Yucatan state.—A great deal of variation was found in CAL upsurge probabilities between periods, except in transitions 0→0 and 0→1 of periods 1 and 2. In the first period, transition 1→1 (0.57) was highest, indicating years with contiguous upsurges. The second period was characterized by a reduction in upsurge frequency of 1→1 (0.4). In the third period, this transition had its biggest reduction (0.25), indicating an increase in “recession years,” and the transition 0→0 was increased to 0.5 to 0.71 . During periods 4 and 5, the values of the transition matrix were very similar (0→0: 0–0.2, 0→1: 0.8–1, 1→0: 0.67–0.72, and 1→1: 0.28–0.33). Thus, an upsurge appeared in one year, and in the next, it was reduced. The last period was very similar to the second period, where the recession years were increasing 0→0 (0.58) and 1→0 (0.66) and remained high. From 1948 to 2018, there were 33 upsurges at an average of 2.15 per period and with a range of 4 to 7. Periods 1 and 5 had a major upsurge, and periods 3 and 6 had a minor locust presence.

In 4 of 5 cases, the correlation between the matrix and probability n₂ in the next period was negative, and the P-value was not statistically significant (P > 0.05). In the period 1972–1983, the correlation was high, positive, and statistically significant (P ≤ 0.01).

Campeche State.—In the matrix, the three periods of CAL upsurge in Campeche State were different. In period 1, which was the shortest, 0→1 (1) and 1→1 (0.72) stood out. Periods 2 and 3 showed identical values–1→0 (1) and 1→1 (0)–and had similar 0→0 (0.57–0.75) and 0→1 values (0.43–0.25).

The number of upsurges per year decreased; the first period had the highest number of upsurges (7), followed by periods 2 (4) and 3 (3).

The Pearson correlation was different in the two periods. In 1986–1994, it was negative, and in 1995–2006, there was a positive association. However, the differences were not statistically significant (P > 0.05).

Quintana Roo State.—In the 24 years of data (1995–2018), only one year had a CAL upsurge: 2006. Therefore, the probability for 1→0 and 1→1, equal to 1 and n₂ (Table 5), could not be obtained. According to data from the Quintana Roo Plant Health locust control from Yucatan migrated and caused damage to corn and bean crops and cultivated grasslands and caused defoliation in a nature reserve and on urban trees from August–September. In 2006, locust control operations were undertaken in 1,381 ha.

These swarms were able to oviposit in Quintana Roo and complete the second generation. They also returned to Yucatan at the end of 2006 as swarms. In that generation, 173 ha required control operations. In subsequent years, the locust population was present at a low density in the solitarious phase.

Fig. 1 shows a tendency for upsurges to peak every four years (2006, 2010, 2014, and 2018), except for an additional two peaks in 2004 and 2009, from 2010 to 2018, this tendency was clearer than from 2003 to 2009.Therefore and consequently it was assigned values from years 1 to 4, starting with the maximum peak, e.g: year 2006 (year value 1), 2007 (2), 2008 (3), 2009 (4), 2010 (1), 2011 (2) so on (Table 6); from 1952–1955 and 1977–1989, the tendency of the maximum peaks was less clear, and the treated area was larger than in recent years.

This information was used to identify the upsurge years (Table 6). Then, the probability of an upsurge in the past and current periods was determined (Table 7).

For the period 2003–2018 in Yucatan, the highest probability of upsurge was in year 4 (P: 1). There was no probability of an upsurge (P: 0) in year 1 and a minimal probability (P: 0.25) in years 2 and 3. These results were different from the data from the past (1952–1955 and 1977–1988), where years 1 and 2 were similar (P: 0.5) and years 3 and 4 were similar (P: 0.75). For Campeche, the P(1) was 1 in year 1, and years 2–4 had no values. In Quintana Roo, there was only a remote probability of an upsurge, but the probability increased if Yucatan had an upsurge so intense (similar to 2006) that it resulted in locust invasion.

Validation.—According to SENASICA (Table 8), the area treated for locust control was 2,224 ha in 2019 and 3,714 ha in 2020. This information was used to validate the model.

In Yucatan state starting in 2018, which had a value of 1, the transition 1→0 (one step: 0.66, n₂:0.6) had the highest value. Therefore, the following year, 2019, an upsurge value of 0 would be expected and starting in 2019 as upsurge value 0, the transition (0→0: 0.58, 0.61) was the highest value, so it would also be expected an upsurge value 0 in 2020, both results obtained of the probabilistic model correspond to the results of the low treated area (Table 8). In Campeche in 2018, value = 0, the transition 0→0 (0.75; 0.81) had the highest value, a year with value 0 was expected, but it was not fulfilled, in 2019 according to the treated area the value was 1. The value 1→0 (1, 0.75) was highest for 2020 and it was the upsurge value, through the treated surface (Table 8). In Quintana Roo, despite good results in the probability of 0→0 for 2019 and 2020, no application was made in transition n₂ with an origin of 1 (1→1 or 1→0) because it is an invasion area and not a locust breeding zone.

