Research Article |
Corresponding author: Mario A. Poot-Pech ( mpootpech@gmail.com ) Academic editor: Hojun Song
© 2023 Mario A. Poot-Pech.
This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Citation:
Poot-Pech MA (2023) Probability of a Central American locust Schistocerca piceifrons piceifrons upsurge in the Yucatan Peninsula, Mexico. Journal of Orthoptera Research 32(1): 33-42. https://doi.org/10.3897/jor.32.73824
|
From ancient times to the present, infestations of the Central American locust (CAL) [Schistocerca piceifrons piceifrons (Walker, 1870)] have occurred periodically and with varying intensities in the Yucatan Peninsula (YP), Mexico. Despite efforts to survey the recession zone, an upsurge is still difficult to predict and prevent, and high economic costs are incurred in controlling this pest. For this study, two models were developed to determine the probability of an upsurge in the YP. The first was the Markov chain (MC) with transition probability matrix, which estimates probability by determining the proportion of times that the system moved from one state to another (n2) over 71, 33, and 24 years in Yucatan, Campeche, and the Quintana Roo States, respectively, divided into different periods; a correlation of the matrix and probability (n2) of the next period was performed to evaluate the accuracy of the estimation. The other method is the classic probabilistic (CP) model, which uses the number of times the upsurge could happen and the number of possible events. In the MC model, great variation was found in CAL upsurge probabilities between periods, with a similar number of upsurges from the past to the present but with varying intensity. In recent years, the treated area with insecticides has been less than that of the past. The CP model revealed that the locust population reached its maximum peak every four years, with the migration of swarms to neighboring states at the end/start of the year. Validation of the MC and CP models was performed considering information on areas treated in 2019 and 2020, and good accuracy was obtained. Both models provide information on the probability of an upsurge in the YP. This information can be incorporated into economic models to improve management decisions, such as when to announce early warnings, and to implement preventive control strategies.
early warning, forecast, preventive management, recession period
Locusts are among the most devastating pests of human agriculture (
CAL damage has been documented from the Mayan culture and colonial period, which reported drought and hunger as results of this pest (
An important CAL breeding zone is located in the Yucatan Peninsula (YP), Mexico (
Currently, CAL in Mexico are controlled through government regulations and advice from the International Regional Organization for Plant and Animal Health (OIRSA), an intergovernmental organization founded in 1953. OIRSA was created as a cooperative effort of locust control between Central American countries that are part of the insect’s migration path (
Locust plagues occur after a series of events that increase the number of locusts. The series normally begins with a calm period of recession followed by localized outbreaks and upsurges from which a plague may develop and eventually decline (
The CAL is an old pest in Mexico (
The strategies for locust control have has recently changed, with attempts focusing on prevention with the use of forecasting tools. Methods for producing Short- and medium-term forecasts have been made indicating potential locust migration and breeding areas (
The objective of this research was to develop and compare two models that can produce probability estimates for future upsurges in the YP by analyzing non-weather-related historical CAL data.
Data acquisition.—To document the occurrence of CAL upsurges, the following sources of historical information on locust were used:
For Yucatan state, CAL data for 71 years (1948–2018) were available (every year had a value). Data for 33 years (1986–2018) were available for Campeche, and 24 years of data (1995–2018) were available for Quintana Roo.
Locust upsurge definition.— Upsurges were used instead of outbreaks because there were two high-density generations–transients-to-gregarious or gregarious-to-gregarious–and migration to other regions (
Markov chain probabilistic model.—The data were organized by assigning “0” to years with none or low intensity of CAL swarms and “1” to those in which an upsurge occurred. Second, the data were organized into periods of upsurge based on number of years, resulting in 5 periods of 12 years and one of 11 years in Yucatan state; 3 periods of 12 years, except for the first period of 9 years, in Campeche; and 2 periods of 12 years in Quintana Roo.
Classic probabilistic model.—The maximum peak years were obtained using the treated area (ha) in Yucatan state from 2003–2018. Subsequently, a consecutive number was assigned to each of the following years, finalizing in the next peak. A probabilistic analysis of occurrence was performed for each consecutive year. The probability of occurrence in the most recent years (2003–2018) was compared with that of previous periods [1977–1989 (
Model validation.—The probabilistic results of the two models were compared to the results of the treated area in the YP in 2019 and 2020.
