The possibility to detect time trends in fish stocks through
catch-rate data and to evaluate the effectiveness of fisheries management on
that basis depends both on the strength of the time trend and the variance
around it (Peterman, 1990; Pet-Soede *et al*. 1999; Densen, 2001; Zwieten,
Njaya and Weil, 2003). Ultimately, the capacity to detect a trend is determined
by the statistical power of the information examined, which in turn depends
entirely on the variance of the data, given the number of observations and
statistical decision levels. Aggregation of independent observations belonging
to the same distribution lowers the number of observations but at the same time
reduces the variation around a possible trend as well. The time series of
estimated monthly catch-rates from CEDRS surveys of Chilwa by major stratum
represent the lowest level of data aggregation for this lake that in Malawi is
used in reports on the status of the fishery. The capacity of the Malawian
fisheries authorities to perceive trends and relate these to changes in the
fishery is given with these time series of catch and effort data (Zwieten *et
al.*, 2003).

**2.1 Structure of the paper**

After a description of data collected and methods of analysis we will:

(1) Examine trends and variability (between years, seasonal) in the catch-rates of Lake Chilwa;

(2) Examine changes in water levels and relate these to changes in catch-rates;

(3) Examine trends in fishing effort and relate them to trends in catch-rates taking into account the effect on catch-rates due to changes in water levels;

Data used to examine trends and variability are monthly average catch-rates by species (or species groups) and gear, fishing effort by gear and daily water levels from 1976 to 1998. The analysis will lead to conclusions on the possibility to detect trends and relate these to changes - natural or fishing effort - observed. Thereafter we will shortly address the present fisheries management set up of Lake Chilwa, and discuss whether the present CEDRS and the type of conclusions that can be drawn from it will address the information needs. We will

(4) Discuss present management strategies before, during and after recessions;

(5) Discuss the required information in relation to management of catch and fishing effort; and finally

(6) Ascertain whether the present CEDRS and monitoring of water levels fulfils the requirements related to the management of the fisheries resources in the lake

**2.2 Research strategy**

A short explanation on the research strategy contained in points 1-3 is needed:

*(1) Examine trends and variability in the catch-rates and
fishing effort of Lake Chilwa;*

Catch-rate - i.e. the catch per time unit and per unit of fishing effort (C/f) - is an important indicator both for the average income of fisherman and the abundance of stocks. As an indicator of abundance a constant efficiency in the fishing methods over time and constant average fish behavior is assumed. Though the assumption of constant efficiency is problematic, the idea is that if a number of different fishing methods employed in more or less the same way over the period examined give similar trend information, the signal is clear. Trend here is loosely understood as a long-term change in the mean levels of the catch-rates (Chatfield, 1996) and the basic question is whether the catch-rate has gone up, remained stable or has gone down over the period over which there are data. For that reason it is sufficient to define trend as a linear regression over time. Obviously it is the downward trend that is most interesting, as this is the main management concern: how do catch-rates develop with increasing fishing effort given the natural variation of the lake system.

The next question is whether such a trend can be perceived
within a time window that is useful in a management context. In other words: how
variable are the catch-rates around the trend, and in what way does this
variation obscure the general trend so that it may not be detectable within time
windows of decision making and evaluation given a management framework.
Variability can be attributed to predictable variation, e.g. seasonality, and
temporally unpredictable variation, which we will call basic uncertainty
(Zwieten *et al*, 2002). Quantifying these attributions will give a first
indication of the possibility to perceive a trend.