The comparison of the probability of an upsurge P(1), with previous information 2003–2018, with values 2019–2020 indicate that in Yucatan it was according to the model in 2019 and very close to 2020 (P(1)=0.25, value=0), in Campeche and Quintana Roo as predicted.

Yucatan State.—The CAL upsurge from 1948 to 2018 was a sign that the frequency of occurrence had changed, as there were no equal periods. The transition 1→1 had the highest value in the first period (1948–1959); therefore, it was called a “plague period” in which “favorable breeding conditions are present and control operations fail… two or more regions are affected simultaneously” (Symmons and Cressman 2001). Upsurge had a higher value in the past than in recent years because there was no organization in charge of a permanent locust control program. Control measures were more recently undertaken over gregarious populations, mainly swarms (Marquez 1963). From 1941–1942, CAL swarms invaded Mexico and Central America,originating from some area of this same region. In 1947, the International Committee for Locust Control (CICLA) was formed; in 1955, the name was changed to OIRSA to include locust surveillance (Marquez 1963, Trujillo 1975). In 1948, the Mexican General Direction of Agricultural Protection was created, an institution that consolidated technical cooperation with CICLA. The first period (1948–1959) in Mexico was characterized by the creation of national and international institutions for locust management (Ortíz and Zuleta 2020).

In the second period (1960–1971), the transition 1→1 decreased, perhaps as an effect of more organized locust control and unfavorable weather conditions, and the number of upsurges per period was reduced from 7 to 5. In period 3, 1972–1983, the transition 0→0 was the highest (0.71). Consequently, because of the fewer number of upsurges (4), the locust was declared to be in its recession period, i.e., a period of several years when the locust population is low (Symmons and Cressman 2001).

In periods 4 (1984–1995) and 5 (1996–2007), the values of the transition matrix were very similar, the transition 0→1 and 1→0 were high, that is the upsurges occurred approximately every 2 years. When starting with a solitarious population, CAL needs three generations to reach the gregarious phase (Barrientos et al. 1992). The CAL presents two generations per year (Astacio 1966, Trujillo 1975); therefore, a third generation is achieved within two years, which concurs with the calculations of Marquez (1963), who indicated that “the locust does not form suddenly; it takes two or more years to develop.” In periods 4 and 5, transition 1→1 was reduced because locust management was strengthened with the creation of state-run locust control programs. For example, in 1988, the Ministry of Agriculture and Water Resources of Mexico granted greater autonomy to phytosanitary programs in each state, including the locust control program. The Federal Plant Health Law (Ley Federal de Sanidad Vegetal 1994) created plant health committees to develop multiple crop protection programs with government funding. These programs encompassed the locust control campaign. In Yucatan, such a committee was created in 1997 and is currently responsible for the permanent monitoring and control of this pest.

Although Yucatan periods 1 and 5 had similar upsurge years (7), the severity differed. The overall area treated with insecticides in period 1 (1952–1955) was 56,000 ha (Márquez 1963), while it was 26,363 ha in period 5 (2003–2006), which was 47% less than in the first period.

Only 1 out of 5 correlations between the probability n₂ and the matrix was positive and significant. This may be because the outcome of the Markov chain depends on the outcome of previous events, meaning that the next state of the system depends on the present state, and locust outbreaks are erratic events (Symmons 1992). Showler (2002) outlined broad strategic approaches to locust outbreaks based on intervention timing (prevention or reaction) and tactics (survey, control, economic effects, insecure areas, and contingency planning). Management, weather, climate change [World Meteorological Organization-Food and Agriculture Organization (WMO-FAO) 2016], and political decisions differ in different periods, making it difficult to obtain reliable probability.

Markov models have limitations, are problematic with short time intervals, cannot be derived rigorously from deterministic, dynamic models, and rarely provide the range of time for which the model is appropriate (DelSole 2000). However, they permit knowledge of the outbreak population in each period without the necessity of searching for causation through correlative procedures (Kemp 1987). Weather conditions that could have an influence on outbreaks include the amount of rain in the year (Steinbauer 2011), temperature, relative humidity (Al-Ajlan 2007), wind for migration (WMO-FAO 2016), ENSO (Contreras and Galindo 2014), and precipitation in previous years (Skinner and Child 2000, Chiconela et al. 2003).

