with
N0 12, R 1.63, K 368 974
In your spreadsheet, you should set up a new
column labeled Weather A. Weather is a random
number in our model, so ask MSExcel to generate a
random number each year
RAND()
At this point, no two of us are going to have the
same weather conditions. Every time you do
something to the worksheet, your weather
conditions will change (as they will too if you
press the F9 key). You can convert the constantly
changing numbers into values using the edit,
copy, paste special, values function BUT DONT
yet
The next thing we need to do is to ask MSExcel to
identify the weather each year as Good, Bad or
Normal, and we do this using the IF function.
The logic of the IF function is as follows. We
ask MSExcel to look at the contents of a
particular cell address and if the contents
conform to some pre-established condition, then
it will return one answer and if it doesnt then
it will return another answer
33
For example Set up a dataset spanning four
columns (A-D) and 10 rows. Put titles to each
column in row 1 as indicated, and fill column A
with random numbers.
In column B, we are going to ask MSExcel to look
at each cell in column A and, if it is smaller
than 0.20, to return a value of YES in the
corresponding cell of Column B. Otherwise to
return a value of NO The signs are
important when dealing with text in formulae, but
should be ignored if using numbers
IF(A2lt0.20,YES,NO)
Repeat the exercise for column c
You can combine IF arguments. For example, in
column D we are asking MSExcel to look at the
contents of cells in column A and then IF they
are larger than 0.9 to assign an answer of BIG,
IF they are smaller than 0.2 to assign an answer
of SMALL, otherwise to return an answer of
Average
IF(A2lt0.20,SMALL,IF(A2gt0.90,BIG,Average))
34
Okay having set up our weather (in Weather A),
define it as GOOD, BAD or NORMAL in a Weather B
column using the IF Function
35
How?
36
(No Transcript)
37
You must now make your population numbers reflect
this new K value
REMEMBER NO TWO will have the same results
38
Okay having now built weather into your model
for an unexploited population you must now
build it into your Fixed Yield and Fixed Effort
harvesting models
Remember the population must not crash in your
simulations, the Final R (R99) should be greater
than or equal to 1.0000, and you should aim to
maximize the harvest over the 100 year period
PLAY
Your model run is from a single simulation
based on the particular set of random numbers
generated in that single run. Ideally you need
to repeat the simulation (looking at final R,
total harvest, and whether the population crashes
or not) thousands of times for each starting
time, fixed yield and fixed effort model that you
use in order to come up with appropriate values!
You can do this using macrosbut that is
another story!
39
The models built to date assume that all
individuals in the population are equal
Age Structured Harvesting
We know that this is not reasonable
How can we build harvesting into an age-specific
model?
Not easily..certainly not in this course
40
That said when you start to harvest from a
population (inevitably during its growth phase),
the population is maintained in a constant state
of growth
Population (growing under intra-specific
competition) Harvest (MSY) Population (growing
without intra-specific competition)
As a consequence, using Fixed R Models may not be
unreasonable.
41
So
Start off with the basic life table, calculate p
and m, and project the population into the future
(e.g.) 100 time units. Plot total population
size against time
Calculate Reproductive Value
42
Set up a parallel table with harvest information
i.e. the number of individuals of each age
class you will harvest each year Use a fixed
yield model i.e. harvest a fixed number (h) of
individuals of each age class at each time
interval and make each value in the harvest
column for a particular age class equal to the h
value for that age class at t0, all h values
0 harvest 1 0 year old from t1 keep a running
total
43
(No Transcript)
44
Optimising harvest in an age-structured model can
be time-consuming! Better yields were (in any
case) obtained from harvesting under a constant
effort scenario in our previous models and there
is no reason to suppose that this will be
different here! It is also quicker!!!
Start off as before with a population table and a
parallel harvest table. Set the harvest table up
with an Effort row, an Efficiency row and an EE
row (Effort x Efficiency). All values in the
Efficiency row should equal 1 (i.e. the
harvesting method is 100 efficient). In the
first instance make all values of Effort 0,
except E0 (0.00000001). That means all values of
EE will equal 0, except EE0, which will equal
0.00000001
45
You now need to make the harvest of a particular
age class at a particular time equal to EE
multiplied by the number of individuals of that
age class at that time. Having done that, you
will need to subtract this number from the number
of individuals of that age at that time from the
population table. This will inevitably result in
Circular Argument errors in MSExcel.which means
that you need to build the formulae projecting
populations into the future into the harvest
table too! Ensure that harvest at t0 0
With such a low level of Effort, you should only
start to harvest any whole organisms at time 32
46
Adjust Effort of each age class, adjust time of
first harvest in order to maximize total harvest.
REMEMBER Population must not crash!
PLAY