The development of catch-rates under increasing fishing effort in a system like Chilwa is unlikely to be linear, and fluctuations as a result of strong environmental signals may take place. These fluctuations will be seen as reversals in the direction of long-term trends, and will show as non-random residuals around a linear trend that we will call long-term persistence. The effect of “favorable” or “unfavorable” environmental conditions caused by variation in average water levels could induce persistence in stock biomass of longer lived species. A first approach to examine whether such reversals in trends take place, and obtain an indication how a linear description of a trend diverts from more complex descriptions, is by fitting more complex regression models to the data. We follow the method as outlined by Fiorentini, Caddy and Leiva (1997). They examined a large number of time series catches of different species in the Mediterranean Sea by fitting a simple polynomial regression model to the data. Based on the shape of the resulting fit they decided whether a trend in catches could be described as increasing, stable or declining - including dome shaped fits - with varying speed. Periods of natural increase or decrease in abundance or availability of the resource, followed by a reversal will result in a dome shaped trend, which could be a result either from over-fishing or a change in environment. The peak or trough gives an indication of the period in which a reversal of catch-rates took place, and can be used as a starting point for further analysis of possible events leading to such reversals. Thus, the extra information obtained compared to a linear description of trend is an indication at what stage of development a stock is - increasing, decreasing, collapsed or recovering -, the speed with which this takes place, and, most importantly, the timing of possible reversals.

The relationship of trend and variability can be understood as
a signal-to-noise ratio. An analysis of this ratio gives an indication of the
time frame needed for trends to be detected, which is in fact an analysis of
statistical power. To answer the question on trend perception in statistical
terms, we examine the change in the slope of a linear trend over time in
relation to the variation around the slope. We can investigate how this
*trend-to-noise *ratio changes over time by stepwise increasing the number
of data in the analysis. We take two approaches:

(1) Every month more data are added, and this will affect the

trend-to-noiseratio. We are interested in changes in strength (slope) of trends and timing of reversals in the direction of a trend: when is a negative/positive trend first seen in a long-term perspective?(2) Questions of effectiveness of regulative management measures often need to be answered in a short time frame. Whether or not a regulation, or measure, intended to change the usage of a natural resource is working, should usually be answered within a framework of around 3-5 years. By investigating trend-to-noise ratio’s over five year steps, we will obtain a feeling for the strength of short-term trends and the timeframe over which reversals of trends can be seen.

Finally, we will examine the effect of multi-annual environmental variation, on the possibility to perceive trends caused by the fishery, or, in other words: which driver, fishing or environment has the strongest effect on the variability observed.

*(2) Examine changes in water levels and relate these to
changes in catch-rates*

Sorting out empirically correlations of time series of processes that have only one realization, such as the processes underlying the relation between catch-rates, fishing and water level in lake Chilwa, is fraught with difficulties (Bakun, 1996). Time series of continuous processes, be it catch-rates or water levels, contain considerable auto-correlation or persistence. Persistence is simply the correlation of the present observation of a parameter with previous observations in time, i.e. yesterday’s water level or fish-biomass will to a large extent determine today’s level or biomass. This has as consequence that when two auto-correlated time series are cross-correlated, significant but uninformative correlations will always be found. To answer the question whether a fish population, as indexed by catch-rates, collapses due to fishing effort or due to natural variation - where water level is used as a proxy environmental indicator - is typically a situation where auto-correlated time series are involved. One way to address this problem is to correlate the time-series of water level and catch-rates after removing long term and seasonal trends. This will remove most of the auto-correlation, while both series will then be reduced to series revealing possible “anomalies” -i.e. variations deviating from trend and seasonality - that can be subsequently correlated with each other. This could result in statistically significant, and possibly meaningful, correlations of fluctuations in water level explaining fluctuations in catch-rates. This analysis leads to information on:

The amount of variation in the annual catch-rate series that can be explained by “anomalous” (i.e. non-average) changes in water level, and the possibility to perceive such a signal in the catch-rate data.

The lag in time (years) over which changes in water level are reflected in changes in catch-rates of fish and hence the regenerative speed of fish production.

Water level is considered an environmental driver, which
through a complex of natural processes regulates fish stocks (Junk, 1989;
Karenge and Kolding, 1995; Kolding, 1994; Leveque and Quensiere, 1988; Furse
*et al*., 1979). This is of course obvious for the years of complete
recession - where there is no water there is no fish. But the question is
whether changes in water levels have a predictive value for the periods when the
lake is filled, and how well observed fluctuations in catch-rates can be
explained by such changes.

