Depending on availability of data and trend of such plot with time you may some modified exponential, logistic or other such types of model to estimate specific growth/ mortality rate etc.

A recent ref:

Powers, J. E. Age-specific natural mortality rates in stock assessments: size-based vs. density-dependent. – ICES Journal of Marine Science,

doi.10.1093/icesjms/fst226

You will find some alternatives in:

Froese & Binholan 2000

Sparre & Venema 1997

Cadima 2003

Pauly 1983

This document (Brodziak et al. 2011) also contains information regarding age/size-dependent natural mortality in stock assessment with examples:

http://spo.nwr.noaa.gov/tm/119.pdf

May be you can find something in this article

Alba,

Take a look at my review of the available methods:  Kenchington, T.J. 2013. Natural mortality estimators for information-limited fisheries. Fish and Fisheries  DOI: 10.1111/faf.1027.

The Government of Canada holds the copyright for that and nobody will make up their minds whether or not I am free to upload it to ResearchGate but I can send a copy to (almost) anyone who wants one. (I had a request from a scientist in Iran, which fell foul of the crazy Canadian export restrictions.)

The short answer is that you cannot get a reliable, accurate estimate of the natural mortality rate without gathering a lot of data. None of the methods which claim to offer estimates without years of labour are really adequate and some (including Chen and Watanabe's) can return absurd results. If you have a good estimate of K, either Pauly's equations or Jensen's M=1.5K can work well with many fish but fail badly with those species that have atypical relationships between growth and survival. If you have a good estimate of maximum age in the absence of exploitation, Hoenig's M=4.3/Tmax can work well but it is seriously erroneous if the maximum age is drawn from an effective sample size (meaning the size of a random sample that would have yielded the same maximum age) of more than a few hundred individuals or if the species has pronounced senescence -- as some do. In short, before even selecting a method, you need to know quite a lot about the biology of the species.

And, at best, your estimate cannot be trusted to more than one-significant-figure precision. Order-of-magnitude errors are probably more typical of these methods.

There is some free software you can download that does a good job.

http://r4d.dfid.gov.uk/Output/122112/

One year of data makes it hard to find cohorts through time but you can get a rough idea.

The only kind of mortality rate that length-frequency analysis can provide is the total mortality rate, Z. Unless you have extensive length data from a population that is experiencing minimal fishing mortality (which is conceivably possible but very unusual), Z will be much greater than M, the natural mortality rate.

Of course, an estimate of Z would be useful to Alba if she has a way of independently estimating fishing mortality.

dear Alba,

in the STECF Mediterranean expert group we have often to deal with M estimation for stock assessment. In the case of  most of the exploited stocks in this area, due to their early age of capture, the assumption of a constant and low M value may produce misleading results. in consequence we are obliged to use some vector of M declining with age. This assumption is reasonable considering younger age classes more exposed to predation and food shortage likely due to a major competition for food. In the meeting quoted below, special attention was paid on two approaches that allows estimating an M at age vector   

Scientific, Technical and Economic Committee for Fisheries (STECF)

Report of the Workshop on Mediterranean Stock Assessment Standardization SGMED workshop 09-01 (formerly labeled as SG-ECA/RST/MED 09-01) 2-6 March 2009, Murcia, Spain

The two candidate methods for estimating M  recommended, providing  there  is  a reasonable degree of confidence in growth parameter estimates are the following:

 Gislason et al. (Gislason et al., 2008a; Gislason et al., 2008b):

 LnM=a+bLnL+cLnL¥ +dLnK

 Where a,b,c and d are parameters and L¥ and K are the vonBertalanffy’s growth equation parameters

 and

 ProdBiom  (Abella  et  al.,  1997)  based  on  considerations  about  production  and  losses  of  biomass due to natural mortality which uses the Caddy (1991) equation:

 Mt=a+b/t

 where Ma is the asymptotic M and β is the curvature parameter.

In the description of both methods there are details on how to estimate the parameters

there are in alternative many other possible empirical equations as the

Beverton &Holt  invariant     M =constant x K (costant =1.6 or 1.8 for fish);

The Alagaraya's method:   M = -Ln(0.01/t max );

The Charnov method:       ln(M) = 0.5 + 0.95 * ln(K)

Several approaches were tested during the Mediterranean EWG meeting:

Chen & Watanabe, Hoenig, Richter & Efanov, Alagaraja, Gunderson & Dygert, Jensen, Hoenig variant of Hewitt, Taylor, Gulland, Pettersen & Wroblewsky, Csirke & Caddy, Lorenzen, Paloheimo, Silliman, Caddy, Pauly, Roff, Beyer, Gislason et al, Abella et al, Munro, Anderson & Ursin, Myerrs & Doyle

References

Abella  A.,  Caddy  J.F.,  Serena  F.  (1997)  Declining  natural  mortality  with  age  and  fisheries  on  juveniles:  a Mediterranean demersal fishery yield paradigm illustrated for Merluccius  merluccius. Aquatic Living Resources 10: 257–269.

Caddy, J.F. (1991). Death rates and time intervals: Is there an alternative to the constant natural mortality axiom? Rev. Fish Bio/. Fisheries, 1: 109-13 8.

Gislason,  H.,  Pope,  J.  G.,  Rice,  J.  C.,  and  Daan,  N.  2008.  Coexistence  in  North  Sea  fish  communities: implications for growth and natural mortality. ICES Journal of Marine Science, 65: 514–530.

Gislason, H., Daan, N., Rice, J. C., and Pope, J. G. 2008. Does natural mortality depend on individual size?ICES CM 2008/F:16 (mimeo.)

Gislason, H., Daan, N., Rice, J. C., and Pope, J. G.. Size, growth, temperature and the natural mortality of marine fish. Fish and Fisheries. 

I hope my comments will be useful for your work. Please do not essitate to contact me whenever you need further info on any of the mentioned approaches

Alvaro J. Abella

A number of methods have to be used for that . Cushing and Pauly's method can be tried and also use the Rikhter and Efanov'e method provided you have the age at first maturoty data .