Markov chain probabilistic model.—The probability of matrix transition for every period was estimated by determining the proportion of times that the CAL upsurge situation, 0 and 1, moved from one state to another (
Matrix (one-step transition) and n2, for CAL upsurges in a 71-year period.
Number | Years | Yucatan | Number of years | Upsurge years | Upsurge average | Probability n2 | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Matrix (One-step transition) | ||||||||||||
0→0 | 0→1 | 1→0 | 1→1 | 0→0 | 0→1 | 1→0 | 1→1 | |||||
1 | 1948–1959 | 0.5 | 0.5 | 0.43 | 0.57 | 12 | 7 | 1.71 | 0.46 | 0.54 | 0.46 | 0.53 |
2 | 1960–1971 | 0.5 | 0.5 | 0.6 | 0.4 | 12 | 5 | 2.40 | 0.55 | 0.45 | 0.54 | 0.46 |
3 | 1972–1983 | 0.71 | 0.29 | 0.75 | 0.25 | 12 | 4 | 3.00 | 0.72 | 0.28 | 0.72 | 0.28 |
4 | 1984–1995 | 0.2 | 0.8 | 0.67 | 0.33 | 12 | 6 | 2.00 | 0.57 | 0.43 | 0.35 | 0.65 |
5 | 1996–2007 | 0 | 1 | 0.72 | 0.28 | 12 | 7 | 1.71 | 0.72 | 0.28 | 0.2 | 0.8 |
6 | 2008–2018 | 0.58 | 0.42 | 0.66 | 0.34 | 11 | 4 | 2.75 | 0.61 | 0.39 | 0.60 | 0.4 |
71 (total) | 33 (total) | 2.15 (mean) |
The elements P00 and P01 refer to the probability that in X year (present), the following year’s CAL population will be classified as low (P00) or high (P01) if X year has low densities. Alternately, if X year has a high locust density, P10 is the probability that the following year’s populations will be classified as having a low density, and P11 is the probability that the state will continue to be classified as having a high density of CAL the next year (
The probability of correctly determining the locust density in the next period was obtained using the recursive properties of a two-state Markov chain (
P 00 ( n ) = P00(n-1)P00 + P01(n-1)P10;
P 01 (n) = P00(n-1)P01+ P01(n-1)P11;
P 10 (n)= P10(n-1)P00 + P11(n-1)P10;
P 11 (n) = P10(n-1)P01 + P11(n-1)P11
The correlation between the probability n2 of the two-state Markov chain and the probability of the next period (one-step transition)–for example, the probability n2 of period 1 with the matrix of period 2–was determined using Pearson correlation (p < 0.05) in R software version 3.6.0 (
Classic probabilistic model.—We obtained the classic probability using P(1) = #1/M, where P(1) is the probability of an upsurge, #1 is the number of times the upsurge can happen, and #M is the number of possible events (
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).
Pearson correlation of the matrix and probability n2 in Yucatan state (P < 0.05).
Period | Correlation | P-value |
---|---|---|
1960–1971 | -0.65 | 0.34 |
1972–1983 | 0.98 | 0.01 |
1984–1995 | -0.26 | 0.73 |
1996–2007 | -0.75 | 0.24 |
2008–2018 | -0.64 | 0.35 |
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).
Matrix (one-step transition) and n2, for CAL upsurges in a 33-year period.
Number | Period | Campeche | Years | Upsurge years | Upsurge overage | Probability n2 | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Matrix (one-step transition) | ||||||||||||
0→0 | 0→1 | 1→0 | 1→1 | 0→0 | 0→1 | 1→0 | 1→1 | |||||
1 | 1986–1994 | 0 | 1 | 0.28 | 0.72 | 9 | 7 | 1.29 | 0.28 | 0.72 | 0.2 | 0.8 |
2 | 1995–2006 | 0.57 | 0.43 | 1 | 0 | 12 | 4 | 3 | 0.75 | 0.25 | 0.57 | 0.43 |
3 | 2007–2018 | 0.75 | 0.25 | 1 | 0 | 12 | 3 | 4 | 0.81 | 0.19 | 0.75 | 0.25 |
33 (total) | 14 (total) | 2.3 (mean) |
Pearson correlation of the matrix and probability n2 in Campeche (P > 0.05).