In some species of Orthoptera, there has been a decrease in outbreaks; for example, outbreaks of rangeland grasshoppers in Wyoming are highly erratic events, with instances of infestations persisting for multiple years being quite low, so there is little basis for prorating the benefits of control beyond the year of treatment (Zimmerman et al. 2004).

Campeche state.—Historically, the Campeche state has been invaded by swarms from Yucatan (Márquez 1963). The entry and migration routes are found in the north, but these swarms can quickly move to the south of the state (Chi 2000). This movement is made by the second generation and at the beginning of the year (Cullen et al. 2017). In the second period (1995–2006), there was a reduction in the number of upsurges per year, probably because the locust campaign of Yucatan Plant Health established control operations in 1997, reducing the possibility of migration to Campeche. Before this period, the largest number of upsurges occurred, with the transition 1→1 indicating several continuous years with an upsurge or a reduced recession period (0→0). In the third period, there was an increase in the recession period 0→0 because the upsurge was dependent on outbreak and migration from Yucatan every 4 years (2006, 2010, and 2014). The probability of upsurge in 2019 was expected because of the migration of swarms from Yucatan in 2018.

With the information obtained on the control and migration of swarms, it was possible to construct the migration route of CAL to Campeche. At the beginning of the year, Campeche is an invasion zone (Fig. 2) for swarms originating from places in Yucatan, where it is difficult to undertake survey and control operations. Therefore, it is important to carry out locust management tasks in Yucatan state with new methods to reduce migration to Campeche. Despite the large number of swarms formed in Yucatan in the upsurge year, the damage was minimal for two reasons: a) in the maximum period of migration that occurs at the end-beginning of the year, there is less cultivated area, as most of the agriculture occurs in June–September when there is a greater amount of precipitation to help rainfed crops, and b) the size of the swarms, according to the classification of Cressman (2001), corresponds to very small swarms (<1 km²) due to preventive management of first stage nymphs.

Quintana Roo State.—Vegetation is very important for locust development (Sword et al. 2010). Its distribution (Despland et al. 2000), coverage, and status (green or dry) influence locust gregarization (Cisse et al. 2013). Models could be enhanced by using associations between plant communities and insects to predict risk areas (Van Der Werf et al. 2005). The CAL is highly associated with the grass Panicum maximum (Poot-Pech et al. 2018); however, in Quintana Roo, the vegetation is 90% tropical forest, 3.3% agriculture, 3.2% grasses, and 3.5% other uses (INEGI 2011). According to survey information from the locust campaign, P. maximum is not the dominant grass in Quintana Roo.

In Yucatan in 1952–1955 and 1977–1988, there were 10 upsurges and 6 recession years, while in 2003–2018, there were 6 upsurges and 10 recession years. This may be because the structure of the locust program was modernized during the latter period, with greater autonomy and economic resources for developing the program and prevention strategies (Rodríguez 2000). The locust program in Mexico receives technical support from OIRSA (Ortíz and Zuleta 2020), and in general, biological and ecological knowledge about locusts has increased, which has helped create better management practices for this pest (Lecoq 2021).

Periods of 4 years (Table 7) were formed, and a linear regression of areas treated for CAL was obtained (Figs 3, 4), finding a positive relationship. Generally, the first year had the least amount of treated area, and the fourth year had the most amount of treated area. In the fourth year, there was a high migration of swarms to Campeche (Fig. 2), so the gregarious area remained at low infestation for three generations. Two years later, the population became high once again (Márquez 1963, Barrientos et al. 1992). However, this pattern occurs when the swarms are controlled along their migration route; if the swarms are not controlled, then year one would have a high infestation when the swarms oviposit and return in the next generation, flying in the opposite direction (Cullen et al. 2017) and repeating the pattern presented in previous periods (1952–1955 and 1977–1988; Tables 6, 7) with at least two years of high infestation. This has been seen recently, such as in the upsurge in 2019 and 2020 of the desert locust in Pakistan (Sultana et al. 2021) and Africa (Peng et al. 2020, Salih et al. 2020).

Fig. 3. 

Linear regression of the treated area in periods of 4 years from 2003–2018 in Yucatán (SENASICA information).

Fig. 4. 

Linear regression of the treated area in periods of 4 years from 1952–1955 (Marquez 1963) and 1997–1988 (Pereyra 1991) in Yucatán.

