This PPT deals with Mortality concepts, which are widely used in fish stock assessment studies.

1. KANTHARAJAN G
ICAR-CIFE, MUMBAI
Exponential Decay Model
and
Total Mortality
- KANTHARAJAN G

2. Mortality in Fish Stock Assessment
 The life history of a fish is a series of time intervals through which an individual
survives several risks.
 Risks rarely occur sequentially, but instead occur simultaneously And a fish can
only die once (and once it’s dead, it’s dead!)
 Need to understand the dynamics of mortality

3. Mortality
Total
Mortality
(Z = F + M)
Predation
Disease
Spawning
stress
Senescence
Stranding
Abiotic
(Temp,
Pollution)
Fishing
Starvation
Johan Hjort described extreme mortality rates (>99%) of
marine fish larvae within days of hatching - hydrodynamic
starvation
Ichthyophonus hoferi – Phocomycetes fungi which gives
disease induced mortality in North sea herring.
In 1989 – 1, 300, 000 t  1991, outbreak  in 1994, 760,000
t (Patterson, 1996).
Water temperature - effect on spawning and survival of larvae
and juveniles (IPCC report, 2001).
Wild Atlantic salmon (Salmo salar) and marine Mammals

4. Natural Mortality (M)
• Interested in knowing the effect of fishing on fish stocks - clear distinction between
mortalities caused by fishing and those caused by other factors needed.
• The mortality created by all other causes than fishing, e.g., predation including
cannibalism, diseases, spawning stress, starvation, and old age.
• Predation and starvation mortalities - linked to the ambient ecosystem
• Same species - different natural mortality rates in different areas - density of predators
and competitors - influenced by fishing activities
• K - linked to the longevity of the fish and longevity is related to mortality
• High K-value have a high M-value
• Low K-value have a low natural mortality
• A slow growing species (low K) simply cannot bear high natural mortality - if it did it
would soon become extinct.
• Natural mortality - Asymptotic length and weight - large fish have fewer predators than
small fish.

5. Types of Natural Mortality
• Physiological mortality – Caused solely by diseases, old age or both leading to death
without he intervention of predators. (K , Purely physiological mortality)
• Selective mortality – caused by disease, old age or both in a certain no of fish being
characterized by a lack of performance which makes them accessible to predators.
(Middle aged group)
• Chance mortality – Mortality unrelated to physiological mechanisms and proportional
only to a number of possible encounter with potential predator. (Small fish, Place in a
food chain)

6. Fishing Mortality (F)
Mortality due to fishing; death or removal of fish from a population due to fishing
F value ranges - from 0 for no fishing
- to very high values 1.5 or 2 (1.5 or 2 times as many fish have been caught as were present at the beginning of
the fishing season)
F = qf
q = catchability coefficient
- The proportion of a fish population caught by one unit of fishing effort.
- q = (C/E) (1/N)
- q depends on,
The distribution of fishing effort
Effectiveness of finding fish of the vessel
Selectivity of the gear
Fishing Effort (f)
- The amount of fishing gear of a specific type used on the fishing grounds over a given unit of time
(e.g). hours trawled per day, number of hooks set per day or number of hauls of a beach seine per day.
- When two or more kinds of gear are used, they must be adjusted to some standard type.
- Increasing skills of skippers and fishing crews also contribute to the effectiveness of fishing effort and capacity

7. Mortality concepts

8. Exponential Decay Model
• It is a corer-stone of the theory of exploited fish stocks, because in exploited fish stock numbers
surviving end to decrease exponentially with time and age according to Z.
• The higher the value of Z the faster the decrease in numbers and the lower the maximum age.
• It is usually easier to understand the concept of mortality and survival if the number of survivors
at a certain moment is expressed as a percentage of the original number.
• Table gives the percentages of survivors after one and two years respectively of two populations
subject to two different total mortality rates, Z = 0.5 and Z = 2.0.
Total mortality rate Z
percentage of survivors *
after 1 year
100*N(Tr+1)/N(Tr)
after 2 years
100*N(Tr+2)/N(Tr)
0.5 61% 37%
2.0 14% 2%
*) Percentage of survivors = 100*exp(-Z*(t-Tr)) and t-Tr = 1 and 2 respectively

10. N(t) – No. of survivors from a cohort attaining age t
N(Tr) – No. of recruits to the fishery
The rate of change in numbers is written:
D N(t)/D t
where D t is the length of the time period
The rate of change in numbers per year, D N(t)/D t depends on the number of survivors, N.
N more – more will die.
D N(t)/D t = -Z N(t)
If Z is constant throughout the life,
N(t) = N(Tr)*exp[-Z*(t-Tr)]  Exponential decay model

11. Exponential decay of a cohort with recruitment N(Tr) = 100000 and total (constant) mortality Z
= 1.5 per year.
Equation D N/D t = -Z*N is fulfilled for various ages of the cohort (t)
age of cohort
t years
number of survivors
N(Tr)*exp(-Z*(t-Tr))
change in numbers
during on day, D N
Z
Tr+0.0+D t 99590 -410 1.5
Tr+0.6+D t 40490 -167 1.5
Tr+1.5+D t 10497 -43 1.5
Tr+3.5+D t 522.60 -2.15 1.5
Tr 100000

12. Exponential decay curve with N(Tr) = 100,000 recruits and Z = 1.5 Z remains constant
for all ages, t

13. REFERENCES
• Patterson K R., (1996). Modelling the impact of disease – induced mortality in an exploited population: The
outbreak of the fungal parasite Ichthyophonus hoferi in the North Sea herring (Clupea herengus). Canadian
Journal of Fisheries and Aquatic Sciences, vol. 53 pp: 2870 – 2874.
• Daniel pauly. (1980). On the interrelationships between natural mortality, growth parameters and mean
environmental temperature in 175 fish stocks, J. Cons. Int. Explor. Mer, 39(2): 175 – 192.
• Per Sparre., Erik Ursin., Venema C. (1989). Introduction to tropical fish stock assessment Part 1 – Manual
(FAO Fisheries Technical Paper 306/1).

14. THANK YOU