Period | Correlation | P-value |
---|---|---|
1986–1994 | -0.88 | 0.11 |
1995–2006 | 0.67 | 0.32 |
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
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.
This information was used to identify the upsurge years (Table
Upsurge value for 2003–2018 in the YP and 1952–1955/1977–1989 in Yucatan state.
States | Upsurge value per year | |||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
2003 | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | |
Yucatan | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 |
Campeche | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
Q. Roo | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Yucatan | 1952 | 1953 | 1954 | 1955 | 1977 | 1978 | 1979 | 1980 | 1981 | 1982 | 1983 | 1984 | 1985 | 1986 | 1987 | 1988 |
1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | |
Year value | 1 | 2 | 3 | 4 | 1 | 2 | 3 | 4 | 1 | 2 | 3 | 4 | 1 | 2 | 3 | 4 |
Probability of an upsurge, P(1), from 1952–1955/1977–1988 and 2003–2018.
Year value | 1952–1955 and 1977–1988 | 2003–2018 | ||||||
---|---|---|---|---|---|---|---|---|
Yucatan | Campeche | Q. Roo | ||||||
Upsurges | P(1) | Upsurges | P(1) | Upsurges | P(1) | Upsurges | P(1) | |
1 | 1,0,1,0 | 0.5 | 0,0,0,0 | 0 | 1,1,1,1 | 1 | 0,0,0,0 | 0 |
2 | 1,0,0,1 | 0.5 | 1,0,0,0 | 0.25 | 0,0,0,0 | 0 | 0,0,0,0 | 0 |
3 | 1,1,0,1 | 0.75 | 0,1,0,0 | 0.25 | 0,0,0,0 | 0 | 0,0,0,0 | 0 |
4 | 1,1,0,1 | 0.75 | 1,1,1,1 | 1 | 0,0,0,0 | 0 | 1,0,0,0 | 0.25 |
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
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
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” (
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 (
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 (
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 (
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 (
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 (
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 (
Campeche state.—Historically, the Campeche state has been invaded by swarms from Yucatan (
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.
Quintana Roo State.—Vegetation is very important for locust development (
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 (
Periods of 4 years (Table
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 (
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.
In his book, An Account of the Things of Yucatán, written in 1566, Diego
Results of Markov matrix in 2018 compared to results from 2019 and 2020 upsurge values.
State (value year 2018) | Matrix | Values | Upsurge value | ||||
---|---|---|---|---|---|---|---|
0→0 | 0→1 | 1→0 | 1→1 | 2019 | 2020 | ||
Yucatán | One-step transition (2018=1) | 0.58 | 0.42 | 0.66 | 0.34 | 0 | 0 |
n2 | 0.61 | 0.39 | 0.6 | 0.4 | |||
Campeche | One-step transition (2018=0) | 0.75 | 0.25 | 1 | 0 | 1 | 0 |
n2 | 0.81 | 0.19 | 0.75 | 0.25 | |||
Q. Roo | One-step transition (2018=0) | 1 | 0 | 0 | 0 | 0 | 0 |
Probability of an upsurge P (1) and results of upsurge values 2019 and 2020 in the YP.
Year value | Years | Yucatan | Campeche | Q. Roo | |||
---|---|---|---|---|---|---|---|
P (1) | Value | P (1) | Value | P (1) | Value | ||
1 | 2019 | 0 | 0 | 1 | 1 | 0 | 0 |
2 | 2020 | 0.25 | 0 | 0 | 0 | 0 | 0 |
3 | 0.25 | 0 | 0 | ||||
4 | 1 | 0 | 0.25 |
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 (
The
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 (
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 (
Curiously, from 2003–2018, the largest treated area against CAL (Fig.
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.
I thank the field locust officers of the YP, SENASICA, and OIRSA. Special thanks to Mario Marin-Correa and Eudaldo Pereyra-Cuevas, retired YP locust officers who helped rebuild history. I also thank CONACyT (Consejo Nacional de Ciencia y Tecnología) and ITC (Instituto Tecnológico de Conkal) for their support of my PhD studies. Special thanks to the reviewer of this document for his insightful comments and corrections.