There were intermediate years–year 2 in 2004 and year 3 in 2009–which were likely the result of suitable weather conditions such as precipitation in the breeding zone. A marked increase in locust numbers on a local scale due to concentration, multiplication, and gregarization can lead to the formation of hopper bands and swarms (Roffey and Popov 1968).

In 1952–1955, there was a “plague” of CAL, requiring 4 years of intense control; gradually, the size of the controlled area was reduced. The opposite situation occurred in 1977–1980 and 2007–2010, with an intermediate rebound in 1979. This situation lasted until 1981, and the treated surface area was reduced until 1984. There was another plague from 1985–1989, with 1986 having the largest controlled area.

From 1952–1955, as shown in Fig. 4, there was a negative regression, indicating a plague of CAL (Symmons and Cressman 2001). Efforts were made to reduce the population each year, but control was aimed at the gregarious phase and mostly swarms (Márquez 1963). International cooperation among countries was still in development (Yam and Zuleta 2020). In 1977–1980, there was a positive regression; an increase in the population occurred in 1979–1980, but in 1981–1984, there was again a negative regression, with a rebound in 1981. Finally, in 1985–1989, the regression value was low because in 1986, there was a higher peak; however, in the period 1986–1987, there was a plague.

In his book, An Account of the Things of Yucatán, written in 1566, Diego de Landa (2003), bishop of Yucatan, wrote about the consequences of locusts and noted the 4-year recession period, saying, “the locust developed for 5 years, which left no green thing, it was so hungry that people fell dead on the roads ... with 4 good years after the locust population had improved somewhat.”

Infestation of the desert locust, S. gregaria, in Africa occurred in four out of five years between 1860 and 1963, and subsequently, in one year out of six (Symmons 1992). In India, from 1863–1962, there were 10 locust infestations, with 5–6 consecutive years of widespread reproduction, swarm production, and damage to crops, followed by 1–8 years of low activity; from 1963 to 2012, there were 18 upsurges (Sharma 2014).

The WMO-FAO (2016) listed the effects of the following factors on the development of a locust outbreak or upsurge: management; the failure to implement a preventive control strategy; inexperienced field survey teams and campaign organizers; insufficient or inappropriate resources; lack of training of the field officers; inaccessibility to important breeding areas; the weather (precipitation, temperature, and wind); and climate change. These factors are likely to have influenced the high occurrence of CAL in the intermediate years (years 2 or 3).

Additionally, limited financial capacity and ongoing armed conflicts could have rendered some of the locust breeding areas inaccessible, and the coronavirus pandemic lockdown has further hampered control efforts (Salih et al. 2020). Political and socio-economic conditions (Meynard et al. 2020) can also greatly influence the likelihood of locust outbreak by affecting management decisions (Gay et al. 2018). In period 2003–2018 there was an important change of government in 2007 in Yucatan State (https://www.yucatan.gob.mx/?p=cronologia) that included a change in locust-control decision-makers. A clear difference between the periods 2003- 2010 and 2011–2018 can be seen: Four upsurges were present in the first period, with only two in the second. In the second period, upsurges only occurred every four years as a result of the preventive actions and the incorporation of new technologies in the locust-control program (Barrientos et al. 2021).

Plagues arise when locusts breed frequently and successfully over a period of one or more years, with repeated and widespread rains in successive, often widely separated, seasonal breeding areas. This allows swarms to form and invade the agricultural zones surrounding the recession area. Pest control, drought, and migration to unsuitable areas can have an effect on ending plagues, although their relative importance is not always clear (Pedgley 1981). The uncertainty of pest outbreaks and associated damage (risk) can be reduced by preventive practices and by the selective use of pesticides based on monitoring and forecasting (Daamen and Rabbinge 1991). It is very important to predict and identify locust recession periods because these populations begin the invasion when ecological conditions become favorable (Lazar et al. 2016), and early prevention strategies have been proven to prevent damage to major agricultural zones in the invasion area (Sharma 2014). However, the response to an alert must be quick; otherwise, swarms will invade several regions, making the forecast pointless (Ceccato 2007).

Curiously, from 2003–2018, the largest treated area against CAL (Fig. 3) coincided with the years in which a soccer championship was held (2006 Germany, 2010 South Africa, 2014 Brazil and 2018 Russia), so in Yucatan these CAL upsurges are known as “soccer world cup locusts”.

Both probabilistic models are functional as long as the permanent monitoring system is sustained and allocated resources are maintained or increased. A reduction in budget would risk the development of the pest, as has occurred in the past. The results of the models discussed here provide insights into the probabilities of CAL upsurges in the YP, and this information can be incorporated into ecological models to improve CAL monitoring and aid management decisions.