*(3) Examine trends in fishing effort and relate them to
trends in catch-rates taking into account the effect of changes in water
levels*

Further problems arise when attempting to assess multiple causes, in this case distinguishing between the simultaneous effect on catch-rates both of changes in fishing effort and of changes in water levels. In a multiple-gear fishery it is generally not possible to give a single definition of fishing effort, and it is difficult to standardize the fishing effort of different gears. Furthermore the different gears used often target the same stocks of species either in the same or at different stages of their life cycles, leading to so-called technical-interactions, i.e. the outcome of one fishery will affect the outcome of the other. Both problems in defining fishing effort and interactions are important reasons why standard stock-assessments could fail in these situations.

The problem of technical interactions adds another level of
difficulty in the statistical approach to explain the relative effects of
changing environment and fishing effort. However, if it appears that effort
development is mainly due to simple addition of numbers of gears and people -
more of the same - then selectivity and technical interactions can be assumed
“constant”. This means that a multiple regression of fishing effort by
gear type and water levels on catch-rates by gear - using the time lags found in
the correlations of the de-trended time series of water levels versus
catch-rates - could make sense. But selectivity and technical interactions
cannot not be considered “constant” if shifts in fishing patterns have
taken place - due to changes in technology or changes in spatial allocation of
effort - as a reaction of fishermen to changes in stocks. A multiple regression
of fishing effort by gear type on catch-rates by gear will be impossible, or at
least difficult, to interpret. We will see that the condition of constant
selectivity and technical interaction is generally met in the case of Chilwa
(but not in Malombe: see Zwieten *et al*., 2003). Therefore, before
analysing the combined effect of fishing effort and water levels an analysis of
changes in fishing effort is needed:

a. Effort defined as the number of active fisherman and boats disregarding types of fisheries will give an indication of the demographic changes in fishing effort.

b. Effort analysed by gear will indicate possible shifts in fishing patterns. Such shifts can then be examined on changes in available biomass (indicated by changing catch-rates).

Another difficulty in assessing multiple causes is when trends in the explanatory variables (i.e. effort and water level) are confounded. Confounding will take place if no reversals in trends have taken place in both of two explanatory variables. As an example we discuss three possible situations of trends in the annual data:

a.

Both water levels and effort levels are increasing.In this case it cannot be decided directly if a possible downward trend in catch-rates can be attributed to either variable. An analysis where both variables follow the same trend stands a high possibility that either one or both explanatory variables will not be significant. However, a correlation analysis of deviations obtained by de-trending water levels and de-trending catch-rates may indicate a positive correlation between water level and catch-rates, possibly with a certain time lag. From this it can be inferred that fluctuations (“rates of change”) in water levels have a positive effect on changes in catch-rates (“growth rates”). In principle the same could be done with de-trended effort levels, though this requires a high reliability in total effort data. If this relation is negative, it could be inferred that the decline in catch-rates could be attributed to the increase in effort, but delayed by increasing water levels.

b.

Water levels are decreasing while fishing effort is increasing and catch-rates are decreasing.In this case the time series are entirely confounded and it will be difficult to distinguish cause and effect. Correlation of de-trended series will give an indication of effects but again no decision on size of each effect (proportion of total variation explained) can be reached.c.

Water levels are fluctuating while fishing effort is increasingHere downward trend in catch-rates will be attributed to fishing effort, and it can be decided how much of the variation around the trend can be attributed to a changing environment.

From this discussion it will be clear that no decision on effects of effort and environment can be reached if there is no contrast in at least one of these two parameters over time, while the other parameter remains either stable or is continuously changing in the same direction. For example, if fishing effort is continuously increasing only a significant increase and subsequent decrease in water levels or vice-versa can provide for the necessary contrast and the effects of both parameters for changes in stocks can be determined.